Muriel Fadairo
email: muriel.fadairo@univ-st-etienne.fr

Jianyu Yu
email: yujianyu@swufe.edu.cn

Economic Rationales of Exclusive Dealing; Empirical Evidence from the French Distribution Networks 1

Keywords: Exclusive dealing, Vertical restraints, Competition policy JEL Classification Numbers: C12, L42

This paper investigates the rationales of exclusive dealing (ED), which is one of the most common forms of vertical restraint and attracts intense policy debates in anti-trust regulations.

Based on a survey of the theoretical literature, we derive several hypotheses relative to the anti-and pro-competitive motivations of ED. These hypotheses are submitted to French data regarding several types of distribution networks in a wide range of sectors. Considering the industry features, our empirical analysis indicates that in the French distribution system, ED contracts tend to be procompetitive. The evidence suggests that the motivation of ED mainly lies in its positive role to foster the investment of upstream firms.

Introduction

As one of the most common forms of vertical restraint and as a prevalent device in franchising networks, exclusive dealing (ED) has been attracting the attention of industry players and competition policy authorities for decades (Lafontaine and Slade, 2012).Vertical restraints are contractual provisions imposed by a producer to constrain the action of one or several retailers. ED clauses, as components of contracts between manufacturers and distributors, require the purchase of products or services exclusively from only one supplier for a period of time. These agreements prohibit the distributor from carrying the products of rival manufacturers.

The regulations in the United States (US) and in the European Union (EU) were traditionally hostile to these restrictions and were viewed with suspicion. This position has evolved over time.

Currently, the French legal environment regarding vertical restraints is defined by the Treaty on the Functioning of the European Union (TFEU). Article 101(1) of the Treaty prohibits agreements that prevent, restrict or distort competition. However, agreements that create sufficient benefits to outweigh the anti-competitive effects are exempt from this prohibition under Article 101(3) of the TFEU. In addition, the European Commission has adopted the Block Exemption Regulation (BER) on vertical restraints, which entered into force on June 2010 and will remain in force until May 2022 (Regulation (EU) No 330/2010). This regulation provides a safe environment for most vertical agreements, including ED. It renders, by block exemption, the prohibition of Article 101(1) of the TFEU inapplicable to vertical agreements that fulfil certain requirements. Franchising is not specifically mentioned in the regulation itself, but is dealt with in the guidelines on vertical restraints (SEC (2010) 411). These guidelines describe the approach taken towards vertical agreements not addressed by the BER. In particular, the BER does not apply if the market share of the supplier and/or buyer exceeds 30 %. However, exceeding the market share threshold of 30 % does not create a presumption of illegality as this threshold serves only to distinguish those agreements that benefit from a presumption of legality from those that require an individual examination 2 . Indeed, as for the other vertical restraints, the anti-trust effects of ED are complex and appear as a main controversial issue in the courts and among economists. For example, studying the ED case of Ticketmaster in Ireland, [START_REF] Gorecki | Form-Versus Effects-Based Approaches to the Abuse of a Dominant Position: The Case of Ticketmaster Ireland[END_REF] uses two distinct methods. In so doing, he arrives at opposite conclusions on the abuse of a dominant position of the company. For this reason, most economists consider that the rule of reason approach is better than a per se prohibition and should be generalised, as it allows assessing for each case if the pro-competitive impacts of the contract are 2 The guidelines assist firms in carrying out such an examination. likely to outweigh the exclusionary effects.

The traditional argument regarding ED considers foreclosure as the main anti-competitive effect of such vertical restraint, when it allows a dominant firm to deter an efficient entry (Marvel, 1982;[START_REF] Ater | Vertical Foreclosure using Exclusive Dealing: The Case of Hamburger Restaurants in Shopping Malls[END_REF][START_REF] Nurski | Exclusive Dealing as a Barrier to Entry? Evidencefrom Automobiles[END_REF][START_REF] Hiller | Exclusive Dealing and Its Effects: The Impact of Large Music Festivals on Local Music Venues[END_REF]. However, this argument is challenged by the potential efficiency gains, as ED may be a relevant solution to upstream and downstream free-riding problems and opportunistic behaviours [START_REF] Besanko | Equilibrium Incentives for Exclusive Dealing in a Differentiated Products Oligopoly[END_REF][START_REF] Heide | Exclusive Dealing and Business Efficiency: Evidence from Industry Practice[END_REF][START_REF] Asker | Measuring Cost Advantages from Exclusive Dealing An Empirical Study of Beer Distribution[END_REF]2005;[START_REF] Sass | The Competitive Effects of Exclusive Dealing: Evidence from the US Beer Industry[END_REF]Chia-Wen, 2013).

Despite an extensive analysis of such exclusionary contracts in the theoretical field, the empirical literature on ED is limited.

As emphasised by [START_REF] Lafontaine | Exclusive Contracts and Vertical Restraints: Empirical Evidence and Public Policy[END_REF], most studies focus on a single industry.

Examples include beer retailing [START_REF] Slade | Regulating Manufacturers and their Exclusive Retailers[END_REF][START_REF] Slade | Competition Policy Towards Brewing: Rational Response to Market Power or Unwarranted Interference in Well Functioning Markets[END_REF][START_REF] Asker | Measuring Cost Advantages from Exclusive Dealing An Empirical Study of Beer Distribution[END_REF]2005;[START_REF] Sass | The Competitive Effects of Exclusive Dealing: Evidence from the US Beer Industry[END_REF][START_REF] Klick | The Effects of Vertical Restraints on Output: Evidence from the Beer Industry[END_REF][START_REF]Does Exclusive Dealing Matter? Evidence from Distribution Contract Changes in the U.S. Beer Industry[END_REF], car market [START_REF] Brenkers | Liberalizing a Distribution System: the European Car Market[END_REF][START_REF] Nurski | Exclusive Dealing as a Barrier to Entry? Evidencefrom Automobiles[END_REF],video rental industry [START_REF] Mortimer | Vertical Contracts in the Video Rental Industry[END_REF], hamburger chain market [START_REF] Ater | Vertical Foreclosure using Exclusive Dealing: The Case of Hamburger Restaurants in Shopping Malls[END_REF], and live music industry [START_REF] Hiller | Exclusive Dealing and Its Effects: The Impact of Large Music Festivals on Local Music Venues[END_REF].This body of literature investigates the outcomes of the exclusionary clauses with respect to prices [START_REF] Slade | Regulating Manufacturers and their Exclusive Retailers[END_REF][START_REF] Sass | The Competitive Effects of Exclusive Dealing: Evidence from the US Beer Industry[END_REF], costs [START_REF] Asker | Measuring Cost Advantages from Exclusive Dealing An Empirical Study of Beer Distribution[END_REF][START_REF] Brenkers | Liberalizing a Distribution System: the European Car Market[END_REF], profits (Mortimer,2008), market-shares [START_REF] Nurski | Exclusive Dealing as a Barrier to Entry? Evidencefrom Automobiles[END_REF][START_REF]Does Exclusive Dealing Matter? Evidence from Distribution Contract Changes in the U.S. Beer Industry[END_REF], and sales and consumption [START_REF] Sass | The Competitive Effects of Exclusive Dealing: Evidence from the US Beer Industry[END_REF][START_REF] Klick | The Effects of Vertical Restraints on Output: Evidence from the Beer Industry[END_REF][START_REF] Ater | Vertical Foreclosure using Exclusive Dealing: The Case of Hamburger Restaurants in Shopping Malls[END_REF].These papers use various econometric methods including cross-sectional data (e.g., [START_REF] Sass | The Competitive Effects of Exclusive Dealing: Evidence from the US Beer Industry[END_REF], panel data (e.g., [START_REF] Slade | Regulating Manufacturers and their Exclusive Retailers[END_REF][START_REF] Mortimer | Vertical Contracts in the Video Rental Industry[END_REF][START_REF] Hiller | Exclusive Dealing and Its Effects: The Impact of Large Music Festivals on Local Music Venues[END_REF], reduced form models (e.g., Wen 2013) or structural models (e.g., [START_REF] Asker | Measuring Cost Advantages from Exclusive Dealing An Empirical Study of Beer Distribution[END_REF][START_REF] Brenkers | Liberalizing a Distribution System: the European Car Market[END_REF].

However, there has been little focus to date on the motivations for ED contracts.

The work of [START_REF] Heide | Exclusive Dealing and Business Efficiency: Evidence from Industry Practice[END_REF] provides some insight into the rationales of ED. Studying the industrial machinery-equipment, electronics and electric equipment sectors, the authors use primary data to estimate a binomial logit model regarding the choice to include an exclusionary clause in the contract. The paper focuses on the determinants of E rather than on the impact of such agreements. The ex ante assessments by the managers are taken into account as explanatory variables. These assessments concern the free-riding on manufacturer services, the transaction costs, the cost imposed on the customers due to the exclusionary clause, the manufacturer differentiation, and the likelihood of competitive entry. The authors find evidence that the manufacturers who care more about their promotional efforts, training, or general support from distributors are more likely to use ED clauses.

This key empirical result is consistent with the efficiency theories of ED. More particularly, Segal and Whinston (2000b) emphasise the impact of the nature of the investments made in the vertical relationships, thus distinguishing several categories of investments with varied influences regarding the exclusionary contracts.

Our paper is set in the research field initiated by [START_REF] Heide | Exclusive Dealing and Business Efficiency: Evidence from Industry Practice[END_REF] and takes into account the theoretical developments since this initial article. While most of the evidence concerns the consequences of ED, we study the empirical rationales of this vertical restraint.

More precisely, this paper reviews the recent development of the theoretical literature that provides explanations of the strategic, anti-competitive motives of ED and the pro-competitive motives of ED in promoting efficient enhancing investment, following the typology of Segal and Whinston (2000b). In doing so, we identify the industrial determinants that may affect the choice for ED agreements and derive testable hypotheses from the theoretical framework. These hypotheses are then submitted to French primary data regarding a wide range of sectors. Our empirical results provide insights into the anti-trust regulation of ED contracts in the European context.

In contrast with the existing empirical literature, this paper addresses several sectors and several types of distribution networks, thus allowing us to compare the market structures that affect directly the motivations for ED. In addition, taking into account the potential endogeneity bias, we control for the influence of the presence of other vertical restraints in the contract -exclusive territories and tying -on the choice to use ED. This is specific to our study as is the control for the potential impact of the geographical location of the suppliers. This paper proceeds as follows. Section 2 discusses the theoretical background and derives the testable hypotheses. Section 3 provides specifications regarding the French distribution system, the sample and the study variables. Section 4 contains the estimations, and concluding comments are presented in section 5.

Theoretical Motivations and Hypotheses

Likelihood of exclusive dealing and anti-competitive motives

Background

The rationales of ED have been extensively discussed in the theoretical literature. The Chicago School critique, led by [START_REF] Bork | The Antitrust Paradox[END_REF] and [START_REF] Posner | Antitrust Law: An Economic Perspective[END_REF], notes that the motive for an exclusive contract is mainly because of efficiency. To induce downstream buyers to sign ED contracts, the upstream incumbent firm must compensate the downstream buyers with at least the same rent that entrant can offer. That is, if the entrant were more efficient, the incumbent would not find it profitable to pay buyers not to trade with the entrant. As a result, if the incumbent succeeds in concluding an ED contract with buyers, it is basically because the incumbent is more efficient.

The Chicago School critique, however, is being challenged. Over the last two decades, increasing attention has been paid to the strategic motives of ED. Although it is widely accepted that ED may have anti-competitive effects, the existing literature provides different rationales under various economic environments. [START_REF] Rasmusen | Naked Exclusion[END_REF] and Segal and Whinston (2000a) argue that if the entrant firm has to trade with a sufficient number of buyers to achieve scale economy, the incumbent monopolist may opt to use exclusive contracts to deter efficient entry. The intuition of such "naked exclusion" is mainly due to contract externality: if the incumbent has buyers to sign the exclusive contract, the purchase of remaining buyers may not be sufficient to cover the minimum efficient scale of the entrant, and hence, entry will not occur. To this extent, the signed buyers exert a negative externality on other buyers, thus facilitating the incumbent to use a divide-and-conquer strategy to deter efficient entry.

Contract externality is also exploited in [START_REF] Innes | Strategic Buyers and Exclusionary Contracts[END_REF], where the buyer has the choice to sign a contract and obtain vertical profit with the entry; in [START_REF] Berheim | Exclusive Dealing[END_REF], where buyers are independent in different markets and the entrant is viable only if it serves in all the markets; and in Karlinger and Motta (2013), where a product has value only if enough buyers purchase.

Another stream of literature, pioneered by [START_REF] Aghion | Contracts as a Barrier to Entry[END_REF], investigates "partial E". In their framework, the buyer is allowed to breach the exclusive contract and pay damage compensation to the incumbent. In this way, the incumbent can extract some of the surplus created by the efficient entrant by accommodating entry. Similar results are derived by [START_REF] Spier | On the efficiency of privately stipulated damages for breach of contract: entry barriers, reliance and renegotiation[END_REF], who generalise Aghion and Bolton's model in the context of a renegotiated contract.

The literature discussed above provides useful insights on the rationales of ED. However, these papers generally assume that the buyers at the downstream level are either final consumers or independent retailers and that the upstream market contains only an incumbent and a potential entrant, whereas in the real world economy, both the upstream and downstream competition matter in the designing of vertical contracts. A volume of recent literature focuses on these aspects.

Upstream competition

A few papers investigate the effect of upstream competition on the possibility of signing an exclusive contract. In a framework where the incumbent seller can merge with the potential entrant, Fumagalli et al. (2009) suggest that if the buyer expects weak competition from the entrant, he will be willing to accept exclusivity behind a small compensation, and therefore, ED may occur. In a setting where the incumbent faces multiple potential entrants, [START_REF] Kitamura | Exclusionary vertical contracts with multiple entrants[END_REF] argues that the anticompetitive ED is more likely to be observed in industries with few alternative factor inputs, products and technologies.

Based on these results, in which strategic ED is more likely to occur when the upstream competition is weak, we derive the following testable hypothesis: H1 -The more concentrated the upstream market, the more likely it is that the upstream incumbents sign ED contracts for anti-competitive purposes.

Downstream competition

With respect to downstream competition, current analyses reach different conclusions. Fumagalli and Motta distinguish two channels that intensify the downstream competition: the number of downstream firms and the degree of substitution of the final products. In [START_REF] Fumagalli | Exclusive Dealing and Entry, When Buyers Compete[END_REF], exclusion is less likely to occur in case of fierce Bertrand-like downstream competition.

Likewise, [START_REF] Fumagalli | Buyers. Miscoordination, Entry and Downstream Competition[END_REF] show that the larger number of downstream buyers, the more difficult it is for them to coordinate, and hence, the easier it is for the upstream incumbent to exploit contract externality and foreclose the efficient entrant.

In this framework, and considering the number of firms as a measure of the degree of downstream competition, we formulate the following hypothesis:

H2a -The larger the number of downstream units, the more likely it is that the upstream incumbents sign ED contracts for anti-competitive purposes.

With respect to product substitution, [START_REF] Fumagalli | Buyers. Miscoordination, Entry and Downstream Competition[END_REF] demonstrate that if the downstream competition stems from the substitution of products, a buyer can obtain greater profit by switching to an efficient entrant who offers a competitive wholesale price. Hence, the incumbent cannot profitably foreclose the entrant. As a result, the intense downstream competition based on the substitution of products makes strategic ED less likely. This argument is, however, challenged by the recent analysis that argues that [START_REF] Fumagalli | Buyers. Miscoordination, Entry and Downstream Competition[END_REF] framework is based on a strong assumption that the downstream buyers can be inactive under fierce Bertrand-like competition. Simpson and Wickelgren (2007) find that if buyers are allowed to break the contract and pay expected damage to the incumbent (as in the Aghion and Bolton framework), ED is more likely to occur if downstream competition becomes intense. The reason for this is that the downstream buyers, although in competition, always remain active in the market. When entry occurs, the intense inter-and intra-brand competition eliminates almost all the vertical profit. As a result, it is easier for the incumbent to sign an exclusive contract with the buyer to foreclose the entrant and obtain monopoly profits of the industry. Similar results are found in [START_REF] Abito | Exclusive dealing with imperfect downstream competition[END_REF], [START_REF] Wright | An evidence-based approach to exclusive dealing and Loyalty discounts[END_REF] and [START_REF] Gratz | On the Competition Enhancing Effects of Exclusive Dealing Contracts[END_REF].

With respect to the degree of substitution, we follow the argument of Simpson and Wickelgren(2007), [START_REF] Abito | Exclusive dealing with imperfect downstream competition[END_REF], [START_REF] Wright | An evidence-based approach to exclusive dealing and Loyalty discounts[END_REF] and [START_REF] Gratz | On the Competition Enhancing Effects of Exclusive Dealing Contracts[END_REF] to derive the following hypothesis:

H2b-The more substitutable the final products are, the more likely it is that the upstream incumbents sign ED contracts for anti-competitive purposes.

The literature and the embodied rationales for strategic ED contracts can be summarised as follows (Table 1): Basic structure: Upstream incumbent and entrant competing for independent downstream buyers [START_REF] Rasmusen | Naked Exclusion[END_REF], Segal and Whinston (2002a), [START_REF] Innes | Strategic Buyers and Exclusionary Contracts[END_REF], [START_REF] Berheim | Exclusive Dealing[END_REF], Karlinger and Motta (2013) Naked ED: incumbent can block efficient entrant using ED contract.

If buyers cannot coordinate and entry requires enough buyers to purchase, there is contract externality of ED that prevents entry.

Agion and Bolton (1987), [START_REF] Spier | On the efficiency of privately stipulated damages for breach of contract: entry barriers, reliance and renegotiation[END_REF] Partial ED: incumbent signs ED and entry occurs.

Incumbent can extract some rent from efficient entrant through the contract-breach compensation stipulated in the ED contract. Upstream competition or coordination Fumagalli et al.(2009) Kiamura (2010) H1: The more concentrated the upstream market, the more likely that the upstream incumbents sign ED contracts.

Intensive upstream competition gives buyers more outside options, making it difficult to accept. Downstream competition stemming from number of firms and product substitution [START_REF] Fumagalli | Exclusive Dealing and Entry, When Buyers Compete[END_REF], [START_REF] Fumagalli | Buyers. Miscoordination, Entry and Downstream Competition[END_REF] H2a: The larger the number of downstream units, the more likely that the upstream incumbents sign ED contracts.

A large number of downstream buyers make it difficult for them to coordinate; hence, ED is easier to achieve. Harsh downstream competition. Simpson and Wickelgren (2007), [START_REF] Abito | Exclusive dealing with imperfect downstream competition[END_REF], Wright (2008), [START_REF] Gratz | On the Competition Enhancing Effects of Exclusive Dealing Contracts[END_REF] H2b:

The more substitutable the final products, the more likely that the upstream incumbents sign ED contracts.

The intense inter-and intra-brand competition reduces the potential rent that entrants can offer to buyers, and hence, it is easier to accept ED.

Exclusive dealing and investment incentives

Background

The literature highlighting the efficiency aspects of ED mainly focuses on the strong link between exclusionary provisions and the beneficiary's investment incentive. The conventional perspective in this field recognises that exclusive contracts can be used to protect the investment of a party in the vertical relationship and that, as a result, they can foster such an investment (see, for example, Marvel 1982, Fransco 1991, Mastern and Snyder 1993 for informal discussion). This notion has been exploited in [START_REF] Besanko | Equilibrium Incentives for Exclusive Dealing in a Differentiated Products Oligopoly[END_REF], who argue that an ED contract can be used to prevent the free-ride of the competitors on non-relationship-specific investments. In fact, under ED, an investment becomes specific to the vertical relationship, and hence, it eliminates the interbrand externality among retailers. Segal and Whinston (2000b) analyse the relationship between investment and ED in a more general framework. Unlike the conventional perspective, these authors argue that whether ED fosters investment depends on who invests in the vertical relationship and on the nature of the investment. In particular, if the investment is complementary, in that it increases the value of trade between the entrant and buyers, then ED fosters the investment of the incumbent seller while reducing the investment incentive of downstream buyers. On the other hand, if the investment is substitutable, in that it reduces the trade value for the entrant and the buyers, ED reduces the incumbent seller's investment but increases the investment of downstream buyers. As the investment only affects the internal trade value of contractually locking parties, ED is irrelevant for these parties' investment decisions.

Following the work of Segal and Whinston (2000b), a number of papers challenge the irrelevance result of ED. Che and Sakovics (2004) argue that the irrelevance result does not hold in a dynamic model in which the timing of investments and bargaining is endogenous. Meza and Selvaggi (2007) suggest that ED can increase the recipient's bargaining power, thus enabling such power to extract an increased share of the surplus created by its investment. However, de Fontenay et al. ( 2010) generalise the model of Segal and Whinston and find that their irrelevance results still hold in their setting. [START_REF] Fumagalli | Exclusive Dealing: The Interaction between Foreclosure and Investment Promotion[END_REF] argue that because ED affects the investment incentive depends on the investment cost, the irrelevance result holds if the investment cost is small. However, ED promotes investment and forecloses entry if the investment cost is large.

Upstream investment

Thus, the literature shows that there is no general conclusion on the linkage between ED and investment, in particular, for the internal, relation-specific investment and that the work of Segal and Whinston (2000b) remains central. For this reason, we base our hypotheses on this key reference with the aim being to study whether the theory still holds in the real world economy.

Accordingly, we derive the following hypotheses regarding the upstream investments:

H3a -In the presence of upstream complementary investments, it is more likely that the upstream incumbents sign ED contracts for efficiency purpose.

H3b -In the presence of upstream substitutable investments, it is less likely that the upstream incumbents sign ED contracts.

Downstream investment

In addition, the following testable propositions can be considered regarding the downstream investments:

H4a -In the presence of downstream complementary investments, it is less likely that the upstream incumbents sign ED contracts.

H4b -In the presence of downstream substitutable investments, it is more likely that the upstream incumbents sign ED contracts for anti-competitive purposes.

The economic rationales of pro-competitive efficient ED are summarised in Table 2:

Empirical Specifications

The French system

The French distribution system is characterised by a diversity of organisational forms. The two main organisational forms are company-owned chains, where the outlets belong to the upstream firm or to one of its subsidiaries, and franchised networks, where the upstream firm transmits its business format and monitors the independent downstream units to maintain the brand's reputation.

Other types of governance forms in the French system include (i) retailer cooperatives, where the upstream unit in charge of the promotion of the common brand belongs to the retailers; (ii) brand licensed networks, which are similar to business format franchises, but less constraining for the downstream units; (iii) concession networks, which are similar to traditional franchises; and (iv) commission-based affiliations (CBA), which are similar to business-format franchises but more constraining as the stock shares at the downstream level are owned by the upstream firm.

Each of these networks may choose to include an ED clause in the vertical contracts. Notably, as mentioned by [START_REF] Lafontaine | Franchising and Exclusive Distribution: Adaptation and Antitrust[END_REF], the European legal environment provides franchisors great flexibility to impose or rely on ED.

The sample

Between 2006 and 2008, the French National Institute of Statistics and Economic Studies (INSEE) conducted several surveys to collect information regarding the distribution networks over seven units. The networks, and more precisely, the upstream units (i.e., the head-ends), were surveyed through a questionnaire distributed by postal mailing.

The original dataset used in this study compiles primary data produced by the INSEE. This dataset is exhaustive and covers all retail sectors. As a result of matching and of the retropolation of the data, our cross-sectional dataset refers to the year 2007.

The sample consists of 504 networks of independent retailers using the same brand name.

As presented in Table 3, seven types of networks are distinguished in the sample. More than half of the networks (53 %) use the same type of vertical contract with all of their outlets. The other networks mix several types of relationships. In the sample, each network is allocated a type according to the share of the network turnover achieved by each type of outlet. The algorithm successively tests the condition in the second column of Table3 and stops when a condition is deemed true. Three types of franchised networks are distinguished to consider the presence of integrated retail outlets that are owned and directly operated by the upstream firm for each franchised network.

These three categories of franchised networks include franchised and slightly mixed with owned retail units, franchised and highly mixed with owned retail units, and predominantly integrated network.

Distribution of the ED clause

Tables 3 to 5 present the distribution of the ED clause in the sample networks (Table 5), within the 15 sectors (Table 6), and within the network types (Table 7). The precise question in the survey questionnaire reflects the possible duty of the independent retailers in the network. This question is as follows: "Do you impose on your retailers an ED with the network central purchasing unit or with referenced suppliers?" The possible responses are "yes" or "no".

As highlighted in Tables 3 to 5, the distribution of the ED clause is quite balanced in the sample (46.43 of the sample networks use ED), within the retail sectors, and within the network types.

However, its prevalence in the sectors "Retail sale of food in specialised stores" (69 %) and "Clothing retail" (67 %) with respect to the organisational forms "Predominantly integrated" (68 %)

and "Commission-based Affiliation" (70.6 %) are evident.

The study variables

The study variables are presented in Table 6. The dependent variable is a dummy denoting the presence of an ED clause in the vertical contract. The core explanatory variables derived from the analytical framework relate to the upstream and downstream competition levels and to the upstream and downstream investments. In addition, we add several control variables.

Upstream competition

The market concentration is measured in four ways. First, we use the market share of the network, defined as the network turnover divided by the sector turnover. Each of the 15 sectors in the dataset relates to a market where the upstream firms compete. Second, we calculate the Herfindahl-Hirschman index (HHI) for these markets. Third, we take into account the interaction between the market share and the Herfindahl-Hirschman index with a multiplicative variable (Market share * HHI). Finally, we consider the size of the market segment, i.e., the number of networks for each segment. Again, we use the INSEE nomenclature for this complementary and finer classification of activities and distinguish 25 segments in the sample.

Downstream competition

The features of the downstream competition are related to the number of downstream units and to the type of product, more or less substitutable.

We measure the number of downstream units for each network (size of the network) and for each market (size of the market, which is 15 markets). A multiplicative variable cannot be introduced due to multicolinearity problems.

In addition, two types of products are distinguished: substitutable and non-substitutable. Substitutable products are characterised by automatic, high frequency purchases such that no substitutable products involve well-thought-out purchasing decisions or higher research costs for consumers.

Such a proxy variable was previously used by [START_REF] Brickley | Incentive conflicts and contractual restraints: evidence from franchising[END_REF]. Table 8 presents the sector distribution used to construct the dummy variable: substitutable or non-substitutable.

Upstream investment

With respect to investments that benefit the trade between the upstream competitors and the downstream units, upstream complementary investments are closely related to the initial training provided by the upstream unit to the downstream firms and to the transmission of expertise by the upstream structure to the downstream units.

In contrast, upstream substitutable investments have a negative impact on the trade between the upstream competitors and the downstream units. We construct an index of the upstream substitutable investment with seven variables related to the functions possibly performed by the upstream firm in the vertical relationship: the definition of the assortment of the stores, logistics functions (storage, warehousing, delivery to retail outlets), the definition of the services provided to the consumers, the tracking of sales, the diffusion in the network of the performances regarding the outlets sales, invitations to be part of the strategic commissions of the network (marketing, communication, etc.), the help to transmit the outlet. In the dataset provided by the INSEE, each of these variables is taken into account as a dummy. Our index is defined as the sum of these seven dummy variables. The higher the index is, the more substitutable the upstream investment.

Downstream investment

The downstream complementary investment refers to the efforts exerted or investments made by the retailers in favour of the trade with the upstream competitors. Such investment is measured as the services provided by the network outlets to the final consumers, such as advice, or by demonstration sessions.

With respect to the downstream substitutable investments, which impede trade with the upstream competitors, we use an index constructed with four dummy variables regarding the investment of the downstream units in the vertical relationships: the payment of an entrance fee or the subscription of shares, the payment of fixed contributions, the payment of royalties related to the turnover of the outlet, and the financial participation in advertising campaigns.

Control variables

We add ten control variables. First, considering that the network experience may influence the contractual design, we control for the impact of the age of the network and the impact of an upstream unit of another branded network on the choice to use ED.

Second, because it is relevant to study each contractual provision as part of a whole, we control for the influence of other vertical restraints included in the contract on the decision to use ED. As mentioned by [START_REF] Slade | The Effects of Vertical Restraints: An Evidence Based Approach[END_REF], vertical restraints are often analysed in isolation, whereas theory demonstrates that they can be substitutes or complements. Aiming at controlling for such relationships, we consider the presence of an exclusive territory clause granted to the downstream units, as well as the presence of tying imposed on the downstream units. However, this issue may raise endogeneity problems, which are taken into account.

Third, we control for the influence of the type of network, taking into account the distinction among the seven distribution networks in the French system (see Table 1). The aim is to study the potential impact of the organisational form on the contractual design. For example, as argued by [START_REF] Innes | Strategic Buyers and Exclusionary Contracts[END_REF], if the downstream buyers can vertically integrate with the upstream entrant, ED is generally efficient as it deters inefficient entry. Hence, the organisational form may also be an important factor affecting ED. Finally, we add dummies regarding the geographical location of the upstream structure, which is new in the empirical literature on ED. This original perspective enables us to take into account three main types of structural determinants that may affect the individual choice to include ED in distribution contracts: the geographical dimension, the industrial features that comprise the market structure, and the network organisational form. Five locations are considered: the area of the capital city, the north-eastern part of the country, the north-western part of the country, the south-eastern part of the country, and the south-western part of the country. Dummy variables (0/1): 0 = no; 1 = yes Dummy variables (0-2) used to construct UPSUBSTI: 0 = no; 1 = yes partially; 2 = yes completely Dummy variable (0-2) OTHERNET: 0 = yes; 2 = no Dummy variables (0/1) SUBSTITUTE: 0 = substitutable; 1 = non-substitutable

Empirical Determinants of Exclusive Dealing

Specification tests

The Breusch-Pagan test is performed and allows concluding for heteroscedasticity.

Accordingly, the standard errors are corrected using White's method.

The low values of the variance inflation factors suggest that there is no multicolinearity problem (see Appendix 1), while the Pearson chi-square tests, which are applied to determine whether a relationship exists between the categorical variables, highlight a dependence between OTHERNET and TYING (critical probability3 : Pr = 0.035), between OTHERNET and TYPENET (critical probability: Pr = 0.000), between EXCLUTERRI and TYING (critical probability: Pr = 0.007), between EXCLUTERRI and TYPENET (critical probability: Pr = 0.020), between TYING and TYPENET (critical probability: Pr = 0.000). Accordingly, we provide estimates using a step-by-step econometric approach and introduce these regressors gradually (Table 11). In addition, we introduce the estimation of models including these variables simultaneously (Table 10). CAPITALCITY is the reference for the location of the upstream unit.

Estimation results

The results are robust and qualitatively similar to those of another reference.

These estimates enable us, first, to comment on the quality of the econometric models. The good global significance of the models is highlighted by the pseudo R-squared, which is quite high for cross-sectional data (between 0.11 and 0.27), by the chi-square probabilities, which are systematically equal to 0, by the percentage predicted (between 68.28 and 74.16), and by the area under the receiver operating characteristic (ROC) curve (between 0.80 and 0.82).

The comparison of the estimated models shows that the results are robust.

Regarding the control variables, the results suggest that the age of the network and the type of network have no influence on the decision to impose ED. The probability for ED is higher when the upstream unit operates a single-branded network. This result supports the argument of Besanco and Perry (1993), in which an ED contract can be used to eliminate the inter-brand externality of the upstream firms when the inter-brand competition is strong. Interesting results are obtained concerning the impact of the other vertical restraints (exclusive territory, tying) and of the geographical location of the upstream structure (head-ends) such that the probability for ED is higher when the vertical contract encloses other vertical restraints. In addition, the results highlight the influence of geographical features. More precisely, the probability for ED is higher when the upstream unit is located in the area of the capital city (models 1 to 4). Furthermore, when using CAPITALCITY as the reference, the probability for ED is lower when the upstream unit of the network is located in the northwest of France.

The core explanatory variables are first concerned with the upstream competition. While the market share of the network, the Herfindahl-Hirschmann index, and the interaction of these two variables have no influence on the decision to ED, the size of the market segment exerts a significant positive influence.

Regarding downstream competition, the number of retail units has no significant influence regarding the intra-brand downstream competition (SIZENET) or the intra-and inter-brand competition (SIZEMARKET). However, the results suggest that the type of product affects the choice for ED (SUBSTITUTE), even if the sign is the reverse of that which is predicted.

Finally, estimates dealing with investment issues highlight the relationship between the upstream investments, either complementary or substitutable, and ED. In all cases (INITRAIN, TRANSF, UPSUBSTI), the sign is positive, that is, it is the reverse of the prediction concerning the upstream substitutable investments. On the other hand, we do not find evidence regarding the influence of downstream investments on ED.

Endogeneity and robustness checks

Endogeneity problems can be suspected regarding the variables OTHERNET, EXCLUTERRI, TYING, TYPENET, DOWNSTREAMSI compared to other vertical restraints (EXCLUTERRI, TYING, DOWNSTREAMSI) or to strategic choices of the upstream unit (OTHERNET, TYPENET).

For this reason, we perform Hausman tests comparing probit and bivariate probit models fitted to binary endogenous regressors. The results show that it is not possible to conclude for endogeneity regarding OTHERNET (critical probability 4 : Prob>chi2 = 0.2485), EXCLUTERRI (critical probability: Prob>chi2 = 0.2925), TYPENET(critical probability: Prob>chi2 = 0.2951)

or DOWNSTREAMSI (critical probability: Prob>chi2 = 0.2016).

A low risk of endogeneity is highlighted regarding TYING (critical probability: Prob>chi2 = 0.0946). For this reason, we provide the estimation results of bivariate probit models (11 and 12) and seemingly unrelated bivariate probit models with sector dummies (13 and14), thus controlling for the potential endogeneity of this variable (Table 12). The estimates are qualitatively similar to the other estimation results. 4 The null hypothesis H0 is the hypothesis of exogeneity. Finally, the inclusion of sector dummies in the probit models allows checking for the robustness of the results, which are, again, qualitatively similar, with the exception of the variable SUBSTITUTE, as highlighted in Table 13.

Interpretation of the results

Summary comments are provided concerning the testable predictions subjected to data for analysis.

Regarding the first hypothesis (H1), which predicts a positive influence of the concentration on the occurrence of an ED contract, our results suggest a reverse relationship. More precisely, when the subsectors are taken into account, we find that the size of the market segment is positively related to the likelihood of ED.As the size of the market segment indicates the number of upstream firms within a subsector of the sample, the result suggests a positive relationship between the number of upstream firms and the likelihood of ED. Hence, the hypothesis H1, in which anti-competitive ED is more likely to occur for more concentrated upstream industries, does not hold. In other words, the French distribution data do not support the anti-competitive rationale that ED is used by dominant upstream firms to foreclose the trade of potential competitors with downstream retailers. Therefore, our results provide evidence that the ED contract used in the French distribution network is mainly for the purpose of improving efficiency. Indeed, as suggested in [START_REF] Kitamura | Exclusionary vertical contracts with multiple entrants[END_REF], "if ED is signed in industries with many alternative factor inputs, products and technologies, then it is likely to be signed for efficiency reasons".

Our empirical findings regarding H1 are complemented and enhanced by the results concerning the geographical location of the upstream units. To understand explain the impact of the geographical dimension and, more precisely, the positive influence of the location in the capital city on the choice to use ED, we suspect a link between geographical features and the level of upstream competition. Simple statistics as those provided in Appendix 2 confirm this relationship. First, we see that the number of networks with an upstream unit located in the capital city is higher (Table 15). Considering the empirical finding that when the upstream unit is located in the capital city the likelihood for ED is higher, the results suggests that the upstream competition level positively impacts the choice for ED, which is contrary to the anti-competitive argument. To study the robustness of the link between the geographical location and the level of competition, we perform Pearson chi-square tests between the location of the upstream unit and several competition variables. All results clearly show that the hypothesis of independence must be rejected. In other words, whatever the competition criteria (number of units, networks or outlets in the sector or the segment, etc.), there is a statistical dependence between the location of the upstream unit and the level of competition (Table 16).

Regarding downstream competition, we do not find evidence that the number of downstream units for each network (intra-brand downstream competition) or for each market (intra-and inter-brand downstream competition) impact the choice for ED (H2a). However, our empirical results in models 4, 5, 6, 7 and 10 suggest that the more substitutable the products, the lower the probability of observing ED, which is precisely the reverse of H2b. Analogous to the analysis of the upstream competition, when the downstream competition is taken into account, our results

do not support the anti-competitive motive of using ED, a finding that is consistent with Simpson and Wickelgren (2007), [START_REF] Wright | An evidence-based approach to exclusive dealing and Loyalty discounts[END_REF], etc. 5 Thus, it appears that in the French distribution system, ED is used neither to exploit contract externality of buyers when buyers are difficult to coordinate (i.e., retailers are numerous), nor to restore monopoly power when intensive downstream competition squeezes the vertical industry profit.

In addition, our results provide empirical support for H3a regarding the positive relationship of the upstream complementary investments and the likelihood of observing ED. The results

show that the upstream substitutable investments also relate positively to the choice for ED. This last result is contrary to H3b. Finally, we do not find evidence for hypotheses H4a and H4b, which are related to the downstream investments.

To summarise, it appears that only upstream investments, whether they are complementary or substitutable, impact the choice for ED. In both cases, we find evidence that the more the upstream firm invests in the vertical relationship, the more likely the firm is to sign ED contracts 5 Noting that Fumagalli and[START_REF] Fumagalli | Exclusive Dealing and Entry, When Buyers Compete[END_REF](2008) suggest that the anti-competitive ED is more likely to occur if downstream products are substitutable. However, their analysis is based on the assumption of harsh, Bertrand-like downstream competition in which buyers are driven out of the market if they bear higher wholesale prices from the less efficient incumbent. This assumption seems to be less consistent with the French distribution network, as many retail stores are horizontally differentiated and are not easily driven out if their competitors have cheaper supply sources.

with downstream retailers. This result suggests that the suppliers do not distinguish between the different types of investments and that they tend to impose more restrictive contractual clauses because their level of involvement in the vertical relationship is higher.

The efficiency motive of ED finds strong support when we take into account the nature of the investment. The fact that both complementary and substitutable investments by upstream suppliers are positively related with the adoption of an ED contract suggests that ED can be used to foster the upstream investment. As investigated by Segal and Whinston (2000b), the upstream complementary investments, such as efforts for training the downstream staffs and the transmission of knowledge, also benefit the trade between retailers and competitors. Therefore, ED can be used to protect the investment from free-riding by the upstream competitors. In this case, ED is efficiency improving. A similar explanation can also be found in [START_REF] Besanko | Equilibrium Incentives for Exclusive Dealing in a Differentiated Products Oligopoly[END_REF], where investment has a positive inter-brand externality to the competitor's chain.

However, when the upstream investment is substitutable, in that it reduces the value of trade between the retailers and the upstream competitors, Segal and Whinston (2000b) find that the investment incentive of the supplier tends to be higher in the absence of ED, as the exclusive contract can worsen the position of the upstream competitors with investments. This rationale is obviously anti-competitive. However, as our empirical finding regardingH3b suggests a reverse result, it again appears that the anti-competitive rationale for ED does not hold in the French case.

Conclusions

This paper investigates the rationales of ED, which is one of the most common forms of vertical restraint, in attracting intense policy debates in anti-trust regulations. Based on a survey of the theoretical literature, we identify the determinants that may result in this contractual arrangement for anti-competitive and pro-competitive reasons. In particular, we consider the industry features, such as the upstream and downstream competition, as well as the nature of the investments undertaken in the vertical relationship. Several hypotheses are derived from the theoretical framework and tested using French data from several types of distribution networks in a wide range of sectors.

The results highlight the good explanatory power of the estimated probit models (good fit statistics). These results are robust and suggest that taking into account the market structure and the upstream and downstream investment nature, ED contracts are primarily used for procompetitive reasons in the French distribution system. More precisely, we find that contrary to the theoretical prediction regarding the anti-competitive rationales of ED, the larger the number of upstream firms within a subsector of the sample, the more likely these firms are to reach ED agreements with downstream retailers. Meanwhile, there is no evidence that the number of downstream units for each network (intra-brand downstream competition) or for each market (intra-and inter-brand downstream competition) affects the choice for ED. Instead, we find that the more substitutable the final products are, the more likely it is that there will be ED contracts.

Therefore, it appears that in the French distribution networks, ED is used neither to exploit contract externality of buyers when buyers are difficult to coordinate (i.e.. when retailers are numerous) nor to restore the monopoly power when intensive downstream competition squeezes the vertical industry profit.

It seems that the motivation for ED is primarily the result of its positive role in fostering the investment of the upstream firms. Indeed, we find that the more the upstream firms invest in the vertical relationship, the more likely that they sign ED contracts, a finding that corresponds to the theoretical prediction on the efficient motive of ED (Segal andWhinston 2000b, Besanko and[START_REF] Besanko | Equilibrium Incentives for Exclusive Dealing in a Differentiated Products Oligopoly[END_REF]: the upstream investments, such as efforts for training the downstream staffs and the transmission of expertise, also benefit the trade between retailers and competitors. Therefore, ED can be used to protect the investment from the free-riding of the upstream competitors.

Our empirical results provide interesting insights for competition authorities. The traditional regulation of the competition agencies is usually hostile towards ED agreements. As noted by Motta et al. (2012), "The decisions in cases involving ED are often controversial as the promotion of relation-specific investment must be balanced against the threat of foreclosure of potential competitors". Our results suggest that when an industry or a sector is taken into account, ED exhibits a pro-competitive nature in promoting the relation-specific investment, rather than enhancing the dominant position of the incumbent. The reason can stem from two facts. On the one hand, our results may suggest that the competition authority has successfully blocked the anti-competitive ED, leaving the pro-efficiency ED prevailing in the industry. On the other hand, the results may imply that the studied industry structures and the market environments are unfavourable for anti-competitive ED. This second interpretation of our empirical findings is consistent with the critics of the Chicago School [START_REF] Bork | The Antitrust Paradox[END_REF][START_REF] Posner | Antitrust Law: An Economic Perspective[END_REF] who contend the incumbent would not find it profitable to sign an anti-competitive ED contract and to pay buyers not to address the efficient entrant.

As the first explanation raises a problem of selection bias, future studies in this direction would be interesting. Other limits of this paper include the definition of the dummy variable capturing the product level of substitution and the identification of the nature of the investments,

Table 1 -

 1 Anti-competitive motives for exclusive dealing

	Industry Structure	References	Results	Basic Rationales

Table 2 -

 2 ED and investment incentives

	Reference	Upstream incumbent invests		Downstream retailers invests
	Segal and Whinston (2000b)	Hypotheses	Basic Rationales	Hypotheses		Basic Rationales
	Complementary investments: benefit the trade between competitors and retailers	H3a: Efficient ED is more likely.	ED can protect the investment of incumbent from the free-ride of	H4a: Anti-competitive ED is less likely.	ED reduces the incentive of retailer to invest in favour of the competing sellers and, hence, can help the
				competitors.			incumbent to dampen the
							position of competitors.
	Substitutable	investments:	H3b:	Incumbent	has	H4b:	ED gives the retailer more
	reduce the trade between	ED is less likely.	incentive to invest	Anti-competitive	incentive to invest as it
	competitors and retailers		and dampen the	ED is more likely.	dampens the position of
				position of its		competitors to the benefit
				competitors. ED is		of	trading	with	the
				of no use.			incumbent.

Table 3 :

 3 Seven types of distribution networks(INSEE definition)

	Network type	Condition
	Franchised slightly mixed	More than 50 % of the network turnover (NT) is achieved by franchised units
	Franchised highly mixed	Between 20 % and 50 % of the NTis achieved by franchised units
	Predominantly integrated	More than 50 % of the NTis achieved by company-owned outlets
	Brand License	More than 50 % of the NTis achieved by outlets with a brand license contract
	Commission-based affiliation	More than 50 % of the NTis achieved by outlets with a CBA contract
	Concession	More than 50 % of the NTis achieved by outlets with a concession contract
	Cooperative	More than 50 % of the NTis achieved by outlets whose members belong to a
		cooperative

The sample covers a wide range of activities grouped into 15 sectors according to the INSEE classification. The sector-based distribution of the sample networks is presented in Table

4

. This table shows that the two main sectors are « Clothing retail » (20.24 % of sample networks) and « Home equipment » (19.05 % of sample networks).

Table 4 :

 4 Sector-based distribution of the sample networks

	Number of	% in sample
	networks

Table 5 :

 5 Distribution of the ED clause in the sample networks

		Freq	%
	No-ED	270	53.57
	ED	234	46.43
	Total	504	100

Table 6 :

 6 Distribution of the ED clause within the 15 sectors

	Sectors	No-ED ED Total
	Maintenance and repair of motor vehicles and automotive equipment trade	11	5
	Retailing predominantly in food supermarkets	4	1
	Retailing general supply or frozen products in small stores	3	6
	Equipment for individuals	30	21
	Culture-leisure-sports	31	15
	Home equipment	49	47
	Development of housing	36	10
	Non-food, non-specialised retail stores	5	0
	Craft businesses	8	7
	Trade and repair of motorcycles	4	1
	Retail sale of food in specialised stores	9	20
	Retail sale of medical and orthopaedic devices	7	4
	Other retail stores specialising in non-food items	28	17
	Clothing retail	34	68
	Retail shoes	11	12
	Total	270	234

Table 7 :

 7 Distribution of the ED clause within the network types

	Network type	No-ED	ED	Total
	Brand license	31	11	42
	Concession	23	16	39
	Franchised and slightly mixed	71	47	118
	Franchised and highly mixed	21	27	48
	Predominantly integrated	47	102	149
	Cooperative	72	19	91
	Commission-based affiliation	5	12	17
	Total	270	234	504

Table 8 :

 8 Construction of the dummy variable: substitute

	Sector	Type of product
	Maintenance and repair of motor vehicles and sale of motor vehicle parts and accessories	non-substitutable
	Large-scale food retailing stores	substitutable
	Retailing general supply or frozen products in small stores	substitutable
	Personal and household goods (except clothes and shoes)	non-substitutable
	Cultural and recreation goods stores	non-substitutable
	Home equipment stores	non-substitutable
	Development of housing	substitutable
	Retail non-food non-specialised stores	substitutable
	Craft businesses	non-substitutable
	Trade and repair of motorcycles	non-substitutable
	Retail sale of food in specialised stores	non-substitutable
	Retail sale of medical and orthopaedic	non-substitutable
	Other retail stores specialising in non-food	substitutable
	Clothes stores	substitutable
	Shoe stores	substitutable

Table 9 .

 9 Summary statistics (504 distribution networks)

	Variables	Definition	Mean	Std. Dev.	Min	Max	Type
	Dependent variable
	ED	Exclusive dealing clause included in the vertical contract	.4642857 .4992184	0	1	Dummy variable
	Explanatory variables derived from the hypotheses
	MARKETSHARE	Market share of the network (network turnover/market turnover) .0297619 .0698682 .0000693 .6048392	Quantitative variable
	HHI	Herfindahl-Hirschmann index	9.615324 8.760991 3.146751 44.62323	Quantitative variable
	MARKSHARHHI	Market share * HHI (multiplicative)	.0029568 .004568 .000017 .0312769	Quantitative variable
	SIZESEGMENT	Size of market segment (number of networks)	39.19841 35.14079	1	102	Quantitative variable
	SIZENET	Size of network (number of downstream outlets)	180.004 488.4781	7	7770	Quantitative variable
	SIZEMARKET	Size of market (number of downstream outlets)	9689.278 5098.248	227	16402	Quantitative variable
	SUBSTITUTE	Type of product: substitutable versus non-substitutable	.5337302 .4993566	0	1	Dummy variable
	INITRAIN	Initial training provided by upstream to downstream units	.7777778 .4161528	0	1	Dummy variable
	TRANSF	Transmission of expertise by upstream to downstream units	.8214286 .3833736	0	1	Dummy variable
	SERVICE	Services provided by downstream units to final consumers	.4801587 .5001025	0	1	Dummy variable
	UPSUBSTI	Upstream substitutable investment	8.234127 2.823634	0	13	Index summing 7 dummies
	DOWNSUBSTI	Downstream substitutable investment	2.236111 1.221822	0	4	Index summing 4 dummies
	Control variables
	AGE	Age of network	21.31092 19.81727	0	184	Quantitative variable
	OTHERNET	Operation of upstream unit of another branded network	1.333333 .9437458	0	2	Dummy variable
	EXCLUTERRI	Exclusive territory granted to downstream unit	.7142857 .4522028	0	1	Dummy variables for the
	TYING	Tying imposed on downstream unit	.6468254 .4784313	0	1	impact of another restraint
	TYPENET	Type of network (7 organisational forms distinguished)	3.119048 1.614335	0	6	Qualitative variable
	CAPITALCITY	Area of capital city	.4146825 .4931566	0	1
	NORTHEAST	Northeast area of country	.1190476 .3241663	0	1	Dummy variables for the
	NORTHWEST	Northwest area of country	.156746 .3639224	0	1	geographical location of the
	SOUTHEAST	Southeast area of country	.1845238 .3882962	0	1	upstream unit
	SOUTHWEST	Southwest area of country	.125	.3310475	0	1

  p< 0.05, ** p< 0.01, *** p< 0.001

		(0.223)	(0.00915) (0.226)	(0.0125) (0.224)	(0.0138) (0.226)	(0.0138) (0.224)
		Table 11. Step-by-step probit estimates for exclusive dealing
	MARKSHARHHI NORTHEAST	-0.129	21.54 -0.135	35.92 -0.133	31.09 -0.252	25.92 -0.0796
		(6) (0.211)	(19.70) (7) (0.213)	(20.99) (8) (0.207)	(22.84) (9) (0.211)	(22.87) (10) (0.206)
	SIZENET AGE NORTHWEST	-0.00167 -0.720 *** (0.00328) (0.204)	-0.00180 -0.760 *** (0.00329) (0.204)	-0.0000986 (0.000157) -0.00206 -0.787 *** (0.00327) (0.200)	-0.0000357 (0.000179) -0.00244 -0.760 *** (0.00336) (0.207)	-0.0000366 (0.000178) -0.716 *** -0.00218 (0.00330) (0.202)
	SIZEMARKET OTHERNET cons	0.263 *** -2.961 *** (0.0727) (0.450)	-3.142 *** 0.256 *** (0.0730) (0.457)	-0.0000424 (0.0000264) -2.594 *** (0.431)	-0.0000436 (0.0000285) -2.588 *** (0.427)	-0.0000484 (0.0000288) -2.561 *** (0.431)
	SIZESEGMENT EXCLUTERRI SUBSTITUTE Prob> chi2 Pseudo R 2 % TYING Predicted Area under ROC curve	0.0000 0.2385 74.16 0.8080	0.371 * (0.153) 0.0000 0.2464 72.27 0.8140	0.0145 *** (0.00353) 0.392 ** 0.287 0.0000 (0.151) 0.2271 (0.171) 71.22 0.8038	0.0142 *** (0.00379) 0.394 * 0.0000 0.2451 (0.185) 0.628 *** 73.11 (0.146) 0.8132	0.0153 *** (0.00383) 0.0000 0.2220 0.422 * 72.69 (0.186) 0.8000
	INITRAIN TYPENET Standard errors in brackets				0.569 ** (0.212)	0.563 ** (0.0457) (0.216) 0.0774
	TRANSF MARKETSHARE	0.232 (1.424)	0.124 (1.427)	0.131 (1.459)	0.716 ** (0.245) -0.00398 (1.445)	0.727 ** 0.266 (0.243) (1.451)
	SERVICE HHI	0.00530 (0.0139)	0.00823 (0.0143)	0.00751 (0.0143)	0.137 (0.142) 0.00373 (0.0136)	0.134 0.00222 (0.142) (0.0138)
	UPSUBSTI MARKSHARHHI	11.96 (21.58)	18.22 (21.62)	15.19 (20.70)	0.126 *** (0.0287) 20.03 (21.10)	0.126 *** 5.563 (0.0296) (20.66)
	DOWNSUBSTI SIZENET	-0.0000466 (0.000134)	-0.0000742 (0.000156)	-0.000105 (0.000150)	-0.0996 (0.0619) -0.0000472 (0.000138)	-0.102 -0.0000517 (0.0626) (0.000130)
	SOUTHEAST SIZEMARKET	Table 10. Probit estimates for exclusive dealing -0.0000432 -0.0000392 -0.0000338 -0.0000373 (0.000028) (0.000028) (0.000027) (0.000027)	-0.396 * -0.0000451 (0.192) (0.000027)
	SOUTHWEST SIZESEGMENT	(1) 0.0152 *** (0.00372)	(2) 0.0148 *** (0.00371)	(3) 0.0135 *** (0.00368)	(4) 0.0134 *** (0.00374)	(5) -0.225 0.0145 *** (0.231) (0.00369)
	AGE NORTHEAST SUBSTITUTE	-0.00112 (0.00338) 0.415 * (0.176)	-0.00190 (0.00344) 0.386 * (0.177)	-0.00167 (0.00356) 0.324 (0.175)	-0.00226 (0.00338) 0.304 (0.178)	-0.00239 (0.00342) -0.205 0.428 * (0.218) (0.177)
	OTHERNET NORTHWEST INITRAIN	0.132 * (0.0660) 0.659 ** (0.214)	0.144 * (0.0667) 0.609 ** (0.213)	0.147 * (0.0682) 0.586 ** (0.210)	0.229 ** (0.0744) 0.545 * (0.214)	0.224 ** (0.0751) -0.763 *** 0.680 ** (0.212) (0.215)
	EXCLUTERRI _cons TRANSF	0.510 *** (0.137) -1.475 *** (0.220) 0.793 ** (0.244)	0.513 *** (0.139) -1.462 *** (0.251) 0.709 ** (0.247)	0.560 *** (0.142) -2.031 *** (0.357) 0.646 ** (0.250)	0.373 * (0.156) -3.872 *** (0.467) 0.712 ** (0.238)	0.404 ** (0.155) -3.492 *** 0.759 ** (0.487) (0.246)
	TYING SERVICE TYPENET Prob> chi2 Pseudo R 2 % Predicted UPSUBSTI	0.784 *** (0.130) 0.268 * 0.0735 0.0000 (0.137) 0.1130 (0.0385) 68.28 0.131 *** Area under ROC curve 0.799 *** (0.131) 0.240 0.0699 0.0000 (0.138) 0.1175 (0.0386) 67.23 0.136 *** (0.0284) (0.0284)	0.784 *** (0.134) 0.200 0.0738 0.0000 (0.137) 0.1531 (0.0417) 69.12 0.136 *** (0.0279)	0.562 *** (0.147) 0.128 0.0756 0.0000 (0.139) 0.2635 (0.0475) 73.95 % 0.126 *** 0.8222 (0.0281)	0.566 *** 0.223 (0.150) 0.0000 (0.135) 0.2728 0.0826 74.79 % 0.122 *** (0.0474) 0.8270 (0.0284)
	CAPITALCITY Robust standard errors in brackets 0.292 * (0.126) DOWNSUBSTI -0.0647 * p< 0.05, ** p< 0.01, *** p< 0.001 (0.0618)	0.273 * (0.129) -0.0788 (0.0631)	0.332 * (0.135) -0.108 (0.0622)	0.407 ** (0.148) -0.100 (0.0601)	-0.110 (0.0605)
	MARKETSHARE SOUTHEAST	-0.356 (0.188)	-0.266 (1.380) -0.392 * (0.191)	-1.070 (1.379) -0.353 (0.192)	-0.461 (1.402) -0.342 (0.190)	-0.119 -0.295 (1.407) (0.188)
	HHI SOUTHWEST	-0.375	-0.00683 -0.365	0.0114 -0.367	0.00659 -0.278	0.00557 -0.332

*

Table 12 .

 12 Bivariate probit and seemingly unrelated bivariate probit estimates for exclusive dealing (potential endogeneity of TYING)

		(11)	(12)	(13)	(14)
	Dependent variable: ED
	SOUTHEAST	-0.295		-0.337
		(0.182)		(0.183)
	SOUTHWEST	-0.356		-0.284
		(0.204)		(0.220)
	NORTHEAST	-0.139		-0.238
		(0.198)		(0.222)
	NORTHWEST	-0.772 ***		-0.728 ***
		(0.194)		(0.219)
	CAPITALCITY		0.384 **		0.387 **
			(0.133)		(0.142)
	MARKETSHARE	-0.313	-0.627	0.0935	-0.152
		(1.397)	(1.413)	(1.517)	(1.462)
	HHI	0.00682	0.00796	0.00273	0.00323
		(0.0125)	(0.0124)	(0.0137)	(0.0135)
	MARKSHARHHI	10.42	16.30	18.91	22.44
		(20.24)	(20.51)	(21.96)	(21.26)
	SIZESEGMENT	0.0132 ***	0.0123 ***	0.0124 **	0.0109 **
		(0.00361)	(0.00357)	(0.00422)	(0.00410)
	SIZENET	-0.000105	-0.000108	-0.0000460	-0.0000489
		(0.000146)	(0.000152)	(0.000180)	(0.000178)
	SIZEMARKET	-0.0000331	-0.0000286	-0.0000348	-0.0000301
		(0.0000263)	(0.0000262)	(0.0000273)	(0.0000269)
	SUBSTITUTE	0.334	0.305	0.253	0.206
		(0.171)	(0.169)	(0.197)	(0.191)
	INITRAIN	0.484 *	0.501 **	0.537 **	0.535 **
		(0.194)	(0.189)	(0.206)	(0.203)
	TRANSF	0.675 **	0.672 **	0.709 **	0.685 **
		(0.227)	(0.227)	(0.232)	(0.227)
	SERVICE	0.222	0.235	0.148	0.160
		(0.129)	(0.128)	(0.141)	(0.136)
	UPSUBSTI	0.141 ***	0.139 ***	0.123 ***	0.119 ***
		(0.0264)	(0.0258)	(0.0290)	(0.0290)
	DOWNSUBSTI	-0.0696	-0.0687	-0.0980	-0.0959
		(0.0577)	(0.0571)	(0.0600)	(0.0591)
	AGE			-0.00271	-0.00264
				(0.00330)	(0.00323)
	TYING			0.975	1.142 *

Table 13 .

 13 Probit estimates for exclusive dealing with sector dummies

		(15)	(16)	(17)	(18)	(19)
	AGE	-0.000561	-0.000591	-0.000357	0.000115	-0.000576
		(0.00382)	(0.00388)	(0.00393)	(0.00383)	(0.00387)
	OTHERNET	0.244 **	0.233 **
		(0.0768)	(0.0772)
	EXCLUTERRI		0.416 *	0.444 **
			(0.165)	(0.163)
	TYING				0.581 ***
					(0.154)
	TYPENET					0.0527
						(0.0480)
	CAPITALCITY	0.343 *	0.369 *	0.355 *	0.348 *	0.307 *
		(0.148)	(0.151)	(0.150)	(0.151)	(0.147)
	SIZESEGMENT	0.00433	0.00162	-0.00172	0.00105	0.00127
		(0.00667)	(0.00673)	(0.00648)	(0.00660)	(0.00646)
	SUBSTITUTE	0.241	0.148	0.286	0.186	0.472
		(0.424)	(0.416)	(0.402)	(0.412)	(0.418)
	INITRAIN	0.745 ***	0.695 ***	0.677 **	0.648 **	0.750 ***
		(0.209)	(0.211)	(0.210)	(0.210)	(0.210)
	TRANSF	0.822 ***	0.723 **	0.679 **	0.738 **	0.797 ***
		(0.238)	(0.245)	(0.246)	(0.236)	(0.236)
	SERVICE	0.329 *	0.308 *	0.269	0.157	0.283 *

The null hypothesis H0 is the hypothesis of independence.

We are grateful to the French National Institute of Statistics and Economic Studies (INSEE) for allowing use of its original dataset. We also thank Laure Turner (INSEE) and Emilie Dargaud

which may be not well specified. Here, again, complementary empirical results would be useful in dealing with such variables.

Finally, our results regarding the control variables open interesting avenues for further study.

While the age and the type of the network have no influence on the choice to include an ED clause, a strong influence of the geographical location of the upstream firm must be noted. This is an unexplored, yet interesting, dimension of the contractual choices, and the result is robust in this respect. Thus, the choice to impose ED differs regarding the location of the upstream unit, with a main distinction between the capital city area and the rest of the country. The statistical link between the geographical location and the level of the upstream competition, as highlighted in the paper, is a first step in the explanation. The impact of the geographical dimension on the contractual design and, more broadly, on the organisational choices in distribution networks appears as a new and interesting direction for future research.

In addition, our estimations highlight also the strong influence of the other vertical restraints (exclusive territory, tying) on the choice to impose ED. Regarding this issue, we control for endogeneity bias with Hausman tests comparing probit and bivariate probit models fitted to binary endogenous regressors. The estimated positive influence provides evidence of the complementarity between the vertical restraints, thus suggesting that the three studied provisions (ED, tying, exclusive territory) can be considered a "package". This result also calls for further empirical research regarding the interactions between the vertical restraints used in distribution contracts.

Appendix 1.


TRAVAUX DU COMITÉ FRANÇAIS D'HISTOIRE DE LA GÉOLOGIE

-Troisième série -T. III (1989) Hugh TORRENS In Commemoration of the 150th anniversary of the death of William Smith (1769Smith ( -1839)).

COMITÉ FRANÇAIS D'HISTOIRE DE LA GÉOLOGIE (COFRHIGEO) (séance du 31 mai 1989)

It is sadly remarkable that this anniversary is likely to go quite unnoticed in the country of Smith's birth. So I accepted an invitation from France, to attempt this short appreciation of William Smith, with particular delight ; as Smith was one who made, and can be shown to have made, a great original contribution to geology. But I have tried not to be motivated by any chauvinism ; a concept of which the English seemed strangely unaware until educated from France ! RECENT HISTORIOGRAPHY.

William Smith has suffered enormously at the hands of recent historians. We have been told of a "suspicion" that the importance of the verbal dissemination of his results and ideas, before he himself published his major works from 1815 has been "overrated" (Laudan, 1976: 211), but without evidence being adduced. At the same time we were told that "for a long time [Smith's] discoveries remained more or less unknown". He had got it into his head, unfortunately, that his data were of great commercial value, and he accordingly tried to keep them a close secret until his final magnum opus should appear (Allen, 1976: 57). We were even told that Smith "did not have time to identify the strata by their fossils, but used other primary criteria" in his mapping (Laudan, 1976: 210, 212). We are more recently asked to accept that Smith is simply a "cult" figure, not "a figure of historical reality", created in some conspiracy by members of the Geological Society of London to bolster their own work in 1831, when in reality "men like [George] Greenough and [James] Parkinson would be more deserving of any such title as 'Father of English Geology'" (Rupke, 1983: 191-3).

It is perhaps a truism to say that if one repeats something often enough, people will believe it. Present historians certainly face problems in assessing Smith's contribution to geology. In the face of such recent historiography, Smith's main problem seems clearly to stem from his having been the subject of four separate attempts at proper biographical study, none of which have been completed. As a result, there is no definitive study of his life and work, since that of 1844 by his nephew John Phillips (1800-1874), a situation which can only encourage thoughts of nepotism and theories of conspiracy.

PROPER HISTORICAL ANALYSIS.

We have a duty as historians to understand the work of those who developed the science we try to document. While we must always avoid chauvinism, we surely have an equal duty to properly justify any revisionism. I believe all the quotations given above to be simply this. To be true historians we must try to enter the brains of those we study and see through their eyes what they saw and the problems they faced. We have a duty to understand and not to judge, and above all to make close and careful study of original sources (Ellenberger, 1988: 3). Nor are these sources, especially in the case of a practical man like Smith only printed. Such "papyrophilic" attitudes produce, I believe, serious distortions of history [START_REF] Torrens | Hawking History -A vital future for Geology's Past[END_REF]. Sources for Smithian history must involve collections of specimens in museums and study of outcrops and field areas where Smith and others worked ; yet historians continue to issue judgments against William Smith, without using either of these as sources.

A recent new claim draws attention to Smith's scientific isolation ; in his very earliest years a valid enough point, but then 'confirms' this 'isolation' by commenting that "Smith's [surviving] papers contain ... almost no books or articles on geology, British or foreign ... so that he was almost entirely unaware of work going on on the Continent" (Laudan, 1987: 164). While this, if true, would make Smith's contributions even more original, might not the historian's proper duty be to ask whether there are other possible reasons for this absence of evidence ? Any forensic scientist knows such negative evidence can be misleading.

ASSESSING SMITH.

Should historians not take account of Smith's six week imprisonment for debt in London in 1819, a fact on record now for 20 years (Eyles, 1969: 137) ? It has been on record even longer that "the amount of printed matter preserved in the [Smith] collection is comparatively small, for Smith had been obliged to part with all his books [and printed papers] in 1819" as well as his "furniture and collections" ; because he was then in a debtor's prison and his creditors had to be appeased. Even "any [publications] he accumulated in later years were presumably sold on his death" [START_REF] Phillips | Memoirs of William Smith Ll.D[END_REF]: 91 & Cox, 1942: 10). So much for an absence of printed papers and books in the Smith archive. Smith's very great, and long continuing, financial problems, which become even clearer from recent research, should form a central part of a historian's focus. When we consider him properly, we can only agree with the judgement of Dietrich (1961: 259) when comparing Smith and Baron Ernst von Schlotheim, that "in origin, character, social status and calling the two men have hardly anything in common".

As for the oral dissemination of Smith's work, before his financial problems with publication were solved in 1813, should we not also ask if it might have been possible for others to have then disseminated his ideas for him ? Joseph Townsend (1813: V) records how before publication "with unparalleled disinterestedness of mind, Smith scorned concealment, and made known his discoveries to everyone who wished for information". One who played a major role in this diffusion of Smith's results was his fellow land-surveyor and polymath John Farey (1766-1826). Recent work [START_REF] Torrens | John Farey's General View of the Agriculture and Minerals of Derbyshire[END_REF]) reveals the enormous influence Farey then had in many British scientific, agricultural and engineering circles and lists his incredible volume of publications, over 250 in number, many of them urging Smith's case and widely disseminating his results from 1806 on.

Other voices have been raised against recent Smith historiography or 'villainography' as we might call it. Morrell has shown how the idea of any Smith cult having arisen in 1831 is seriously inaccurate chronologically [START_REF] Morrell | The legacy of William Smith -the case of John Phillips[END_REF] and how can the claim, noted above, that Smith did not make use of fossils in his stratigraphic work, have been made without any proper historical analysis of the large collection of some thousands of fossils he certainly did have time to make between 1795 and 1818, and which so largely (at least 75%) still survives [START_REF] Torrens | Hawking History -A vital future for Geology's Past[END_REF]: 87) ?

Smith was not a major contributor to the development of geological theory and as he got older any theoretical ideas he held certainly got ever more divorced from the consensus that slowly developed amongst many of those he had earlier influenced [START_REF] Cox | New Light on William Smith and his Work[END_REF]& Berkeley, 1988: 221). But as a land and mineral surveyor he emerges as a craftsman with a truly incredible eye for three dimensional analysis and the "lie of the land". His major aspiration, which he proudly announced in his first Prospectus of 1801, for a book never published again for clear financial reasons, was as a 'Practical Man' ; to help Land-owners, Farmers, Miners, Canal engineers, Builders and others find the raw materials they needed in a rapidly industrialising Britain [START_REF] Smith | Prospectus of a Work entitled Accurate Delineations of the Natural Order of the various Strata[END_REF].

With such practical activities as mapping and prospecting for minerals it is vital historians use all sources of evidence and especially non-printed ones. My personal private celebration for this 150th Smith anniversary was to take a Russian stratigrapher friend to the tiny chapel of St Giles at Kellaways in Wiltshire ; to show her the stratotype on which the international Callovian Stage of the Jurassic System had been based. Smith first came across the Kellaways Stone rock unit here, and the fossils which he showed so well characterised it, whilst draining near Thomas Crook's house at Tytherington Kellaways in 1800 (Phillips, 1844: 35). A historian has asked us to believe that as Smith mapped each stratum, he would have to "climb slowly up the western [sic !] side of the outcrop of each stratum and then descend rapidly down a sharper scarp slope on the far side" and then that this distribution would allow Smith to everywhere "predict the stratum that would outcrop" (Laudan, 1976: 214).

But there is simply no such natural scarp pattern or outcrop here of any rock unit, now or in Smith's time, since it is only between 2.7 and 4.3 m thick [START_REF] Cope | A correlation of Jurassic Rocks in the British Isles, part Two : Middle and Upper Jurassic[END_REF]. Just as Smith stated "this extraordinary stone from neither its thickness or consistence can properly be called a Rock ... Its course is known only by a few excavations in it, chiefly for road materials which in a country abounding so much with clay [which over and under lies it here] are very scarce. It no where forms any characteristic surface, or rarely a hill or other feature which is distinguishable to any but those who know where to look for the Stratum... From the great obscurity in the course of the Kelloways Stone, the organised Fossils of the Stratum can only be found in excavations, and in the stone used on the roads" (Smith, 1817: 23). Early in 1805 when Smith visited Somerset he found a trial Pit for coal being dug in the Oxford Clay near Bruton, way above any possible productive Coal Measures. This had then reached this Kelloways Rock 37 metres down. Fossils of Gryphaea from these excavations allowed him to predict on the spot and with total certainty that this coal trial was an unscientific prospect (Phillips, 1844: 66). This is Smith's real skill and his contribution to science, as a mineral prospector ; a skill in which he has had few equals, and which must also be analysed 'in the field' and from museum material. His skill as a land surveyor must also be judged in the field. I defy anyone to walk the Hackness hills and outcrops in Yorkshire with Smith's 1832 lithographed map, at 1 : 9500 (or 792 feet to one inch !), in hand to see this as the production of anyone other than a genius at mapping geologically. The tragedy is that the map is now so rare that few can have the chance to have done so (but they might try by study of the material reproduced by Sheppard, 1920: 167-174 & pls xvii-xix).

I have purposefully said nothing about Smith's originality. Proper international assessment is needed here, especially of French antecedents in the use of fossils in stratigraphic analysis. One's view depends largely on whether one wishes to assess only strict 'priority' questions or whether the greater achievement, is more to put something into real and continued practice, than to have the idea in the first place. The former I believe is the case with such a practical subject as stratigraphy. I believe we have much to learn here from historians of technology, who believe any 'palm should be awarded' to those who actually make things work.

We have also still to reserve judgement on Smith's influence in France until more original research is undertaken. The first publication by the Geological Society of London to make a full reference to Smith's work was duly translated into French (Parkinson, 1813: 291) but since this was a literal translation from English, any priority for Smith stated there need only reflect English perceptions, in the absence of any French editorial comment. The main problem for historians is to allow for the fact that between 1793 and 1815, exactly the years of Smith's major achievement, England and France were engaged in a long and bitter war. Indeed Smith later stated that this was one major reason why he had had such financial problems. But scientists on both sides were in very free contact in this period [START_REF] Beer | The Sciences were never at War[END_REF]. A fascinating historical question is posed in one of Joan Eyles' last papers (1985) , in which she points one the great likelihood that Smith's stratigraphic results must have been diffused to France during the short Peace of Amiens in 1802-3. Her paper, which raises questions, is the sort of history of which we should have more.

CONCLUSIONS

We should commemorate this anniversary with a plea to the historical community not to judge, or even worse misjudge, the past. Instead we ask they should try to understand it ; in Smith's case by proper study of his, and his contemporaries' many, publications as well as of his collections which still survive in the British Museum (Natural History) in London. We should urge historians to venture into the natural 'laboratory' which Smith made so particularly his own, the sequences and outcrops of the Carboniferous to Mesozoic rocks all over England. I personally have no doubt, from this third source, that nearly 200 years ago Smith knew parts of these sequences much better than anyone alive today. This is an achievement few living scientists can claim but one which helps to explain the particular problems and pleasures of geology and the importance of its history. I hope, but not with much conviction in view of the philistine treatment of scholarship in British Universities these last ten years, still to be able to celebrate 1994 with a proper biography of Smith. This will be 150 years after the only other such study by his nephew and pupil John Phillips, who may thus not have been the most objective judge of his uncle's work. Certainly there is a desperate need for a properly balanced assessment of Smith's life and work from an international perspective.

Grateful thanks are due to many in my 25 year long attempt to understand Smith's failures and successes ; but particularly to Francois Ellenberger and Joan Eyles both of whom have encouraged me when so few others did, that what I was doing was worth doing.


Laurent Larger
email: laurent.larger@univ-fcomte.fr

Romain Martinenghi

Maxime Jacquot

Yanne K Chembo

Complex photonic nonlinear delay dynamics for high performance signal and information processing Nonlinear delay dynamics for information processing

Keywords: Nonlinear dynamics, delay equations, photonic delay oscillator, complexity, information processing

Delay dynamics are known as infinite dimensional. They exhibit a wide variety of behavior, from stable steady states to chaos, through periodic solutions. Photonic appeared during the last decades as a fascinating physical playground, to both explore this complexity and also use it in signal and information processing applications.

I. UBIQUITOUS DELAY DYNAMICS, AND OPTICS

Although it is rarely taught in any academic program, delay dynamics can indeed be found in many real life situations [START_REF] Erneux | Applied delay differential equations[END_REF]. They emerge from any physical, chemical, biological, etc... situation, where "long" range transport phenomena are present, and are coupled to dynamical phenomena (see Fig. 1). Such transport mechanisms play the role of a memory for traveling temporal fluctuations. The fluctuations are stored within the transport channel, until they exit and they interact again with their source through a feedback mechanism, after having experienced dynamical processes and/or nonlinear transformations. The channel can be blood vessels, heat conduction medium, axons between neurons, and also wires or optical fibers.

The "length" of the transportation medium, or equivalently the delay it produces from the channel input to its output, has to be compared with the elementary duration (τ) allowed by the limiting dynamics (the differential process). This comparison or scaling (τD/τ) is a measure of the dimensionality of the complex dynamics that can be generated by the delay system. The long delay configuration is the one of interest when complex motions are desired. Photonics offers paradigmatic experiments [START_REF] Larger | Chap.4 "Optical Delay Dynamics and its Applications[END_REF] to explore and use the huge complexity potential of delay dynamics. Two such photonic delay systems are particularly popular in the literature, and they have been intensively studied for their numerous and rich dynamical behavior, among which one can obtain high dimensional optical chaos. The external cavity laser diode (ECLD) involves a Fabry-Pérot semiconductor laser subjected to a feedback of one output beam from an distant mirror [START_REF] Broom | Microwave selfmodulation of a diode laser coupled to an external cavity[END_REF]. The Ikeda ring cavity involves a localized Kerr medium inside a long ring cavity seeded by a CW laser beam. The results we report on, are concerned by the second example, however implemented physically with an electro-optic phase change [START_REF] Gibbs | Observation of chaos in optical bistability[END_REF] instead of the Kerr one, as illustrated in Fig. 2. This experimental detail has two main consequences: The dynamics is scaled down to lower speed (however still allwing for the ones of typical optoelectronics telecom bandwidth); The parameter space is however also scaled up to wider ranges enabling experimental access to more complex dynamics. In this situation, the nonlinear transformation f NL [x] is provided by a two wave interference phenomenon, resulting in a cos 2 profile, which operating point (parameter Φ 0 in Fig. 1) can be adjusted through a bias voltage for the electro-optic effect.

II. MODELING WITH SIGNAL PROCESSING VIEWPOINT

In the case of the Ikeda approach, a very convenient feature is to have nicely separated processes, as illustrated in Fig. 1: The dynamical process is a limited rate of change modeled by a linear differential process in time, corresponding to a filtering transfer function H(ω) =FT[h(t)] in the Fourier space (h(t) being the temporal impulse response of the filter, and FT the Fourier Transform operator); The nonlinear transformation fNL[x] performed by a two wave interference phenomenon (supposed to be adiabatic, i.e. instantaneous, without any dynamical limitation); And the time delayed feedback operation xτD(t)=x(t-τD), e.g. obtained through light propagation inside the ring cavity or a any light propagation path of a given length (as a fiber length for the optoelectronic approach). Modeling such a dynamics can be written mathematically in different forms [START_REF] Gibbs | Observation of chaos in optical bistability[END_REF]:

x(t) = [h * fNL(xτD)](t) = ∫ -∞ +∞ h(t-θ) fNL[xτD(θ)] dθ (1) X(ω) = FT[x(t)] = H(ω).FT{f NL [x(t)]}.e -iωτ D (2)
In the case of a first order linear differential process with a characteristic response time τ, h(t) is the standard exponential decaying function e -t/τ (for t>0, whereas h(t)=0 elsewhere), and one obtains the usual scalar delay differential equation (DDE):

x(t)+τ (dx)/(dt)=fNL[xτD(t)], (3)
which is the case of the well-known Mackey-Glass [6] and Ikeda dynamics [START_REF] Ikeda | Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system[END_REF].

In the case of a damped oscillator differential process (damping factor m, central oscillating frequency ω 0 =2πF 0 ,), an integro-differential delay equation (iDDE) is found:

(ω 0 /2m) ∫ t 0 t x(θ)dθ+x(t)+(2m/ω 0 )(dx)/(dt)=f NL [xτD(t)], (4)
where two different situations can be typically encountered, the broadband case for strong damping (m>>1), and the narrow band case for small damping (m<<1). In standard nonlinear dynamic analysis, the integro-differential form is often converted into a set of two coupled first order differential equations [START_REF] Larger | Delay dynamics in optoelectronics: fundamental and applications from chaos to fixed point, through limit cycles[END_REF], introducing an additional variable y, e.g. (dy)/(dt)=x.

In the previous modeling, one has to analyze the evolution dynamics with respect to a bifurcation parameter. This parameter is usually the weight of the nonlinear delayed feedback term. It is referred to as β in the previous equations, and it corresponds to a multiplicative factor in the nonlinear function, as illustrated in Fig. 1. In the physical example of Fig. 2, β is adjusted through the electronic gain G, or even more conveniently through the optical power level of the CW laser seeding the electro-optic Mach-Zehnder modulator.

III. BIFURCATIONS AND BEHAVIORS

When β=0, the system is operating in open loop, without any nonlinear delayed feedback, and its behavior is simply the one of the filter represented by its impulse response For stable filters, a stable steady is obtained at the output. As is increased, the autonomous system in Fig. 1 can develop more and more complex solutions, from the stable steady state, to periodic oscillations, experiencing sometimes the well known period doubling route to chaos. Depending on the properties of the filter H(ω), other even more exotic motions can be obtained [START_REF] Larger | Delay dynamics in optoelectronics: fundamental and applications from chaos to fixed point, through limit cycles[END_REF], such as chaotic breather, slow periodic stable solution, and even virtual Chimera states [START_REF] Larger | Virtual chimera states for delayed-feedback systems[END_REF].

The motion complexity in DDE is both issued from the delay, and from the strength of the nonlinear transformation (parameter β). Because of the delay, the phase space dimension is infinite, since the size of the initial conditions required to uniquely define a solution, is not a finite set of values, but an infinite set of x-values corresponding to a functional x(t) for t in [-τD,0]. This represents the filling of the system memory with a particular waveform on a bounded time interval spanning over one delay.

In chaotic regime, the chaotic attractor of an Ikeda DDE is known to be scaled by the quantity β τD/τ. This quantity represents the strength of the nonlinear creation of new frequencies (β), and the number of shortest time scale allowed by the filter bandwidth (1/τD), which can fill the delay time interval.

IV. APPLICATIONS FOR DELAY DYNAMICS SOLUTIONS

A. Optical Chaos Communications

The discover of chaos in optical systems through Ikeda setups or ECLD triggered a lot of attention. When the area of secure communication was proposed as an application of chaos, thanks to the synchronization capability of these motions despite their sensitivity to initial conditions, photonic was rapidly considered as an attractive area where it could be developed. Fiber optical communication could indeed implement in hardware this concept, thus offering physical layer encryption directly operating at the high speed of these communication systems. This was resulting in strong speed related difficulties for any eavesdropper willing to attack the links with computer-based means. Optical chaos communication was then intensively addressed by many groups worldwide. The European consortium of the OCCULT project succeeded first in a field experiment, reaching Gb/s real time encryption and decryption [START_REF] Argyris | Chaos-based communications at high bit rates using commercial fiberoptic links[END_REF], with both an ECLD setup, and an electrooptic intensity setup very similar to the scheme in Fig. 2. Later, our group pushed this record further to 10Gb/s for a single channel, using a novel electro-optical phase chaos generator [START_REF] Lavrov | Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications[END_REF].

B. High spectral purity microwave oscillator

From a completely opposite perspective, instead of the white noise like motion corresponding to the chaotic optical waveform generated a strongly nonlinear (β~5) delay oscillator, the periodic solution of the same electro-optic delay architecture was also considered as an attractive new oscillator topology. These so-called OEOs (optoelectronic oscillators, [START_REF] Yao | High frequency optical subcarrier generator[END_REF]) were found to have, under specific parameter operating conditions, extremely low phase noise, and thus extremely high spectral purity in the Fourier domain (thus opposed to the flat white noise signature of the chaotic motion). Typical applications targeted by these microwave oscillators (from a few GHz to several 10s of GHz) are high resolution Radars, where the frequency multiplied quartz oscillators (10-100 times 100MHz) can not provide such very low phase noise features.

The typical operating conditions of OEOs, from the modeling point of view reported here, are concerned by extremely long delay lines (few km, instead of a few 10s of cm to meters for chaos communication), and very low damping m so that a single delay mode operation can be obtained in the desired microwave range. Although the dimensionality of the dynamics can be expected to be reduced due to the very small bandwidth of the oscillator (since m<<1), the fact that a large delay line is used counterbalances the bandwidth reduction by an also strongly reduced delay mode spacing. The quantity β τD/τ can thus still be potentially high for increased β: one should expect the high spectral purity microwave to be destabilized for some sufficiently large β, which is indeed what our group could demonstrate theoretically, numerically, and experimentally [START_REF] Kouomou | Dynamical instabilities of microwaves generated with optoelectronic oscillators[END_REF], as illustrated in Fig. 4.

C. Brain-inspired photonic computing

Last, but hopefully not least, we could address a third application concerned by another asymptotic solution of a photonic delay dynamics. This asymptotic solution is surprisingly the most simple one, the single stable steady state (for small β; notice bistability of fixed points is here most probably undesired). Its main attractive feature is related to the fact that it provides a generic property of any stable filter, the fading memory: after any perturbation, the transient dynamics necessarily goes back to this steady state, providing a reference initial condition for a later perturbation. Perturbation has to be viewed here as an input information signal u I (t), as represented in the setup of Fig. 2. This input signal triggers a transient from the stable steady state, which role is to embed the input information into the high-dimensional phase space of the nonlinear delay dynamic (high ratios for τD/τ are thus required). A machine learning approach is then involved to extract from this nonlinear transient, through a linear combination of points in the phase space, some hidden information which is expected to be contained in the input signal. This new computational concept is usually referred as to "Reservoir Computing" (originally named Echo State Network, and also Liquid State Machine), and is originating from the neural network computing and brain research communities.

Within a recent EU project PHOCUS, we demonstrated the first Photonic Reservoir Computer [START_REF] Larger | Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing[END_REF][START_REF] Martinenghi | Photonic Nonlinear Transient Computing with Multiple-Delay Wavelength Dynamics[END_REF], with the architecture as depicted in Fig. 2, where the linear Read-Out was extracted from the output signal of the delay dynamics. Spoken digit recognition, as well as time series prediction were successfully demonstrated, moreover with performances close to, or even beyond, the state of the art.

V. CONCLUSION

We have reported on three original applications, cryptography, high spectral purity microwave source for Radars, and brain-inspired computational approach. The understanding of the underlying complexity and highdimensional nonlinear dynamics features allowed to design real-world photonic setups with which the feasibility of breakthrough concepts have been demonstrated. We anticipate that delay dynamics complexity, and its investigation with reliable and efficient photonic setups, will offer even more perspectives of other advanced applications, as it can be illustrated by very recent fundamental results on delay based dynamics, such as Chimera states in delay dynamics [START_REF] Larger | Virtual chimera states for delayed-feedback systems[END_REF], and also modeling of WGM (whispering gallery modes) seeded by a laser light [START_REF] Chembo | Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whisperinggallery-mode resonators[END_REF].

Fig. 1 .

 1 Fig. 1. Signal processing viewpoint of a nonlinear DDE oscillator. Delay is coupled to a linear filter and a nonlinear transformation within a feedback loop. An tunable gain selects the motion complexity.

Fig. 2 .

 2 Fig. 2. Optoelectronic realization of a DDE oscillator, involving an integrated optic Mach-Zehnder modulator. Signal injection into the dynamics, as well as output monitoring is included, as usually of concern in signal processing application.

Fig. 3 .

 3 Fig. 3. 10Gb/s Eye diagrams of experimental chaos communication demonstration. Left: blurred data by optical chaos. Right: decoded data after chaos replication at the receiver side.

Fig. 4 .

 4 Fig. 4. Time (upper) and Fourier (lower, FFT) domain showing the OEO microwave oscillation before (left) and after (right) its destabilization due to an increased enough feedback gain.

Fig. 5 .

 5 Fig. 5. Photonic Reservoir Computer, implemented with an FPGA (Field Programmable Gate Array) card for the post-processing Read-Out.

ACKNOWLEDGMENT

The authors thank the PHOCUS project and the Labex ACTION program for their financial support (FP7-2009-ICT-240763 and ANR-11-LABX-01-01).