Antoine Feuillet

Nicolas Scelles

Christophe Durand

Keywords: mover advantage, second mover disadvantage, bidding process, broadcast packages

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The winner's curse is a well-known phenomenon in economics. It is one of the negative externalities listed in the auction theory, along with collusions or information asymmetries for example. Andreff (2012, p.120) describes that this curse explains "the underlying causes of the winner's disappointment in the bid, due to costs higher than initially planned. " Thaler (1988, p.192) lists two ways where the winner is cursed: "(1) the winning bid exceeds the value of the tract, so the firm loses money; or (2) the value of the tract is less than the expert's estimate so the winning firm is disappointed". Klemperer (2002, p.173) underlines the winner's curse as the situation "when bidders have the same, or close to the same, actual value for a prize, but they have different information about that actual value". According to the author, the threat is for "the party who has most greatly overestimated the value of the prize". A famous example of this asymmetry situation comes from the article of [START_REF] Akerlof | The market for 'lemons': Qualitative uncertainty and the market mechanism[END_REF] about the secondhand automobile market or "market for lemons". Also related to automobile, [START_REF] Bliss | Dragon-slaying and ballroom dancing: The private supply of a public good[END_REF] take the example of the "game of chicken". This game consists of two cars racing towards each other, the loser (chicken) being the first driver to veer off the collision course. As mentioned by the authors, "The longer each driver waits, the smaller is the value from turning as collision is more likely to be inevitable" (Bliss & Nalebuff, 1984, p.3). As such, this situation is likely to generate two 'winners' who will be cursed. This idea that two (or more) winners may be cursed is relevant to situations where several prizes are allocated, as this can be the case on the market for sports broadcasting rights which is the focus of interest in this paper. Andreff (2014, p.24) considers the winner's curse as a "major concept in sports economics". The most frequent cases are the right to host Olympics, the acquisition of superstars but also the purchase of a franchise in North American professional sports or public subsidies in stadia construction [START_REF] Rosentraub | Negotiating Games: Cities, Sports, and the Winner's Curse[END_REF]. For example, the Olympics in Montreal, Athens, Sochi or Rio de Janeiro widely exceeded the anticipated costs ex post. The winner's curse is also found in the race for free agents, for example in baseball [START_REF] Cassing | Implications of the auction mechanism in baseball's free agent draft[END_REF]. The recent case of Mike Conley Jr illustrates this situation in basketball: this 28-year-old player has never been part of All Star selections (best players of the league) and has signed during the summer 2016 the biggest contract in the history of the NBA with the Memphis Grizzlies for $153m over five years. Such a contract is possible because of the competition between teams. In this case, Dallas Mavericks (the only other team Mike Conley Jr met among several other teams interested) was willing to offer the player a big contract so Memphis did their best to outbid their competitor's offer.

In this paper, we focus on another situation related to the winner's curse in sports economics: the bidding for broadcasting rights. In European football, this has hugely increased over the past 25 years. More and more TV channels have been interested in broadcasting football games, leading to a fierce competition favouring the winner's curse. Our objective is to verify whether this has been the case and, if so, what are the exact causes and who have been cursed. A multiple case study [START_REF] Eisenhardt | Building theories from case study research[END_REF][START_REF] Eisenhardt | Better stories and better constructs: The case for rigor and comparative logic[END_REF][START_REF] Vigour | La comparaison dans les sciences sociales : Pratiques et méthodes [Comparison in social sciences : Practices and methods[END_REF][START_REF] Eisenhardt | Theory building from cases: Opportunities and challenges[END_REF]) is used in this paper. It allows us to make a comparative analysis between two European football leagues: the English Premier League (EPL) and the French Ligue 1 (L1). Their two domestic markets (UK and France) are quite similar in terms of population (respectively 65,111,000 and 64,668,000 inhabitants 1 , even if the demographic structure is different 2 ) and Gross Domestic Product (GDP) (respectively 2420 and 2860 billion US$3 ). As such, we will be able to verify whether the situations are quite similar with regards to the winner's curse in these two leagues that have some similarities in terms of domestic market and an 'historic' domestic broadcaster each: Sky (since 1992) for the EPL and Canal Plus (since 1984) for the L1. The winner's curse in the bidding for broadcasting rights has important economic and social implications for fans: pay-TV channels will seek to increase subscription fees to avoid the winner's curse (costs higher for fans who may become not able to afford them) or will be cursed and possibly become insolvent, meaning that fans will lose their access to games without being reimbursed. This is in line with the conclusion of Noll (2007, p.419): "As time progresses, centralization of the sale of television rights in leagues will cause increasing harm to consumers by restricting choice and raising prices". In Europe, the consumer welfare is even more likely to be impacted because of the prevalence of one single sport, namely football [START_REF] Jeanrenaud | The economics of sport and the media[END_REF].

The paper reads as follows. First, the theoretical framework is developed, based on the characteristics of the bidding system and some explanations of why the winner's curse may happen in this system, along with the specificities of the market for sports broadcasting rights and the indices of a winner's curse identified in the literature for this market. Second, the aim is reminded and the methodology is described. Third, results are provided before being discussed in the fourth section. The last section concludes.

Theoretical framework

Bidding system and winner's curse [START_REF] Milgrom | A theory of auctions and competitive bidding[END_REF] describe the bidding system as a very old practice already found in the Babylonian and the Roman civilizations for the slave's market. This method is now used to sell diverse 'goods'. Indeed, listed by [START_REF] Krishna | Auction theory[END_REF], we find bids on markets such as concessions of mines, tobacco, fish, fresh flowers, scrap, golden ingots, bond issues, long-term titles or public goods. The first analysis dealing with the winner's curse comes from [START_REF] Capen | Competitive bidding in high-risk situations[END_REF] who advance this hypothesis to explain the low returns on investments for companies engaged in competitive biddings for oil and gas leases.

The auction theory highlights four main types of bids, derived from Vickrey (1962). Inspired by [START_REF] Klemperer | What Really Matters in Auction Design[END_REF], Table 1 summarizes these four types of bids.

Table 1 A characteristic of the bids which generates high prices for providers is its uncertainty. It lies in the type of information each competitor can find (or not) about the bid, but also for certain types of bids in the amount of the offers proposed by their competitors. A bid based on the "common value" model reflects this uncertainty. In this type of bid, the "value is not known and the bidders thus have to estimate it based on the information they have" (Avenel et al., 2011, p.43). Bidders make offers based on their estimation and capacities. For example, it is the case in the bidding for treasury bonds or for oil [START_REF] Harbord | Market Definition in European Sports Broadcasting and Competition for Sports Broadcasting Rights[END_REF].

The elements above may generate the winner's curse. More specifically, two approaches are listed by De Bornier (n.d.) to explain such a winner's curse, consistent with [START_REF] Thaler | Anomalies: The winner's curse[END_REF]:

• an objective approach, where the price paid is higher that the real value of the good,

• a subjective approach, which corresponds to the frustration felt by the winner who realises that its surplus could have been much higher when comparing the actual amount paid with that proposed by the second bidder. Naegelen (1986, p. 31) notices that this "ambiguity of the literature arises because in practice it is difficult ex post to distinguish what lies in the regret and what characterizes the curse". Table 2 illustrates these two approaches.

Table 2 The winner's curse has been studied in experimental economy. [START_REF] Bazerman | I won the auction but don't want the prize[END_REF] applied the famous jar experiment to verify the phenomenon of winner's curse in common bids. The real value of every jar was $8. Most of players being risk-adverse, the average value estimate was $5.13. The average value of the winning bid was $10.01. The authors, thus, confirmed the existence of the winner's curse. The overestimation of the good would be due to both the uncertainty on its real value and the number of competing bidders, consistent with [START_REF] Capen | Competitive bidding in high-risk situations[END_REF], [START_REF] Klemperer | What Really Matters in Auction Design[END_REF] and [START_REF] Avenel | La malédiction du vainqueur: Peut-on en tenir compte dans l'analyse des effets unilatéraux ? [The winner's curse: Can we take it into account in the analysis of unilateral effects?[END_REF].

First mover advantages, later entrants' disadvantages and war of attrition

The winner's curse applies to situations where there is one winner that overbids for a single product at a specific time without dynamic perspective (e.g. overbidding in t to take advantage of this in t+1). In the market for sports broadcasting rights, some characteristics may question the winner's curse: the existence of packages meaning there might be more than one winner; auctions every three to four years introducing a dynamic perspective; the uncertainty about the real value even for the seller due to the specific nature of professional sports and the complexity of its market (competition between sports and more generally entertainments and leisure, international competition between leagues). Three phenomena appear to be relevant to understand and explain these characteristics: the first mover advantages, the curse of later entrants and the war of attrition.

The first mover advantages correspond to a well-known concept in the economic literature [START_REF] Stackelberg | Marktform und gleichgewicht[END_REF][START_REF] Gal-Or | First mover and second mover advantages[END_REF][START_REF] Lieberman | First-mover advantages[END_REF][START_REF] Lieberman | First-mover (dis)advantages: Retrospective and link with the resource-based view[END_REF]. According to Benzoni (2007, p. 23), this concept "predicts that a firm which is first to enter a new market (early entrant) will accumulate so many advantages that later entrants will have difficulties to compete on equal terms". [START_REF] Benzoni | The "curse of the later entrants": the case of the European mobile markets[END_REF] goes further in presenting a sequential entry model in the mobile network market where the level of profits for the later entrants depends on the timing of their entry in the market.

He also confirms "the existence of later entrants' inherent disadvantages in a fixed-cost industry with fast growing demand. The later a firm enters such a market, the higher its initial investment must be" (Benzoni, 2007, pp. 27-28). This may explain the presence of one 'historic' domestic football broadcaster both in France and the UK (respectively Canal Plus and Sky). Indeed, it might be too difficult for later entrants to find the funding required to compete with the first mover. Benzoni (2007, p. 28) provides additional elements to explain this situation: "As the later entrant cannot spread its investments over several years, it must immediately offer the same quality of service as an early entrant, and will consequently face a financial abyss at entry, leaving it with no room to manoeuvre to develop its commercial strategy". [START_REF] Benzoni | The "curse of the later entrants": the case of the European mobile markets[END_REF] talks about the "curse of later entrants" to characterise such a situation.

Another relevant concept developed by [START_REF] Benzoni | The "curse of the later entrants": the case of the European mobile markets[END_REF] is the war of attrition. This war can take the form of a loss leader strategy on the short term with profits expected on the long term after having discouraged other competitors. Defined by Andreff (2012, p.51): "This strategy is expensive, because it generates negative profits (losses) […]. The stake of the attrition war is to incite the competitor to give up, but the outcome is uncertain". This "theory of predation" completes the "first mover advantages" and, like the latter, can explain that 'historic' broadcasters retain the rights and their competitors leave the market.

Over-valued markets in sport?

The notion of sports bubble is often associated with the purchase of sports broadcasting rights, transfer fees for players, salaries for superstars or the pursuit of relocation (or expansion) by franchises. North American sports leagues offer an example of the situation where a franchise is in a monopoly position when dealing with potential municipalities in an oligopolistic situation to host a team [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF]. Hosting a sports franchise is a factor of prestige for municipalities and franchises use their power of attraction to generate an intense competition between municipalities which can result in overbidding. [START_REF] Noll | Sports, jobs, and taxes: The economic impact of sports teams and stadiums[END_REF] point that new facilities (relocation or expansion often requires building them) do not provide substantial economic development. Andreff (2014, p.14) explains that '' hosting a franchise can create only a negligible positive economic impact, when not negative''. Coates and Humphreys (2006, p.298) suggest that ''net benefits of stadiums and arenas may be highly localized in areas near these facilities''. This is in line with results establishing that properties gain value when they are close to the facilities [START_REF] Coates | Ring around the rose bowl: The spatial economic impact of stadiums and arenas[END_REF][START_REF] Tu | How does a new sports stadium affect housing values? The case of FedEx field[END_REF].

If the relocation of a team alone cannot provide a substantial economic effect [START_REF] Baade | Sports stadiums and area development: A critical review[END_REF][START_REF] Coates | The growth effects of sport franchises, stadia, and arenas[END_REF]Fort, 2006), being part of a broader strategy affecting a specific area of the city can help participate in an economic redevelopment [START_REF] Siegfried | The economics of sports facilities and their communities[END_REF] Despite this, there is little evidence of the "tulip bulb" phenomenon reaching sport. The recent examples of the expansion of the NHL with Las Vegas Golden Knights (price of $500m in 2016) or the future expansion of the MLS (with the franchise team owned by David Beckham in Miami for a price estimated at $25m) illustrate the power of attraction enjoyed by professional sports even if it can be irrational at an economic level for some stakeholders (with the rise in taxes due to new facilities built with public subsidies). If there would be currently a bubble, citizens or consumers would be those that support it rather than private investors that own sports franchises. Such a bubble is not evident given that sports franchise values in North America have constantly risen since the early 1980s [START_REF] Humphreys | Determinants of franchise values in North American professional sports leagues: Evidence from a hedonic price model[END_REF][START_REF] Scelles | Determinants of professional sports firm values in the United States and Europe: A comparison between sports over the period 2004-2011[END_REF].

Structure of the market for sports broadcasting rights

Before focusing on the types of bids and the winner's curse in the market for sports broadcasting rights, the main characteristics of this market need to be provided. [START_REF] Bolotny | Demand for media coverage[END_REF] describe a double market with upstream the primary market (sports programmes) involving broadcasters (supply) and viewers (demand) and downstream the secondary market (broadcasting rights) involving broadcasters (demand now) and sports organizers (supply) (Figure 1). The secondary market is defined by various forms depending on the characteristics of supply and demand. [START_REF] Bourg | Économie politique du sport professionnel : l'éthique à l'épreuve du marché[END_REF] classify them as in Table 3.

Figure 1 Table 3 For the allocation of football broadcasting rights, Andreff (2014, p.15), following Solberg (2006), specifies that the most common procedures are English auction and sealed-first bid, or combinations of them. Sealed-first bid is the method of allocation used for the broadcasting rights in L1 for example. This league relies on the new modalities of sequential bids used by some professional sports leagues which put up for auction several packages. Sequential bids are different from simultaneous bids since after each package won by a bidder, every competitor is informed about who won and the amount paid. However, during the bidding process, the auction is blind like in the UK.

Famous examples of winner's curse already appeared in European football. Andreff (2012) quotes the examples of Kirch Media in Germany4 , Digital ITV which broadcasted the English football Championship and Alpha Digital Synthesis which broadcasted the Greek championship, all going bankrupt in 2002. The same happened to Telepiu and Stream in Italia. These bankruptcies caused major problems where they happened [START_REF] Solberg | European club football: why enormous revenues are not enough[END_REF]. The main consequences are financial for the clubs. Indeed, the failure of a broadcaster threatens clubs' revenues. 30 English clubs were in trouble in 2002 when Digital ITV began to struggle before another channel (Sky) made a deal to recover the rights 5 . The bankruptcy of Kirch Media is a bit different, because of the emergency fund guaranteed by the German government 6 . In addition to the clubs, consumers are also affected by bankruptcies. Indeed, the product they buy can be depreciated with the risk of insolvency for some teams (Scelles, Szymanski & Dermit-Richard, 2017;[START_REF] Szymanski | Entry into exit: Insolvency in English professional football[END_REF] and the potential departures of star players during the season.

Indices of a winner's curse in the market for sports broadcasting rights

Beyond the illustrations above, it is necessary to identify some indices of a winner's curse in the market for sports broadcasting rights to answer the aim of this paper. Andreff (2014, p.7) claims that "A major difficulty with the winner's curse concept consists in testing its very existence". Regarding the market for sports broadcasting rights, Andreff (2014, p.18) identifies six indices, some of them being supported by other authors: 1) A very swift increase in TV rights fees on a same sporting event from one broadcasting contract to the next one.

2) Financial loss endured by a TV company on a broadcast deal: income derived from televising a sporting event do not cover sunk costs of producing the broadcast, including those rights paid after outbidding competing TV. This is supported by [START_REF] Harry | TV Sports Viewers -Who Are They? A Norwegian Case Study[END_REF] who highlight that quite a number of sports rights deals have ended up being unprofitable for the TV network.

3) A post-bid bankruptcy which exhibits ex post that a TV channel could not afford the bid which it won due to overoptimistic valuation. This is supported by [START_REF] Buraimo | 10 The demand for sports broadcasting[END_REF] who refers to ITV Digital as a case where the winning TV channel is so much cursed that it goes bankrupt. 4) Too many unknown and uncertain details about the date, the place and the participants (qualified teams and athletes) of a sporting event which falls adrift into unexpectedly low broadcast revenues and excessive costs ending up in a loss. These unknown and uncertain details lead the most optimistic highest bidder to win and be cursed [START_REF] Fort | Sports economics[END_REF]. As underlined by [START_REF] Gratton | The economics of sports broadcasting[END_REF], the winner's problem is that he realises this too late. 5) Outbidding newcomers which enter the broadcast market for a given sporting event increase aggressive competition on the demand side and thus make the winner's curse more likely to happen. This is supported by Scelles and Dermit-Richard ( 2016) who find a positive correlation between competition and the amount of TV rights. 6) TV rights re-packaging, in reducing the number of products on sale in the face of a given number of TV channels leads to increased competition that triggers TV rights fees inflation and thus a greater likelihood of the winner's curse. This might be questioned.

Supposing both fewer packages and the same number of bidders might be not realistic because some TV channels might be discouraged to bid due to their insufficient financial resources. As such, it might be the case that re-packaging does not trigger TV rights fees inflation due to fewer TV channels interested and does not lead to a greater probability of the winner's curse.

More generally, the six indices identified by [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF] need to be verified with empirical data. They may also need to be organised in a more logical manner as one would expect that bankruptcy will be the consequence of the other indices and, as such, appears after them in the list. Besides, a seventh index not listed by Andreff ( 2014) is relative to disappointment, which is a central element in the definition of the winner's curse. Disappointment may be the consequence of costs higher than expected ex post [START_REF] Gratton | The economics of sports broadcasting[END_REF] or insufficient returns, due for example to fluctuations in the supply side for advertising [START_REF] Roger | Sports Economics[END_REF].

Aim and methodology

The main aim of this article is to verify the existence of a winner's curse in the domestic markets for broadcasting rights of the French and English football leagues. The underlying objective is to assess whether some indices of this situation are confirmed and can cause a winner's curse.

We rely on the six indices identified by [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF] We have reorganised the order provided by [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF] based on the following assumptions: on the expenditure side, I1 (increase in TV rights) might be explained by I2 (outbidding newcomers) that might be explained by I3 (TV rights repackaging); on the financial side, I4 (unknown and uncertain details) might explain I5 (financial losses) that might explain I6 (bankruptcy) and/or I7 (disappointment). When dealing with I2, we first attempt to verify that outbidding newcomers increase aggressive competition before observing whether this makes the winner's curse more likely to happen; when dealing with I4, we focus only on the existence of unknown and uncertain details and not on their financial consequences since the latter are redundant with I5 (financial losses).

Eventually, the methodology consists in verifying:

(1) the seven indices for the French and English football leagues in their respective domestic markets over the period 1980-2020;

(2) that they led to a winner's curse; and

(3) whether the winners cursed are the main winner (main package), a secondary winner (secondary package) or both ('game of chicken').

Multiple sources are used for the data collection: public reports Ofcom Summary of UK sports rights and Sky annual report (2015,2016) for the UK case; DNCG 7 , CSA (2001), Senat (1996) and [START_REF] Eveno | La télévision entre politique et marché[END_REF] for the French case; and Transfermarkt for player transfers. When another source is used, it is explicitly mentioned.

Results

Very swift increase in TV rights?

We analyse the increase rate from one contract to the next one for the EPL and L1 TV rights respectively in the UK and in France. The problem is to determine what a very swift increase is: +50%? +100 %? Figure 2 shows the evolution of TV rights fees (in euros) to provide an idea about the amounts at stake. Figure 3 is largely supportive of the hypothesis of a very swift increase in TV rights, both for the EPL and the L1 (I1 confirmed). In England, out of 12 variations, 9 increase rates are above 50% (75%), among which 5 are above 100% (42%). In France, out of 22 variations, 8 increase rates are above 50% (36%), among which 5 are above 100% (23%) as for England. Given that more variations (France compared to England) reduce the likelihood of reaching an increase rate of at least 50% for each of them (i.e. it is easier to reach 75% of its increase rates above 50% when there are mainly three to five years between each contract as for England rather than 16 annual variations as for France), we can consider that England and France present a quite similar pattern.

Nevertheless, France has not enjoyed an increase rate above 20% since 2005-2006 (TV rights are negotiated for three to four years since then) whereas three of the last four variation rates have been above 50% for England.

Outbidding newcomers?

In the UK, BBC and ITV cooperated to share coverage rather than compete against each other until 1988, when ITV pushed up the annual fee to £11m in 1988-1992 for its exclusive coverage [START_REF] Gratton | The economics of sports broadcasting[END_REF] 4).

Table 4

In France, Canal+ initially enjoyed a monopoly for the Ligue 1. Its first serious rival was TPS in 1999 which stopped its exclusive coverage. However, Canal+ recovered its exclusivity for the 2005-2008 period. Then, TPS struggled until Canal+ absorbed its competitor. For the 2008-2012 period, Orange obtained three packages before giving up at the end of the contract due to a different strategy adopted by its new CEO9 . To avoid that Canal+ became again the only broadcaster, the president of the LFP Frédéric Thiriez launched in 2011 CFoot, a channel belonging to the league and broadcasting the Ligue 2. The channel stopped less than one year later with only 300,000 subscribers and €15m losses10 .

The last major competitor for Canal+ is BeIN Sports (formerly Al Jazeera Sport) (Table 5). They obtained some packages both for the 2012-2016 and 2016-2020 contracts.

Natixis11 estimated that their cumulated operating deficit will reach €2.2bn for the 2012-2020 period. Their cumulated losses were already €1bn by the end of 201512 .

Eventually, both for the EPL and the L1, outbidding newcomers regularly appeared and increased competition (I2 confirmed).

Table 5

TV rights re-packaging for a given sporting event

In the UK, TV sports rights packaging had been impacted by several interventions from the competition authority. The trend is to have more and more premium live packages to enhance competition and allow more broadcasters to be part of the market. Nowadays, there are seven "premium" packages in the Premier League Figure 5 Eventually, there is no evidence of a link between repackaging and a potential winner's curse (I3 not confirmed). Correlation coefficients between TV rights and number of packages are rather supportive of more packages leading to increased TV rights both in the UK and France even if the limited number of observations means that some caution is required before drawing conclusions. The broader broadcasting market context can be viewed as a variable that impacts the influence of the number of at http://www.lemonde.fr/sport/article/2008/02/07/canal-et-orange-se-partagent-les-droitstelevisuels-du-football_1008332_3242.html 15 Mediasportif (2015) Droits TV -5 diffuseurs se sont positionnés sur les droits de la ligue 1 et de ligue 2 [TV rights -5 diffusers positioned on the rights of the ligue 1 and the ligue 2] Available at http://www.mediasportif.fr/2014/04/02/droits-tv-5-diffuseurs-se-sontpositionnes-sur-les-droits-la-ligue1-et-ligue2/ packages on TV rights. Moreover, there may be other extraneous variables explaining the strong correlation coefficients above.

Unknown and uncertain details?

Regarding the EPL and L1, unknown and uncertain details are about teams and players. They may impact the quality of live games if they relate to the best teams and players. It is scarce that the best teams are relegated at a lower level. This was the case for Marseille in France in 1994-1995and 1995-1996. Canal . Canal Plus profits were lower during these two seasons than in 1993-1994and 1996-1997 (Figure 6 (Figure 6). Nevertheless, it is difficult to establish a relationship between the two events (absence of Marseille and decrease in profits for Canal Plus). To deal with uncertainty about players taking part in the league, a perspective not discussed yet seems fruitful: the indirect competition between Sky and Canal Plus. The idea is that the TV rights offered by the two channels are a main source of income for clubs that is mainly spent in players. As such, a larger amount spent by one channel compared to the other provides a greater likelihood that clubs playing in the league associated to the former attracts better players, including those from the league associated to the latter. This is even more likely since the Bosman case of 1995 reducing the constraints on the number of players from the European Union per club.

Figure 6 Figure 1 shows that, most of the time, the domestic TV rights have been higher for the EPL than L1. The potential impact on spending for players has been amplified by TV rights shared with Ligue 2 clubs in France, international TV rights far higher for the EPL than L1 and English clubs generating more revenues from other sources than French clubs (Scelles & Dermit-Richard, 2016), meaning more overall revenues in EPL than in L1 (Figure 7). Even when Canal Plus spent €600m per year over the 2005-2008 period, French clubs were not able to attract or even retain their best players, e.g. Lyon losing Essien (Chelsea) in 2005, Diarra (Real Madrid) in 2006, and Abidal (FC Barcelona), Malouda (Chelsea) and Tiago (Juventus FC) in 2007. This has become even harder for French clubs since 2007 with the continual growth of the EPL TV rights, relying in particular on Sky's expenditure. Some of the best players having operated in L1 since then moved to the EPL 16 . Over the most recent period, Table 6 and 7 confirm that the EPL attracts the best players from L1 while the contrary is not true 17 . These elements illustrate the uncertainty about players taking part in the competition, while stars have been identified as a key determinant of TV audience in the EPL [START_REF] Buraimo | Uncertainty of outcome or star quality? Television audience demand for English Premier League football[END_REF][START_REF] Scelles | Star quality and competitive balance? Television audience demand for English Premier League football reconsidered[END_REF]. Nevertheless, financial data for Canal Plus (Figure 6) is not supportive of this uncertainty leading to unexpectedly low broadcast revenues and high costs ending up in a loss (I4 not confirmed). An explanation may be that despite the best players leaving the French Ligue 1, its level remains at a sufficiently good standard and/or TV viewers have a sufficiently strong identification to French clubs.

Another explanation may be a sufficiently high number of known and certain details about the dates, the places and the participants due to a relative inertia from one period to another.

Figure 7 Table 6 Table 7 Financial loss endured?

According to the elements developed in the previous subsection, Sky might have developed a financial advantage due to the EPL attracting the best French players (among others). However, Sky might have spent too much to attract the best players (and has not fully achieved this since Messi, Ronaldo, Neymar and even the British Bale do not play in the EPL) compared to the real increase in TV audiences and thus subscription fees they generate. As such, it might be the case that Sky has endured some financial losses, consistent with the winner's curse. Figure 8 shows the evolution of Sky's expenditure for the EPL TV rights and its profit. contract when securing the 2004-2007 contract. Indeed, due to the absence of competitors, it could spend less money in TV rights. A short-term strategy of losses could be a long-term strategy for profits or a "loss-leader strategy with the investments 18 Moreover, we must be cautious about the timing of the amortisation of the TV rights: "The amortisation of an intangible asset begins when the asset is available for use, and is charged to the income statement through operating expense over the asset's useful economic life in order to match the expected pattern of consumption of future economic benefits embodied in the asset" (Sky plc annual report, 2015, p.89). TV rights are amortised when they are made available to clubs (e.g. TV rights for 2016-2017 amortised in 2016-2017 and not before as they begin to be available in July and not before).

planned to be profitable in the long run-for example, by forcing rivals out of the market" (Hammervold & Solberg, 2006, p.148). This is consistent with the elements developed in the theoretical framework about the war of attrition. Figure 6 shows the evolution of Canal Plus expenditure for the L1 TV rights and its profit. As for Sky, some caution should be taken when discussing the relationship between both indicators since Canal Plus does not rely on L1 broadcasting only. It seems that the swift increase in TV rights provided by Canal Plus in 1999-2000 has durably reduced its profit. Nevertheless, the company has always made a profit since then. As such, the hypothesis of a winner's curse for Canal Plus is not supported, consistent with the case of Sky but contrary to the idea that the indirect competition between the two broadcasters might have generated financial losses for Canal Plus. It is likely that Canal Plus could make an extra profit until 1998-1999 due to the absence of competition, which is characteristic of a 'winner's blessing' instead. The 2005The -2008 contracts could have led to a winner's curse for Canal Plus. Nevertheless, it allowed the channel to 'destroy' competition (Canal Plus eventually absorbed its competitor TPS) without damaging its profit and to reduce its offer for the following deals.

Both the cases of Sky and Canal Plus are not supportive of the winner's curse.

Even without having access to their annual profits, their long presence in the market might have been interpreted as the absence of persistent losses, assuming in this case that they would have left the market. As described by Harrison and List (2008, p.823), "It is plausible to assume that survival in the industry as a leader provides sufficient evidence that they do not make persistent losses in their natural market setting". Sky and Canal Plus have enjoyed a long-term overall profitability of their networks from market domination, this profitability supporting the increasing transfer fees paid for players and the rising cost of acquisition of sport assets (broadcast networks and clubs themselves) over time (Scelles et al., 2016). They relate to the long-term returns from securing the long-term benefits of extended contracts. However, the fact that Sky and Canal Plus did not suffer from the winner's curse does not mean that there was not a curse for the winner of specific packages, as exemplified by the cases mentioned in the subsection 'Outbidding newcomers?' that are summarised in Table 8. These examples confirmed the existence of financial losses for some broadcasters (I5 confirmed).

Table 8

Post-bid bankruptcy?

Over the 2007-2010 period, the Irish television station Setanta secured two EPL packages consisting of 46 live games per year at a total cost of £392m, or £131m per year [START_REF] Gratton | The Global Economics of Sport[END_REF]. Industry experts believed that Setanta UK needed 1.9 million curse that results in numerous bankruptcies". In addition, the winner's curse for inexperienced bidders has been proven to be particularly "robust" in laboratory experiments [START_REF] Harrison | Naturally occurring markets and exogenous laboratory experiments: A case study of the winner's curse[END_REF].

Disappointment?

Winner's disappointment is an indication of a winner's curse according to [START_REF] Thaler | Anomalies: The winner's curse[END_REF] and Andreff (2012). Leaving the market can be interpreted as disappointment, even more if it is associated with losses. This situation happened frequently in the market for broadcasting rights in English and French football where the two historic broadcasters remain in place while other broadcasters follow one another, mostly for secondary packages. Nonetheless, exiting the market is not enough of a prove to consider that a broadcaster is disappointed. Comments made by executives and spokespersons of broadcast companies can reveal such a disappointment. Therefore, we looked at the comments made by executives and spokespersons of broadcasters that left the market, especially those associated with losses.

For example, Stéphane Richard, CEO of France Telecom (Orange), said in 2010: "Considering our experience, if I had to make the decision tomorrow to renew the rights for football for 203 million euros a year, I would not make it. 25 " This informs about the disappointment felt by Orange after having acquired the rights in 2008. Orange owned one of the three premium packages (Saturday 9pm prime time, 38 games plus V.O.D 26 highlights of every game). S. Richard recently added that: "The problem with the development of a proprietary offering in sport it that, every four years, you can lose of the programs that make your attractiveness or you can see the price double. The business of sports rights is too volatile and speculative for us" 27 .

Following the bankruptcy of Setanta's UK division, a spokesperson for ITN (producer) said: "We are extremely disappointed by the news that Setanta has today gone into administration and will cease trading"28 . Such comments in both countries confirm the disappointment felt by some broadcasters (I7 confirmed).

Discussion

Our results support four indices provided by [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF] and I7 (disappointment), but not I3 (TV rights repackaging leading to increased competition) and I4 (unknown 26 Video on demand. 27 Les Echos (2017) Stéphane Richard : « Les télécoms doivent devenir multiservices ».

Available at: https://www.lesechos.fr/28/09/2017/lesechos.fr/030634281924_stephanerichard----les-telecoms-doivent-devenir-multiservices-.htm# and uncertain details leading to revenues lower than expected and financial losses) (step 1 in our methodology partially verified). They led to 'a' winner's curse (step 2 verified) but not to 'the' winner's curse. Indeed, broadcasters that have been cursed are not Sky and Canal Plus which always win the best packages but rather those broadcasters which won secondary packages (answer to step 3). The economic theory can help explain these results.

Horizontal and vertical integration

Some economic phenomena can be considered as the consequences or at least be to a sort of blessing or curse such as first mover advantages, the curse of later entrants and war of attrition described in the theoretical framework. Some others not developed in the latter can also be highlighted. For example, horizontal and vertical integration did happen in the industry. In France, some illustrations are the absorption of TPS by Canal Plus (horizontal integration) and the latter being shareholder of Paris Saint-Germain from 1991 to 2006 (vertical integration). It might be argued that the latter is an illustration of an advantage the first mover may have. Indeed, Canal Plus was able to invest in Paris Saint-Germain thanks to its very good start from the end of 1984 (when the TV channel was born) to 1991. This is characterised by the following economic data: turnover from €82.6m in 1985 to €938.6m in 1991€938.6m in and profit from -€50.3m in 1985€938.6m in to €164.8m in 1991€938.6m in (Quélin, 2000)). This may be explained by the exclusivity for broadcasting French football. Investing in Paris Saint-Germain was supposed to enable Canal Plus to build a strong competitor for Olympique de Marseille, of which the increasing domination threatened the interest of the championship (decreasing outcome uncertainty); to increase the attractiveness of Paris Saint-Germain which represents a strong market (Paris); and to reduce unknown and uncertain details in controlling Paris Saint-Germain, decreasing the impact of a clue identified as inducing the winner's curse by [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF]. A similar situation can be identified today with the relationship between BeIN Sports and Paris Saint-Germain. In the UK, Sky attempted a similar vertical integration over Manchester United in 1999 but this was blocked by the UK Government on the recommendation of the Monopolies and Mergers Commission [START_REF] Gerrard | Media ownership of pro sports teams: Who are the winners and the losers[END_REF].

Coming back to horizontal integration, about it is worth noting the recent failed agreement of distribution between Canal Plus and BeIN Sports after the decision of the French antitrust authority not to allow it. Cases of horizontal integration are not specific to French football in Europe. In Italy, Telepiu (loss of around 1.645 billion euros) and Stream (loss of around 595 million euros) merged into Sky Italia in 2003 (Solberg, 2006). In Spain, three competitors merged into Sogecable, known as PRISA TV today.

Impact on consumer welfare

A consequence of the race for the rights is the impact on consumer welfare. History has shown that competition authorities made many interventions on this market to prevent monopoly situations or at least limit them. However, broadcasters are not the only actors to be cursed. Indeed, Seamus Coffey (then Butler, 2015) explained in 2009 the situation of Sky and Setanta as "two monopolies are worse than one" when describing the annual cost to watch every single game for the consumer, based on monthly and fixed costs: It is paradoxical to see that competition leads to a raise of the cost for the consumer in this market where two channels cannot broadcast the same game. In the UK, a rule prevents a broadcaster to retain more than five out of seven packages for broadcasting rights. This may be the reason why there are currently two monopolies in the market (Sky and BT Sport). Nevertheless, the consumer may not be cursed if he only subscribes to the broadcasters that won the 'premium' packages, a sensible hypothesis given that fans prefer to watch the best teams [START_REF] Buraimo | Uncertainty of outcome or star quality? Television audience demand for English Premier League football[END_REF][START_REF] Scelles | Star quality and competitive balance? Television audience demand for English Premier League football reconsidered[END_REF]. In a situation with two main broadcasters, the consumer may be blessed if he chooses to watch the best teams and cursed if he wants to watch every single game broadcast. This might be a direction for further research.

It might also be the case that with two broadcasters, the owner of the premium packages may be able to reduce the cost of subscription for consumers as it pays less money for the rights than in a situation of exclusivity. As such, it may attract more subscribers and be able to make profits. On the contrary, the owner of the other packages may not be able to sell enough subscriptions to be profitable. This would fit with our results showing that the second mover is the one who is cursed.

(2009), managing director of strategy at BT Retail at the time of Setanta's bankruptcy, there is a market failure in pay-TV in the UK and this "gives rise to significant harm to consumers in the form of higher prices, restricted choices and diminished innovation." 30 Interestingly, Sky and BT agreed a deal allowing their respective customers to get access to the other network's channels in December 2017 [START_REF] Sweney | BT customers get to binge on Game of Thrones after landmark Sky deal[END_REF]. This may be a way to avoid the winner's and customers' curse.

It is also important to mention the 'no-single buyer' rule that prevents one channel to acquire all packages in the bidding process. A European Commission decision made in 2006 about the EPL aimed to enhance competition by establishing that a minimum of two broadcasters must own rights of live broadcasting 31 . The problem of this kind of decision is that broadcasters can adopt an illegal agreement behaviour as it happened in Italy between Sky Italia and Mediaset where the 'no-single buyer' rule is also in force. On one hand, this rule can help enhance competition between broadcasters and thus generate a growth in TV rights (e.g. Bundesliga TV rights over the 2018-2021 period). On the other hand, this regulation can affect consumer welfare as "it penalises 30 BBC (2009). Setanta goes into administration. Available at http://news.bbc.co.uk/1/hi/business/8115360.stm 31 European Commission (2006). Competition: Commission makes commitments from FA Premier League legally binding. Available at http://europa.eu/rapid/press-release_IP-06-356_en.htm?locale=en consumers in an almost comical way. It is essentially a remedy that requires football fans to subscribe to two different television services to have full access to the televised games of the championship" (Ibanez Colomo, 2016) 32 . This question the relevance of the 'no-single buyer' rule which is also doubtful for the broadcaster who wins the 'second' package or a set of packages.

Conclusion

The winner's curse is difficult to be clearly identified but a range of indices can enable to evidence its presence [START_REF] Andreff | The Winner's Curse in Sports Economics[END_REF]. The historic broadcasters in the EPL and L1 (respectively Sky and Canal Plus) have not suffered from the winner's curse and they have probably even been blessed at some times, especially in monopoly situation. The second mover in the market for broadcasting rights has been identified as more exposed to the curse. These conclusions are consistent with the economic concepts of "first mover advantages" and "curse of later entrants". Disappointment felt by the winner is a main indicator of a winner's curse according to [START_REF] Thaler | Anomalies: The winner's curse[END_REF] and Andreff (2012), and as such has been added to Andreff (2014)'s indices. Leaving the market can be interpreted as disappointment, even more if it is associated with losses. This situation happened frequently in the market for broadcasting rights in English and French football. Nevertheless, losses on a specific market like that for football TV rights can also be part of a broader strategy. Football rights which are often associated with large TV audiences can constitute a 'drawing card' for broadcasters to attract a mass of subscribers and make profits on other products or with the overall price of the subscription that goes beyond football broadcasting. Costly investments in sports can be viewed as a necessity to promote other programmes that are more profitable. Recent losses in pay-TV subscribers33 can be related to the decrease in these additional programmes where companies make profits by using cross-marketing offerings. Further research may focus on the role of football broadcasting rights in the broader strategy of a TV channel. It may also investigate more in depth the evolution of the costs for TV viewers compared to that of their living standard. As for the second mover in the market for football broadcasting rights, they may be cursed. Beyond football, it may be worth investigating Olympic broadcasting rights, characterised by the rise of streaming activities by the main networks, to establish whether the indices tested in football are confirmed in another sports broadcasting market.

1

  Unesco, 2016. UIS Statistics, Total population, http://data.uis.unesco.org/Index.aspx 2 Baudelle Guy. 2002. Deux systèmes urbains ? Une comparaison hiérarchique de la croissance urbaine de part et d'autre de la Manche [Two urban systems? A hierarchical comparison of the urban growth on both sides of the Channel] (1960-1990). In: L'information géographique, volume 66, n°1, pp. 70-80.

  and disappointment: a) The very swift increase in TV rights fees (I1) is investigated by comparing the evolution and the annual increase in domestic TV rights. b) For outbidding newcomers (I2), domestic broadcasters are listed for both countries since the early 1980s with an analysis of the consequence of their entry in the market. c) For TV rights repackaging (I3), we examine the evolution of the national TV rights in relation to the number of packages since the 1980s. d) For unknown and uncertain details (I4), the evolution of expenditure related to both domestic leagues is analysed together with the level of profits for historic broadcasters Sky and Canal Plus. Moreover, player moves between those two leagues are taken into consideration. e) Financial losses (I5) are investigated for broadcasters of the English and French football leagues other than Sky and Canal Plus. f) For post-bid bankruptcy (I6), we focus on the case of the EPL broadcaster Setanta. g) For winner's disappointment related to the underestimation of the costs and/or overestimation of the return (ex post real value lower than expected) (I7), we look at media interviews of representatives having purchased broadcasting rights in France and the UK.

Figure 2 Figure 3

 23 Figure2

Figure 3 7

 3 Figure 3

  . Sky enjoyed then an exclusive coverage for 15 years and even a monopoly after securing the 2001-2004 deal, leading to a decrease in the price it paid for the 2004-2007 rights. During the life of the latter, the European Commission insisted that at least one of the packages offered for the 2007-2010 period went to a different broadcaster. Setanta, an Irish channel, invested in the Premier League but failed to attract enough subscribers to be viable and was unable to pay what they signed for in 2009. Then, ESPN UK acquired the rights that Setanta gave up (for 2009-2010 but also 2010-2013) before BT entered the market and has become a serious rival for Sky since then (Table

(

  only one from 1992 to 2001 and two from 2001 to 2007 13 ), and one broadcaster cannot have more than five live packages. Figure4suggests a positive correlation between TV rights and number of packages which is confirmed by the calculation of the Spearman correlation coefficient between them (0.88, significant at the 1% level; Spearman correlation due to data being not normal according to the Shapiro-Wilk test both for the number of packages and the amount of TV rights).

Figure 4 In

 4 Figure 4

  16 E.g. Nasri from Marseille to Arsenal in 2008; Chamakh from Bordeaux and Koscielny from Lorient both to Arsenal in 2010; Gervinho and Cabaye from Lille to Arsenal and Newcastle respectively in 2011; Hazard from Lille to Chelsea, Giroud from Montpellier to Arsenal and Lloris from Lyon to Tottenham in 2012; André Ayew and Payet from Marseille to Swansea and West Ham respectively, Martial from Monaco to Manchester United and Kanté from Caen to Leicester in 2015; and Ibrahimović and David Luiz from Paris to Manchester United and Chelsea respectively in 2016. Star moves from the EPL to L1 are much scarce and exclusively to Paris since the Qatari era (begun in 2011-2012), with David Luiz from Chelsea in 2014 (back there in 2016) and Di Maria from Manchester United in 2015.17 See Appendix 1 for details about the players involved.

Figure 8

 8 Figure 8

  Sky suffered again in 2007-2008 after having faced the competition from Setanta for the 2007-2010 contracts. Since then, Sky has always made a profit, despite the competition from BT since the 2013-2016 deal. The evolution of Sky's profit does not support the hypothesis of a winner's curse for the company.

( 2009 )

 2009 Sky without competitor: 12 x €30 + €80 = €440.Sky and Setanta: 12 x €30 + 12 x €18 = €576.(2014) Sky and BT Sports: 600€.

FiguresFigure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7

 1234567 Figures

Table 1

 1 Evolution of expenditure for the EPL TV rights and profit for Sky (in €m) Four types of bids and their modalities

	600
	500			Expenditure
	400			Profit
	300
	200
	100
	0
	-100
	84-85	85-86	86-87	87-88	88-89	89-90	90-91	91-92	92-93	93-94	94-95	95-96	96-97	97-98	98-99	99-00	00-01	01-02	02-03	03-04	04-05	05-06	06-07	07-08	08-09	09-10	10-11	11-12	12-13	13-14	14-15

Type of bid Modality of the bid

	English	Ascending
	Dutch	Descending
	Sealed-first	The highest offer takes it and pays what he has offered
	Sealed-second	The highest offer takes it and pays the highest second offer

Table 2

 2 Illustrations of the objective and subjective approaches

		Objective approach Subjective approach
	EV (estimated value)	120	120
	B (bid)	100	100
	RV (real value)	80	110
	Π e (expected profit) 20 (EV-B=120-100)	20 (EV-B=120-100)

Table 3

 3 Market, supply and demand in sports events broadcasting

	Market	Events	Supply	Demand
	Monopoly	Olympics Winter 2010	IOC	ABC, CBS, FOX, NBC,
		Summer 2012		EPSN, TBS, CNN Sport,
				HBO, Direct TV,
				Newsport, Showtime
			FIFA	ABC, Cable TV, UER,
		Football World Cup 2006		Team AG, Kirch ISL,
				IMG-UFA, CWL
	Supply-side	European Football	UEFA	UER, Kirch, Team AG,
	monopoly	Championship 2004		Octagon
		French football championship	League	France Télévision, TF1,
		2006/2007		Canal Plus, TPS, M6
	Bilateral	European Football	UEFA	UER
	monopoly	Championship 1984
	Oligopsony Baseball championship 1960	Professional	ABC, CBS, NBC
			teams
	Monopsony French football championship	Professional	ORTF
		1973/1974	teams

Table 4

 4 Domestic broadcasters of the English Premier League since 1983

	Period	Channels
	1983-1988	BBC, ITV
	1988-1992	ITV
	1992-2007	Sky
	2007-2009	Sky, Setanta
	2009-2013	Sky, ESPN
	2013-2019	Sky, BT

Table 5

 5 Domestic broadcasters of the French Ligue 1 since 1984

	Period	Channels

Table 6

 6 Player moves between the English Premier League and the French Ligue 1 in

	2014, 2015 and 2016
	L1 to EPL	Name	Type of	Fees in £m (if
			transactions	transfer)
		Cabella	transfer	9
		Origi	transfer	11.35
		Amalfitano	transfer	0.9
		Stambouli	transfer	5.31
	2014	Ospina	transfer	3.60
		Ecuele Manga	transfer	5.67
		Riviere	transfer	5.69
		Falcao	loan
		Gomis	free
		Cabaye	transfer	12.51
		Gueye	transfer	8.10
		Amavi	transfer	9.90
		Ayew	transfer	10.80
		Veretout	transfer	9
		Kante	transfer	8.10
		Gradel	transfer	9
	2015	Njie	transfer	12.69
		Djilobodji	transfer	2.7
		Payet	transfer	13.50
		Martial	transfer	54
		Thauvin	transfer	16.52
		Tabanou	transfer	4.41
		Sylla	transfer	1.35
		Falcao	loan
		Toivonen	loan

Source

: Transfermarkt.co.uk

Table 7

 7 Player moves between the EPL and the L1 in 2014, 2015 and 2016Table 8 Financial losses for broadcasters of the English and French football leagues other than Sky and Canal Plus Les Echos (2012). Orange continue à perdre de l'argent dans la télévision. Available at http://www.lesechos.fr/31/12/2012/LesEchos/21344-081-ECH_orange-continue-a-perdrede-l-argent-dans-la-television.htm 35 L`Express (2012). CFoot victime collatérale d`Al Jazeera. Available at http://www.lexpress.fr/actualite/sport/football/cfoot-victime-collaterale-d-al-jazeera_1077829.html 36 Ecofoot (2015). Beinsport condamné à être déficitaire ? Available at http://www.latribune.fr/actualites/economie/france/20150126trib7b3b3ae64/bein-sports-

	England	France
	Setanta, losses of	Orange, overall losses with their
	£100m a year, 2007-	movie channel of €120m in
	2009	2011 34
		CFoot, loss of €15m in 2012 35
		BeIN Sports, losses of €200m
		per year, 2012-2015 36

34

Unesco, 2015. UIS Statistics, GDP Current US$, http://data.uis.unesco.org/Index.aspx

Kirchmedia went bankrupt with 2, 1 billion euros of debt after acquiring rights for football World cup of 2002 in South Korea & and of 2006 in Germany. L'Obs (2002) Médias : la faillite pour le géant Kirch, Available at http://tempsreel.nouvelobs.com/economie/20020408.OBS4648/medias-la-faillite-pour-le-geantkirch.html

5 Born, Matt, 2002, Sky throws £95m lifeline to football clubs, Telegraph. Available at http://www.telegraph.co.uk/news/uknews/1400516/Sky-throws-95m-lifeline-to-footballclubs

.html 6 Gibson, Owen, 2002, Germany to rescue clubs if Kirch folds, The Guardian, Available at https://www.theguardian.com/media/2002/apr/04/broadcasting.citynews

In France, Figure3shows annual increase rates equal to 0% from1988-1989 to 1991-1992. Nevertheless, it must be noted that this is based on estimated rather than actual amounts.

Ozap (2010). Officiel : Orange ne diffusera plus la Ligue 1 après 2012 [Official: Orange will not broadcast anymore the Ligue 1 after 2012]. Available at http://www.ozap.com/actu/orange-diffusera-ligue-2012-droits-canal/362544

La Tribune (2012). CFoot victime collatérale d'Al Jazeera [CFoot Al Jazeera's collateral victim] Available at http://www.lexpress.fr/actualite/sport/football/cfoot-victimecollaterale-d-al-jazeera_1077829.html

11Ecofoot (2015). Beinsport condamné à être déficitaire ? [Beinsport condamné à être déficitaire ?] Available at http://www.latribune.fr/actualites/economie/france/20150126trib7b3b3ae64/bein-sportscondamne-a-etre-

deficitaire.html 12 Nokovitch, S. (2016, 14 December). Le milliard qui fait peur [Le milliard qui fait peur]. L'Equipe.

Douglas, T. (1999, 12 March). Murdoch's rise to the top. BBC. Available at http://news.bbc.co.uk/1/hi/special_report/1999/03/99/murdochs_big_match/167937.stm

Challenges (2010) INTERVIEW DE... -"France Télécom doit se remobiliser". Available at https://www.challenges.fr/entreprise/interview-de-france-telecom-doit-se-remobiliser_359170

The Guardian (2009) Setanta goes off air with loss of more than 200 jobs, Available at https://www.theguardian.com/media/2009/jun/23/setanta-goes-into-administration

Chillingcompetition (2016). Football, TV rights and the 'single buyer rule': In a world of commitment decisions, bad policy dies hard.

Spangler, Todd (2017) Pay-TV Losses Could Accelerate to More Than 5 Million U.S. Households per Year, Survey Indicates, Variety, http://variety.com/2017/digital/news/paytv-losses-cord-cutting-rbc-survey-1202565269/

Overview on the market for broadcasting rights

The development of football TV rights is supported by two groups of stakeholders who are at risk to suffer from its development:

• Broadcasters if it occurs that they paid too much, whether the price of subscription they set is too cheap and / or the number of subscribers is lower than expected.

Broadcasters should anticipate in the bidding process how not to go beyond a cap where the bid exceeds ex ante the earnings ex post (Les Echos, 2016 29 ).

• Customers who, in many cases, face a situation of monopoly, whether there are only one or two monopolies. It might be the case that the consumer is cursed as soon as he subscribes to pay-TV. This is called "siphoning" and describes a situation where "pay-TV will carry events that were formerly available on free television, so that viewers pay for infra-marginal viewing of games that would have been broadcast anyway for free" (Noll, 2007, p.409). For Sean Williams 29 Lévêque, Francois, "Les surenchères des droits du foot, plus d'argent pour les joueurs, moins pour les téléspectateurs" [The higher bids of the football broadcasting rights more money for the players, less for the televiewers], Les Echos, http://www.lesechos.fr/ideesdebats/cercle/cercle-156798-les-surencheres-des-droits-du-foot-plus-dargent-pour-lesjoueurs-moins-pour-les-telespectateurs-1220448.php, 05/09/16


Y Fialin

S Le Godec

M Benmokhtar

Moutaabbid

A Harbi

H Moutaabbid

Y Li

Carlos Renero-Lecuna

M Fialin

Y Le Godec

S Benmokhtar

M Moutaabbid

The effect of cation disorder on magnetic properties of new double perovskites La 2

The effect of cation disorder on magnetic properties of new double perovskites La2Ni Co1-MnO6 (x = 0.2-0.8)

Introduction

Double Perovskite-type oxides of general chemical formula A 2 BB'O 6 , (where A = alkaline earth or rare-earth ion), the transition metal sites are alternately occupied by two different types of cations B and B'. It is clear that both the valence and the ionic size of B and B' are crucial in affecting the physical properties of the systems. They have been studied

extensively not only due to the versatile nature of their structure but more importantly due to their multifunctional properties [START_REF] Vasala | A 2 B′B″O 6 perovskites A review[END_REF]. Among recent research a wide range of ground states appear, including ferromagnetic metals, orbital-and charge-ordered antiferromagnets, and more complex stripe and spin-glass states [START_REF] Salamon | The physics of manganites: Structure and transport[END_REF]. Simple perovskites Pr 0.5 Ca 0.5~x Sr x MnO 3 [START_REF] Krupicka | Details of structural and magnetic transitions in Pr0.5Ca0.5-xSrxMnO3 perovskites[END_REF] La 0.67 Ca 0.33 Mn 0.9 Fe 0.1 O 3 [START_REF] Cai | Colossal magnetoresistance of spin-glass perovskite La 0.67 Ca 0.33 Mn 0.9 Fe 0.1 O 3[END_REF] exhibits this spin glass behavior but also double perovskite A 2 B'B"O 6 compounds that appear to be spin-glasses, or spin-glass like behavior. For example, spin-glass behavior has been found in the disordered Sr 2 FeB'O 6 compounds with B'= Nb, Ta or Ru [START_REF] Vasala | A 2 B′B″O 6 perovskites A review[END_REF]. The spin-glass behavior likely arises from a competition between ferromagnetic and antiferromagnetic interactions because of local disorder such as in particular La 2 CoMnO 6 . Double-perovskite La 2 NiMnO 6 is a single material platform with multiple functions and is expected to have unprecedented device applications [START_REF] Dass | Oxygen stoichiometry, ferromagnetism, and transport properties of La2-xNiMnO6+δ[END_REF], it has received considerable attention recently because the material has a relatively high Curie temperature (Tc) of 280 K [START_REF] Rogado | Magnetocapacitance and Magnetoresistance Near Room Temperature in a Ferromagnetic Semiconductor: La 2 NiMnO 6[END_REF] and a colossal magneto dielectric coupling (up to ~20%) over a wide temperature range across room temperature [START_REF] Dass | Oxygen stoichiometry, ferromagnetism, and transport properties of La2-xNiMnO6+δ[END_REF][START_REF] Choudhury | Near room-temperature colossal magnetodielectricity and multiglass properties in partially-disordered La 2 NiMnO 6[END_REF]. A giant tunability of dielectric permittivity was also reported [START_REF] Tang | The giant dielectric tunability effect in bulk La 2 NiMnO 6 around room temperature[END_REF]. La 2 NiMnO 6 is a ferromagnetic insulator with a positive super-exchange interaction between Ni and Mn cations [START_REF] Dass | Oxygen stoichiometry, ferromagnetism, and transport properties of La2-xNiMnO6+δ[END_REF][START_REF] Rogado | Magnetocapacitance and Magnetoresistance Near Room Temperature in a Ferromagnetic Semiconductor: La 2 NiMnO 6[END_REF][START_REF] Goodenough | Relationship Between Crystal Symmetry and Magnetic Properties of Ionic Compounds Containing Mn 3+[END_REF][START_REF] Mao | Magnetic properties of double perovskite La 2 BMnO 6 (B = Ni or Co) nanoparticles[END_REF][START_REF] Joseph Joly | Two ferromagnetic phases with different spin states of Mn and Ni in LaMn 0.5 Ni 0.5 O 3[END_REF][START_REF] Dass | Multiple magnetic phases of La 2 CoMnO 6-δ (0<~δ<~0.05)[END_REF]. Such behavior is significant in spintronic materials as it helps to achieve magneto-dielectric properties. These outstanding physical properties arise from competing magnetic interactions of cations, structural (phonons) and polarization (charges) order parameters. La 2 CoMnO 6 shows well-ordered monoclinic symmetry with good ferromagnetic and insulating behaviors [START_REF] Dass | Multiple magnetic phases of La 2 CoMnO 6-δ (0<~δ<~0.05)[END_REF][START_REF] Singh | Evidence of bidomain structure in double-perovskite La 2 CoMnO 6 thin films[END_REF]. Using first principle density functional calculations, it is stated that the insulating state in La 2 CoMnO 6 is driven by the Coulomb-assisted spin-orbit coupling operative within the Co-d manifold [START_REF] Baidya | Electronic structure and phonons in La 2 CoMnO 6 : A ferromagnetic insulator driven by Coulomb-assisted spin-orbit coupling[END_REF]. La 2 CoMnO 6 shows two ferromagnetic transitions at T C1 ~ 225 K and T C2 ~ 150K [START_REF] Baidya | Electronic structure and phonons in La 2 CoMnO 6 : A ferromagnetic insulator driven by Coulomb-assisted spin-orbit coupling[END_REF]. Blasse Mn 4+ superexchange interaction [START_REF] Blasse | Ferromagnetic interactions in non-metallic perovskites[END_REF]. Joy et al. presented the high-spin Mn 3+ and low-spin Co 3+ in rhombohedral phase and high spin Co 2+ and Mn 4+ in orthorhombic phase in La 2 CoMnO 6 [START_REF] Joy | Spin states of Mn and Co in LaMn 0.5 Co 0.5 O 3[END_REF]. By performing X-ray absorption near-edge spectroscopy (XANES) experiments Joly et al. also suggested that the order phase involves Co 2+ and Mn 4+ ions and disorder state corresponds to Co 3+ and Mn 3+ ions in LaCo 0.5 Mn 0.5 O 3 [START_REF] Joseph Joly | The origin of ferromagnetism in the two different phases of LaMn 0.5 Co 0.5 O 3 : evidence from x-ray photoelectron spectroscopic studies[END_REF].

In the present work, the double perovskites La 2 Ni x Co 1-x MnO 6 (LNCMO) with x = 0.2, 0.25, 0.5, 0.75 and 0.8 have been prepared by new solid-state reaction. The powder XRD, IR, UV and Raman spectroscopy at room temperature, has done the structural characterization.

The magnetic properties have been investigated by ZFC-FC and AC magnetic measurements from 2 K to 300 K and the optical properties have been investigated in order to calculate the band gap energy and to study the optical behavior of the samples.

Sample preparation

Polycrystalline samples of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) were synthesized by solid-state reaction. Stoichiometric amounts of La 2 O 3 (99%), CoCO 3 (98%), NiO (99%) and MnCO 3 (99%) were mixed and heated in air at 200°C for 6 h, 500°C for 6 h and finally at 900ºC for 24 h in a conventional tubular furnace. After the first step, the material was re-grounded in an agate mortar, which were subsequently heated at 1000 ºC for 24h in air. The La 2 Ni x Co 1-x MnO 6 compounds were synthesized at the same temperatures.

The chemical reaction is :

La 2 O 3 + x NiO + (1-x) CoCO 3 + MnCO 3 →La 2 Ni x Co 1-x MnO 6 + (1+x) CO 2 ↑
The structural refinements were undertaken from the powder data. Diffraction data were collected at room temperature on a Phillips D 5000 (θ-θ) diffractometer: Bragg-Brentano geometry; diffracted-beam graphite monochromator; Cu(K α ) radiation (40 kV, 40 mA); Soller slits of 0.02 rad on incident and diffracted beams; divergence slit of 0.5º; antiscatter slit of 1º; receiving slit of 0.1 mm; with sample spinner. The patterns were scanned through steps of 0.02 (2θ), between 10 and 100 (2θ) with a fixed-time counting. The full pattern refinements were carried out by means of the Rietveld method using the Fullprof program [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF] integrated in Winplotr software [START_REF] Roisnel | WinPLOTR: A Windows Tool for Powder Diffraction Pattern Analysis[END_REF]. The Rietveld refinement of the observed powder XRD data is initiated with scale and background parameters and successively other profile parameters are included. The background is fitted with a fifth order polynomial. The peak shape is fitted with a pseudo-Voigt profile function. After an appreciable profile

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matching the position parameters and isotropic atomic displacement parameters of individual atoms were also refined.

The chemical composition and purity of each sample was recorded using Cameca SX100 electron microprobe at the CAMPARIS facility (Sorbonne University).

Fourier transform infrared spectroscopy (FT-IR, NICOLET 6700) was used to determine chemical bonding of powders.

The Raman spectra were recorded on HR460 (Jobin-Yvon/Horiba) spectrometer using as excitation source an Ar + laser under 514.5 nm excitation wavelength.

The optical properties UV-visible spectroscopy measurements was done using Perkin Elmer UV-VIS spectrometer (Lambda 1050).

The All direct current (DC) and alternative current (AC) magnetization measurements have been carried out on a Quantum Design MPMS-XL7 magnetometer.

Results and discussion

Structural characterization

The Rietveld refinement of X-ray diffraction patterns of the polycrystalline La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) confirmed the presence of a majority monoclinic structure phase with P2 1 /n space group and a small minority phase marked by ( ) sign was estimated to be around 6.08% for x = 0.2, 6.14% for x = 0.25, 5.6% for x = 0.5, 7.31% for x = 0.75, 6.76% for x = 0.8) of La 2 MO 4 with M = Ni, Co, Mn (orthorhombic, Bbam space group, with a=5.4652 Å, b=5.46869 Å, c=12.67804 Å) previously reported in [START_REF] Pecchi | Catalytic Performance of La 0.6 Ca 0.4 Fe 1-x Ni x O 3 Perovskites in DME Oxidation[END_REF]. The lattice parameters and volume obtained from refinement using monoclinic P2 1 /n space group are found similar to the reported values of monoclinic La 2 CoMnO 6 double perovskite [START_REF] Orayech | Synthesis, structural, magnetic and phase-transition studies of the ferromagnetic La 2 CoMnO 6 double perovskite by symmetry-adapted modes[END_REF].

After the complete refinement, we achieved a good agreement between the observed and calculated XRD patterns at 298K, for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) as shown in Figure 1, respectively as a representative of the series. Table 1 summarizes the lattice parameter, unit cell volume and reliability factors after the Rietveld refinement, one note a strange anomaly of decreasing unit volume with increasing x shown at x = 0.75, probably attributed to the presence of La 2 MO 4 . The selected bond lengths were determined and are listed in Table 2

3.2.

The electron probe microanalysis results

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4

The elementary analysis has been performed by electron Probe Microanalysis in Tables 3, the average stoichiometry of our double perovskite samples can be written as La with M = Ni, Co, Mn.

Raman spectroscopy studies

Figure 3 shows the Raman spectra of the studied compounds. The main features of these spectra are two broad peaks at around 520 cm -1 and 650 cm -1 . According to the bibliography [START_REF] Guo | Supercond, Local Valence and Hole-Doping Effect on Magnetic Properties in Double Perovskite La 2 NiMnO 6[END_REF][START_REF] Iliev | Raman spectroscopy evidence of strong spin-phonon coupling in epitaxial thin films of the double perovskite La 2 NiMnO 6[END_REF][START_REF] Kumar | Raman spectroscopic study of structural transformation in ordered double perovskites La 2 CoMnO 6 bulk and epitaxial film[END_REF][START_REF] El-Kemary | El-Mehasseb, Fabrication and characterization of semiconductor nickel oxide (NiO) nanoparticles manufactured using a facile thermal treatment[END_REF] these bands corresponds to the Ni/Co-O and Mn-O octahedron antisymmetric (B g ) and symmetric (A g ) stretching vibrations respectively, for a monoclinic P2 1 /n crystal. The energy of the phonons and the values of the FWHM for each sample are summarized in Table 4. We observed a hardening in both phonons as the amount of Ni 2+ doping increase. Despite the fact that the ionic radii of the Co +2 and Ni 2+ in octahedral sites are 0.65 Å and 0.69 Å respectively [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] and the average of the distances Co/Ni-O, Mn-O, the octahedron La-O are maintained the same for the different Nickel contents (Table 2). The hardening of the phonons can be associated to a general relaxation of the host lattice, when the photon energy hυ, with help of optical absorbance where α is the absorption coefficient, h is the Plank constant and υ is the frequency of incident light. Tauc's relation is given by [START_REF] Chang | Effect of synthesis on structure, oxygen voids, valence bands, forbidden band gap and magnetic domain configuration of La 2 CoMnO 6[END_REF]:

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT Αhυ = A (hυ-E g ) n
Where E g is the energy difference between valence and conduction band and n is a constant equal to 1/2 for direct band gap materials and 2 for indirect band gap material. The natures of the plots indicate the existence of direct transitions. The band gap E g is determined by extrapolation of the straight portion of the plot to the energy axis as shown in Figure 7. The obtained band gap of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.75, 0.8) is given in Table 5. The T C1 value increases from 232 K to 260 K (see Table 6) when x increases from 0.2 to 0.8.This is expected, as the T C1 value of LNMO oxide reported in the literature are very near room temperature : for example, 270 K for a polycrystalline sample [START_REF] Li | The effect of Ca-substitution in La-site on the magnetic properties of La 2 CoMnO 6[END_REF] and thin film [START_REF] Zhou | Nature of short-range ferromagnetic ordered state above T C in double perovskite La2NiMnO6[END_REF], 284 K for large nanoparticles (d>50 nm) [START_REF] Singh | Long-range Ni/Mn structural order in epitaxial double perovskite La 2 NiMnO 6 thin films[END_REF] and 288 K for a single crystal [START_REF] Zhao | Size-dependent magnetic properties and Raman spectra of La2NiMnO6 nanoparticles[END_REF].

The magnetic properties studies

Whereas T C1 value of pure LCMO oxides are lower and ranges from 210 K to 235 K for polycrystalline samples [START_REF] Gonzalez | Effect of cation disorder on structural, magnetic and dielectric properties of La 2 MnCoO 6 double perovskite[END_REF][START_REF] Devi Chandrasekhar | Synthesis and Magnetic Properties of La2NiMnO6 Nanoparticles[END_REF][START_REF] Egoavil | Phase problem in the B-site ordering of La 2 CoMnO 6 : impact on structure and magnetism[END_REF][START_REF] Xing | Magnetic properties and magnetoresistance effect of La 2 Co 1-x Mg x MnO 6 (0.1 ≤x ≤1.0)[END_REF] and thin films [START_REF] Guo | Structural and magnetic properties of epitaxial thin films of the ordered double perovskite La 2 CoMnO 6[END_REF][START_REF] Kim | Effects of different annealing atmospheres on magnetic properties in La 2 CoMnO 6 single crystals[END_REF]. Obviously, T C1 depends not only on the oxide composition but also on its cation orderings. The strong PM-FM transition in double perovskites is attributed to the long-range magnetic ordering of Mn 4+ -O -M 2+ (M 2+ = Co or Ni or other transition metals) [START_REF] Dass | Multiple magnetic phases of La 2 CoMnO 6-δ (0 ≤ δ ≤ 0.05)[END_REF], which is always in competition with the antiferromagnetic interactions (AFM) of anti-site ions (Mn 4+ -O -Mn 4+ or B 2+ -O -B 2+ ). The later ones are the consequences of the local disorders in double perovskites, such as oxygen vacancy [START_REF] Dass | Multiple magnetic phases of La 2 CoMnO 6-δ (0 ≤ δ ≤ 0.05)[END_REF][START_REF] Iliev | Growth, magnetic properties, and Raman scattering of La 2 NiMnO 6 single crystals[END_REF], Bsite disordering [START_REF] Zhou | Nature of short-range ferromagnetic ordered state above T C in double perovskite La2NiMnO6[END_REF][START_REF] Devi Chandrasekhar | Synthesis and Magnetic Properties of La2NiMnO6 Nanoparticles[END_REF] which reduces the long-range FM ordering of Mn 4+ -O -B 2+ . Even in an ordered LBMO perovskite, the antiphase interface between the two FM regions would have also AFM interactions of antisite ions. Therefore, for a double perovskite of a given composition, a higher T C1 reflects a higher degree of cation ordering. Three of the fives double perovskites with (x = 0.2, 0.25, 0.5) content show also a weak PM-FM transition at T C2

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= 200 K, 200K and 208K respectively. The similar transition occurs often in LNMO oxides and is attributed to the short-range magnetic ordering of Mn 4+ -O -Ni 2+ [START_REF] Zhou | Nature of short-range ferromagnetic ordered state above T C in double perovskite La2NiMnO6[END_REF][START_REF] Zhao | Size-dependent magnetic properties and Raman spectra of La2NiMnO6 nanoparticles[END_REF][START_REF] Li | The effect of Ca-substitution in La-site on the magnetic properties of La 2 CoMnO 6[END_REF]. All values of T C1 and T C2 are summarized in the Table 6 together with the Curie-Weiss parameters, C and Θ. The positive sign of Θ confirms the ferromagnetic ground state in the fives double perovskites. T C1 and Θ show the same tendency of compositional variation and the small difference between them suggests a high degree of cation ordering in double perovskite [START_REF] Balli | A study of the phase transition and magnetocaloric effect in multiferroic La 2 MnNiO 6 single crystals[END_REF].

It's worth noting that in a certain temperature domain above T C1 , χ M -1 versus T (Figure 8 d) presents an upward deviation from Curie-Weiss behavior, as already observed for a polycrystalline LNMO [START_REF] Guo | Effect of oxygen concentration on the magnetic properties of La 2 CoMnO 6 thin films[END_REF] and a nanoparticle LNMO [START_REF] Mahato | Colossal magnetoresistance in the double perovskite oxide La 2 CoMnO 6[END_REF] by S.M. Zhou et al. They explained the phenomenon by the existence of a short-range FM ordered state persisting above T C1 .

The Figure 9 shows the M-H loops of the fives double perovskites at 5 K: (a)

presents the entire M-H loops from -7 T to 7 T and (b), the zoomed loops from -2T to 2T without first magnetizations. Each hysteresis M-H loop is characterized by its specific magnetization at 7 T (M S ), its coercive magnetic field (H C ) and by its specific remnant magnetization (M r ), and the Table 7 summarizes the values of these parameters. For the LCMO and LNMO doubles perovskites these three parameters depend strongly on the content of the antisite ions and of anti-phases. If the disorder increases, both M S and M r diminish, whereas H C decreases [START_REF] Dass | Multiple magnetic phases of La 2 CoMnO 6-δ (0 ≤ δ ≤ 0.05)[END_REF][START_REF] Singh | Long-range Ni/Mn structural order in epitaxial double perovskite La 2 NiMnO 6 thin films[END_REF]. When the M S of a double perovskite approaches its theoretical spin-only value (M S.LCMO = 6.0 µ B /f.u. and M S.LNMO = 5.0 µ B /f.u.), the oxide is considered as well ordered. For example, A J Baron-Gonzalez et al has studied the effect of cation disorder on the structural, magnetic and dielectric properties of two polycrystalline La 2 CoMnO 6 double perovskite with the disorder degree of 95% and 74% respectively [START_REF] Gonzalez | Effect of cation disorder on structural, magnetic and dielectric properties of La 2 MnCoO 6 double perovskite[END_REF], the highly kOe for the former, and 3.7 µ B /f.u. and 1 kOe for the second [START_REF] Zhou | Nature of short-range ferromagnetic ordered state above T C in double perovskite La2NiMnO6[END_REF].

The spin-only saturation magnetization of our double perovskites, M S0 , can be calculated by the following equation:

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7 M S0 = √ (1-x) M S.LCMO 2 + x M S.LNMO 2
The ratio of M S /M S0 allows an estimation of the ordering degree for the five double perovskites (see the Table 7). According to this criterion, the Ni 2+ rich double perovskites (x = 0.75 and 0.80) have a high degree of ordering (> 96%), while the oxide with x = 0.25, the lowest degree of cation ordering. As expected the H c value tend to decrease with Ni 2+ content in the oxides.

The M-H loops curves at 300 K have no hysteresis opening. The Figure 10 shows M-H curves from 0 to 7 T for the five double perovskites. In low field (< 2 T) the M plotted against H are straight lines, but in high field (> 2 T) one observes a notable downward deviation of M from the straight lines for all the fives oxides. This confirms the existence of the short-range ordering above T C1 mentioned above. More is the Ni 2+ content in the oxides, more is the downward deviation of their M-H curves.

The Figure 11 independent, whereas the transition below 100 K (T f1 at 50 Hz , T f2 at 141.6 Hz and T f3 at 400.6 Hz) are strongly frequency dependent. Furthermore, one can observe that the peak relative to the weak PM-FM transition is very large in the χ''-T curve for the double perovskite having x = 0.25, it seems that the broadening of this peak might result from the addition of several short-range FM interactions of magnetic cations. This is consistent with the fact this oxide has the lowest ordering degree (Table 7) and suggests that it might have a less homogeneous structure. The Table 8 lists the values of T C1ac , T C2ac , T f1 , T f2 and T f3 for the five double perovskites.

The low temperature frequency dependent anomaly has been already observed in several LCMO and LNMO double perovskites, and is generally assigned to the spin or cluster glass transition. The spin glass behavior results from the competition between FM and

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8 AFM interactions in many magnetic oxides, which destroys the long-range magnetic order and leaves the system in a random spin configuration of frozen state. If one FM or AFM interaction dominates, the FM-AFM competition is weak; the system will have a short magnetic order, and thus a cluster glass behavior. The spin or cluster glass is characterized by their specific relaxation time τ 0 as well as by their frequency sensitivity factors, called also Mydosh factor K = ∆T f / (T f0 ∆(log 10 f)) [START_REF] Murthy | Size dependent magnetic properties of double perovskite La 2 CoMnO 6 nanoparticles[END_REF][START_REF] Galceran | Engineering the microstructure and magnetism of La 2 CoMnO 6-δ thin films by tailoring oxygen stoichiometry[END_REF].

The relaxation time τ 0 can be derived from Arrhenius law.

τ = τ 0 exp[E a /(k B T f )]
Where E a is the anisotropy energy, τ=1/(2πf) and k B , the Boltzmann constant.

The Table 9 summarizes the τ 0 and K values calculated from χ''-T curves for the fives double perovskites. The τ 0 value of the five oxides varies from 1.963×10 -10 to 2.974×10 -7 s and is greater than the τ 0 value of spin glass (about 10 -13 s). This reveals the cluster glass nature of the low temperature frequency dependent anomalies on the χ''-T curves. The K values greater than 0.1 indicate that the magnetic clusters are non-interacting superparamagnetic single domains.

Conclusion

In conclusion, we succeed in the new solid-state synthesis of five doubles perovskites oxide

Highlights

Highlights

• The effect of cation disorder on magnetic properties of double perovskites La2NixCo1-xMnO6

• Paramagnetic to ferromagnetic (PM-FM) transition

• Existence of super-paramagnetic mono-domains

• Revealing spin glass transition analog.

• Double-perovskite La2NiMnO6 is a single material platform with multiple functions

  et al. showed the presence of ferromagnetic Co 2+ -M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 2

  . The results of Rietveld refinements data showing that the atoms (Ni/Co) and Mn are octahedrally coordinated with the oxygen atoms. The octahedra [Ni/CoO 6 ] and [MnO 6 ] are linked by O 1 and O 3 along (a, b) axis and by O 2 along c-axis in

Figure 2 .

 2 Figure 2.

Ni 2+ is incorporated to the lattice Figure 4 . 5 . 3 . 4 .

 4534 The opposite occurs in the case of the double perovskites La 2 NiMnO 6 and La 2 CoMnO 6 when doped with Ca +2 ions. The hypothesis of this lattice relaxation gets stronger since the observed FWHM does not change with the doping increase Figure Infrared spectroscopy studies.

Figure 6 3 . 5 .

 635 Figure 6 shows FT-IR spectra of the studied compounds. The broad absorption band at about 426 cm -1 and 600 cm -1 can be assigned to the Ni/Co-O and Mn-O bond stretching vibration and deformation modes of the [Ni/CoO 6 ] and [MnO 6 ] octahedra according to the literature [27-28].

Figure 8

 8 Figure 8 summarizes the results obtained from ZFC-FC magnetization in a field of 50 Oe between 2 K and 300 K : (a) shows the thermal variation of molar susceptibilities or susceptibility per formula unit (f.u.) for the five double perovskites; (b), the enlarged ZFC χ M curves in the temperature range of 2 -300 K ; (c), the derivatives of ZFC χ M against T (dM/dT) between 180 K and 300 K (the solid lines are eye guides) and (d), the inverted ZFC molar susceptibility, χ M -1 , against T between 220 K and 300 K (the solid lines represent the data fitted by Curie-Weiss law). All five oxides present a strong paramagnetic (PM) to ferromagnetic (FM) transition with the Curie temperature, T C1 , corresponding to the deepest minimum value of dχ M /dT.

  ordered LCMO (T C1 = 235 K) has a M S value of 5.85 µ B /f.u. and a H C value of 1.50 kOe at 10 K, whereas the lowly ordered LCMO (T C1 = 225 K), a M S value of 4.41 µ B /f.u. and a H C value of 6.75 kOe; M.P. Singh et al has compared the structural, magnetic and optic properties of two LNMO thin films: an ordered La 2 NiMnO 6 film (T C1 = 270 K) and its disordered LaNi 0.5 Mn 0.5 O 3 counterpart (T C1 = 138 K). The M S and H C are respectively 4.8 µ B /f.u. 0.25

  (a) and (j) illustrates the thermal variation of the in-phase (χ') and out-off phase (χ'') components of ac molar susceptibilities for the five double perovskites under an ac field of 3 Oe at three frequencies (50.0 Hz, 141.6 Hz and 400.6 Hz). Both χ' and χ'' display frequency dependence in the whole temperature range of 15 -300 K: their intensities decrease with increasing frequency. The χ'-T curves are very similar to the ZFC χ M -T curve, indicating two PM-FM transitions of the three oxides with x = 0.20, x = 0.25 and x = 0.50, and one transition for the two others rich in Ni 2+ with x = 0.75 and x = 0.80. The χ''-T curves give more information on the multiple magnetic transitions in the oxides: they revealed that the positions of the strong and weak PM-FM transitions at T C1ac and T C2ac are frequency

La 2 Fig. 1 .

 21 Fig.1. X-ray diffraction profiles of experimental (. . .) and calculated patterns (-) for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8). Star represents La 2 MO 4 with M = Ni, Co, Mn (orthorhombic, space group Bbam).

Fig. 2 .

 2 Fig.2. The monoclinic structure with P2 1 /n space group of La 2 Ni x Co 1-x MnO 6 represented on Vesta program ( K. Momma and F. Izumi (2011): J. Appl. Crystallogr., 44, 1272-1276).

Fig. 3 .

 3 Fig.3. Raman spectra of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) compounds.

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig.4. Raman modes energy dependence with Nickel content of La 2 Ni x Co 1-x MnO 6 . Fig.5. FWHM versus the Nickel content of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) compounds.Fig. 6. FT-IR spectra of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) compounds.

Fig. 7 .Fig. 8 .

 78 Fig.7. (αhν) 2 versus photon energy (hν) of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.75, 0.8) compounds.Fig.8.Results from the Magnetization-Temperature measurements for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) in the magnetic field of 50 Oe : thermal variation of ZFc-Fc molar susceptibility (χ M ) (a) and enlarged ZFc χ M (b) in the temperature range of 2 -300 K, derivative of ZFc χ M versus temperature between 180 K and 300 K (c, the solid lines are eye guides) and inverted ZFc χ M against temperature between 220 K and 300 K (d, the solid lines represent the data fitted by Curie-Weiss law).

Fig. 9 .

 9 Fig.9. Field dependent magnetization for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) at 5 K in the field range from -7 T to 7 T (a) and in the field range from -2 T to 2 T (b).

Fig. 10 .Fig. 11 .

 1011 Fig.10.Field dependent magnetization for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) at 300 K in the field range from 0 to 7 T. Fig.11.Thermal variation of the real and imaginary molar susceptibilities (χ ' and χ '' ) for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) in an AC magnetic field of 3 Oe with three frequencies (50 Hz, 141.6 Hz and 400.6 Hz).

3 .mol - 1 )La 2 La 2 La 2

 31222 Ni x Co 1-x MnO 6 Ni x Co 1-x MnO 6 Ni x Co 1-x MnO 6

  2.05 Ni 0.21 Co 0.76 Mn 0,96 O 6±δ , La 2.6 Ni 0.34 Co 0.72 Mn 1.1 O 6±δ , La 1.9 Ni 0.57 Co 0.48 Mn 0.93 O 6±δ , La 2.07 Ni 0.77 Co 0.18 Mn 0.96 O 6±δ , and La 2,05 Ni 0.83 Co 0,25 Mn 1.08 O 6±δ The disagreement with the theoretical stoichiometry, can be justified by the presence of the impurity phase of La 2 MO 4

Table . 1

 . .Crystal parameters and details of the structure refinement for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8).Table.2. Bond distances (Å) for La 2 Nix Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8).Table.3. Results of The electron Probe Microanalysis (EPMA) analysis for the cation composition and concentration for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8). The gap is the difference between experimental and theoretical concentration. Table.4. Raman Lorentzian fitting parameters of the La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8) bands at RT. Table.5. The band gap energy of La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.75, 0.8) compounds and comparison to literature. Table.6. Curie temperatures and Curie-Weiss parameters for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8).Table.7. Characteristics of the M-H loops at 5 K for La 2 Nix Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8).Table.8. Curie temperatures and cluster glass transition temperature determined by the out of phase molar susceptibility, χ '' -T for La 2 Ni x Co 1-x MnO 6 (x =0.2, 0.25, 0.5, 0.75, 0.8). Table.9. Relaxation time τ, activation energy E a and Mydosh factor K determined by the Arrhenius law from the out of phase molar susceptibility, χ''-T for La 2 Ni x Co 1-x MnO 6 (x = 0.2, 0.25, 0.5, 0.75, 0.8).

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	a)La 2 Ni 0.8 Co 0.2 MnO 6 .
	M A N U S C R I P T x = 0.5 x = 0.75 x = 0.8 5.515(6) 5.469(6) 7.752(7) 90.07(8) 233.884(2) 0.0029(3) 0.5194(1) 0.2490(1) 0.8497(3) 0 0 0 0.4482(7) 0 0 0.5 0.2063(3) 0.5 0 0 0.5 0.2063(3) 0.5 -0.7752(2) 0.2641(9) 0.0420(2) 0.9660(6) -0.5690(1) 0.4921(1) -0.2562(2) 0.9660(6) 5.522(2) 5.480(8) 7.766(6) 90.12(1) 235.039(2) 0.0027(8) 0.5218(8) 0.2506(1) 0.6933(1) 0 0 0 1.4434(2) 0 0 0.5 0.1083(8) 0.75 0 0 0.5 0.1083(8) 0.25 -0.7680(5) 0.2618(9) 0.0406(5) 1.0119(2) -0.5757(2) 0.4979(6) -0.2571(4) 1.0192(9) x = 0.25 x = 0.5 x =0.75 x=0.8 Ni Co La/Mn Co/Ni Peak 1 (cm -1 ) FHWM 1(cm -1 ) Peak 2 (cm -1 ) FHWM 2 (cm -1 ) x = 0.25 5.522(1) x = 0.2 5.482(4) 7.768(7) 90.08(2) 235.177(1) 0.0031(2) 0.5218(7) 0.2474(1) 0.7321(9) 0 0 0 0.5478(5) 0 0 0.5 0.3007(9) 0.2000 0 0 0.5 0.3007(9) 0.8000 -0.7786(1) 0.2641(9) 0.0419(6) 1.5307(1) -0.5644(1) 0.4943(5) -0.2677(4) 1.5307(1) 5.518(4) 5.472(1) 7.754(9) 90.08(5) 234.176(3) 0.0031(3) 0.5192(1) 0.250 0.6823(4) 0 0 0 0.9102(5) 0 0 0.5 0.2312(4) 0.25 0 0 0.5 0.2312(4) 0.75 -0.7742(1) 0.2431(3) 0.0510(1) 1.1001(4) -0.5662(1) 0.5001(5) -0.2620(1) 1.1012(4) x = 0.2 La Mn Theoretical formula a (A˚) b (A˚) c (A˚) V (A˚) 3 La: x y z B iso Mn: x y z B iso Ni: x y z B iso Occ Co: x y z B iso Occ O(1): x y z B iso O(2): x y z B iso Atoms Samples experimental formula band gap energy Ref Sample T c (ZFC-FC) Reference Curie-Weiss constants Reference Double Spin-Characteristics of hysteresis cycle at 5 K Double FM transition Frequency dependent transition temperatures of 5.515 (8) 5.467(2) 7.750(1) 90.04(4) 233.673(5) 0.0037(7) 0.5179(7) 0.2484(8) 0.6589(5) 0 0 0 2.5478(5) 0 0 0.5 0.2314(3) 0.8 0 0 0.5 0.2314 (3) 0.2 -0.7733(9) 0.2430(8) 0.0518(2) 0.1576(2) -0.5697(6) 0.4933(7) -0.2589(1) 0.1576(2) M A N U S C R I P T Ni/CoO 6 octahedra Ni/Co-O 1 × 2 Ni/Co-O 2 × 2 Ni/Co-O 3 × 2 MnO 6 octahedra Mn-O 1 × 2 Mn-O 2 × 2 Mn-O 3 × 2 LaO 6 octahedra La-O 1 La-O 1 La-O 1 La-O 1 La-O 2 La-O 2 La-O 2 La-O 2 La-O 3 La-O 3 La-O 3 La-O 3 2.0362(0) 2.1099(1) 2.0964(0) 1.9228(0) 1.8399(1) 1.8642(0) 2.4495(1) 2.5979(1) 2.8211(1) 3.1823(1) 2.4301(1) 3.1044(1) 2.8556(1) 2.6816(1) 3.1421(1) 2.5738(1) 2.8592(1) 2.4934(1) 1.9947(7) 2.0388(6) 2.1495(9) 1.9537(7) 1.9342(6) 1.8019(8) 2.5107(6) 2.5436(6) 2.8661(6) 3.1212(6) 2.3599(3) 3.1674(3) 2.8831(2) 2.6677(2) 3.1327(7) 2.5579(7) 2.8722(7) 2.5032(7) 2.0178(2) 2.0208(7) 2.1609(3) 1.9321(2) 1.9306(7) 1.7924(3) 2.4555(3) 2.5813(3) 2.8396(3) 3.1504(3) 2.3949(2) 3.1232(2) 2.8254(1) 2.7020(1) 3.1468(2) 2.5926(2) 2.8509(2) 2.4668(2) 1.9990(1) 2.0396(1) 2.1483(0) 1.9491(1) 1.9329(1) 1.8023(1) 2.5099(1) 2.5485(1) 2.8617(1) 3.1216(1) 2.3616(1) 3.1659(1) 2.8825(1) 2.6678(1) 3.1307(1) 2.5591(1) 2.8707(1) 2.5049(1) 2.0996(1) 2.0432(1) 2.0478(0) 1.8677(1) 1.9083(1) 1.9063(1) 2.4687(2) 2.4734(2) 2.9551(2) 3.1473(3) 2.3960(1) 3.1233(1) 2.8251(1) 2.7025(1) 3.1216(2) 2.5424(2) 2.8896(2) 2.4807(2) M A N U S C R I P T Experimental 20.75334 9.63132 7.73818 1.8732 2.1547 0.2407 Theoretical 20.0000 10.0000 8.0000 2.000 2 0.25 The gap 0.75334 0.36868 0.26182 0.1268 0.1547 0.0093 b) La 2 Ni 0.75 Co 0.25 MnO 6 . Atoms La Mn Ni Co La/Mn Co/Ni Experimental 20.5958 10.8890 8.3350 2.5380 2.0568 0.3046 Theoretical 20.0000 10.0000 7.5000 2.5000 2 0.33 The gap 0.5958 0.889 0.835 0.038 0.0568 0.0254 c) La 2 Ni 0.5 Co 0.5 MnO 6 . Atoms La Mn Ni Co La/Mn Co/Ni Experimental 19.12193 9.53302 5.70478 4.80597 2.0586 0.842 Theoretical 20.0000 10.0000 5.000 5.000 2 1 The gap 0.87807 0.46698 0.70478 0.19403 0.058 0.158 d) La 2 Ni 0.25 Co 0.75 MnO 6 . Atoms La Mn Ni Co La/Mn Co/Ni Experimental 26.3448 11.16795 3.4892 7.205583 2.3720 2.0934 Theoretical 20.0000 10.0000 2.5000 7.5000 2 3.0000 The gap 6.3448 1.16795 0.9892 0.294417 0.3720 0.9066 M A N U S C R I P T La 2 Ni 0.80 Co 0.20 MnO 6 522 114 663 48 La 2 Ni 0.75 Co 0.25 MnO 6 523 46 667 41 La 2 Ni 0.50 Co 0.50 MnO 6 518 63 658 La 2 Ni 0.25 Co 0.75 MnO 6 516 141 647 55 La 2 Ni 0.20 Co 0.8 0 MnO 6 508 75 651 37 M A N U S C R I P T La 2 Ni 0.75 Co 0.25 MnO6 La 2 Ni 0.25 Co 0.75 MnO6 La 2 Ni 0.2 Co 0.8 MnO6 La 2 CoMnO6 La 2,05 Ni 0.83 Co 0,25 Mn 1.08 O 6 La 2.6 Ni 0.34 Co 0.72 Mn 1.1 O 6 La 2.05 Ni 0.21 Co 0.76 Mn 0.96 O 6 La 2 CoMnO6 1. 65(1) 1.75(1) 1. 62(2) 1.93 This work M A N U S C R I P T x = 0.50 243.0 208.0 This work 5.927 250.24 6.85 This work x = 0.75 255.0 This work 6.857 261.58 6.12 This work x = 0.80 260.0 This work 7.106 266.20 7.49 This work x = 1 280 [35] 5.54 [35] M A N U S C R I P T x =0.80 5.22 5.41 100.00 0.8 1.96 M A N U S C R I P T [29] x = 0.25 238.0 200.0 This work 7.790 246.56 7.483 This work x =0.75 5.27 5.09 96.58 1.0 1.97 This work x = 0.20 232.0 200.0 This work 6.743 236.92 7.52 This work x =0.50 5.52 4.90 88.73 2.0 2.30 This work x=0 210 [33] 7.34 x =0.25 5.77 4.50 77.99 2.0 2.01 [33] 43 (eV) La 2 NiMnO6 La 2 Ni 0.8 Co 0.2 MnO6 La 2 NiMnO6 La 2.07 Ni 0.77 Co 0.18 Mn 0.96 O 6 1.2 1. 66(2) [30] This work T c1 (K) T c2 (K) C Curie (cm 3 .K.mol -(µ B ) x =0.20 5.81 5.14 88.47 3.5 2.56 1 ) Θ (K) Effective moment Perovskite only M S0 (µ B/f.u. ) M S0 (µ B/f.u. ) Order degree (%) H C (KOe) perovskite 's temperature (K) cluster glass (K) M r (µ B/f.u. ) composition T C1ac T C2ac T f1 (50 Hz) T f2 (141.6 Hz) T f3 (400.6 Hz)
	A C C E P T E D O(3): x y z B iso R B R F R P R wp R exp χ -0.2802(1) 0.1887(7) -0.0132(2) 1.5307(1) 3.140 4.719 13.2 9.65 5.77 2.80 -0.2710(2) 0.2110(1) -0.0161(3) 1.1032(4) 3.729 5.562 22.8 17.3 13.41 1.67 -0.2701(1) 0.1810(2) -0.0159(3) 0.9660(6) 6.010 7.300 14.3 10.8 6.24 2.97 A C C E P T E D A C C E P T E D e) La 2 Ni 0.2 Co 0.8 MnO 6 . Atoms La Mn Ni Experimental 20.5053 9.6972 2.188675 Theoretical 20.0000 10.0000 2.0000 The gap 0.5053 0.3028 0.188675 0. 60762 -0.2698(1) 0.1844(1) -0.0109(7) 1.0192(9) 4.348 7.049 23.6 15.7 14.30 1.21 Co La/Mn -0.2873(2) 0.1933(2) -0.0102(7) 0.1576(2) 3.355 6.028 14.3 10.8 6.35 2.91 Co/Ni 7.60762 2.1145 3.4759 8.0000 2 4.0000 0.1145 0.5241 A C C E P T E D A C C E P T E D A C C E P T E D A C C E P T E D A C C E P T E D
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