Wazen M Shbair
email: wazen.shbair@uni.lu

Mathis Steichen
email: mathis.steichen@uni.lu

Jérôme Franc ¸ois † Radu State
email: radu.state@uni.lu

Blockchain Orchestration and Experimentation Framework: A Case Study of KYC

Conducting experiments to evaluate blockchain applications is a challenging task for developers, because there is a range of configuration parameters that control blockchain environments. Many public testnets (e.g. Rinkeby Ethereum) can be used for testing, however, we cannot adjust their parameters (e.g. Gas limit, Mining difficulty) to further the understanding of the application in question and of the employed blockchain. This paper proposes an easy to use orchestration framework over the Grid'5000 platform. Grid'5000 is a highly reconfigurable and controllable large-scale testbed. We developed a tool that facilitates nodes reservation, deployment and blockchain configuration over the Grid'5000 platform. In addition, our tool can fine-tune blockchain and network parameters before and between experiments. The proposed framework offers insights for private and consortium blockchain developers to identify performance bottlenecks and to assess the behavior of their applications in different circumstances.

I. INTRODUCTION

Since the inception of Bitcoin [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF], blockchains are attracting more and more interests. At the heart of any blockchain are cryptographically linked blocks. They contain transactions that modify the state of the blockchain directly or through the execution of smart contracts. Using the public and private keys linked to their respective accounts, users can create transactions and sign them verifiably. This signature is required, as certain actions can only be performed by well specified accounts. This is for example the case when transferring cryptocurrencies from one account to another.

A consensus algorithm defines how blocks can be appended to the blockchain. It dictates which blocks are valid, how they are created and therefore indirectly how quickly they are generated. While Bitcoin relies on Proof of Work, other methods such as Proof of Stake and Proof of Authority exist. The most prominent consensus algorithm, Proof of Work, forces nodes to compete in iteratively computing hashes comprising the block data and a nonce that is incremented to find a hash value that satisfies a predetermined condition. If a node believes to be the first to have found a satisfying nonce, it publishes the block. Other nodes can easily verify a received solution by hashing the block and the nonce exactly once [START_REF] Zheng | An overview of blockchain technology: Architecture, consensus, and future trends[END_REF].

This leads to the following advantages of blockchains. First, because one block is linked to the previous one and because of the consensus algorithm, it is difficult for a single node (or a small group) to arbitrarily modify past transactions. The data stored in a blockchain is thus considered to be immutable. This is true as long as the network as a whole operates correctly. Second, the blockchain, due to its tolerance of adversarial nodes, allows the collaboration of multiple entities, possibly with differing interests, without compromising the system. A user can therefore rest assured that transactions performed on the blockchain will not be removed or arbitrarily modified and that a small group of participants cannot easily modify the blockchain to gain an advantage over other users.

Since blockchains are still relatively new, especially the second generation blockchains [START_REF] Peters | Understanding modern banking ledgers through blockchain technologies: Future of transaction processing and smart contracts on the internet of money[END_REF], this work proposes an easy to use orchestration framework for private and consortium blockchains. As a result, applications deployed or relying on blockchains can be tested at a scale comparable to the public networks. This allows applications to be verified in conditions that are similar to the production environments, and to further the understanding of the application in question and of the employed blockchain. Also experimental conditions can be actually changed to determine good and bad configurations before a real deployment, for example in terms of the underlying network topology. Moreover, the framework can be used to determine which blockchain to use for a given application, while modeling the scale and the occurrences of public blockchain networks. The framework can further be useful to future research as it can be utilized to verify theories and test proposed improvements or modifications. The framework is distributed and available on Github 1This text is presented as follows. Section II describes the mentioned orchestration framework. Section III then introduces KYC (Know Your Customer), a use case that is closely related to the financial industry. The use case is then employed to evaluate and perform experiments on the orchestration framework in Section IV. Section V discusses related work. Finally, the conclusion is given in Section VI.

II. EXPERIMENTATION FRAMEWORK

The experimentation of distributed applications like blockchains needs a highly reconfigurable and controllable environment for fine-tuning blockchain and network parameters in different scenarios. Therefore, there might be significant manual operations which lead to human errors and make it hard to reproduce experiments. Experiment management

Nancy site Nantes site Lille site Luxembourg site N N N N M N N N N SSH N N N N M N N N N N N N N M N N N M N N N N M N N N N

Orchestration Node

Fig. 1: Grid'5000 as blockchain experimentation testbed (N: transaction node, M: mining node).

tools are valuable means for researchers to automate lowlevel tasks like operating system installation and networking configuration. Also, testbeds offer controlled environments that are normally shielded from the randomness of production environments. The researchers can focus on the scientific questions to answer and forget about time-consuming, lowlevel details of experiments. In [START_REF] Buchert | A survey of general-purpose experiment management tools for distributed systems[END_REF] the authors provide an extensive list of features offered by general-purpose experiment management tools and common testbeds.

In the context of blockchain technologies, there are still many open questions related to scalability, security, privacy and service level management. Theses features need to be ensured if this technology is deployed in operational and sensitive environments, such as the financial sector. Most existing approaches for assessing the limits of different blockchain technologies rely either on simulators or virtual environments. However, these cannot accurately predict the performance in the real world, where heterogeneous blockchains nodes are geographically distributed.

Hence, in the next sections we present a large scale experimentation testbed and a novel orchestration tool for dynamically deploying blockchain platforms and smart contracts over a testbed.

A. Experimentation platform

Building a representative evaluation testbed needs a flexible environment for fine-tuning blockchain and network parameters in different scenarios. Grid'50002 is a large-scale testbed environment for experiment-driven research. A large amount of resources (1000 nodes, 8000 cores, 10G Ethernet links), scattered over many geographic sites (in France and Luxembourg), makes it an environment that provides conditions that are very close to real blockchain networks. Indeed, blockchain applications operate over a network, like the Internet, shared by different applications making congestion and message delays unpredictable. Therefore, the blockchain applications should be assessed under real conditions as accurately as possible.

The Grid'5000 platform provides a real physical hardware and networking infrastructure that is equipped with advanced measurement features to evaluate any application, such as blockchains, from different aspects with extensive tests. This can be thus leveraged to gain new and valuable knowledge related to the monitoring and orchestration of blockchain infrastructures. This knowledge is vital for enterprises that use private/consortium blockchain platforms to run their blockchain network within predefined requirements (e.g., transaction throughput and latency). So we can critically study, if a given configuration provides the optimal or an acceptable performance for a particular application scenario.

Figure 1 shows how a possible deployment of blockchain nodes on Grid'5000 can build a blockchain network over different geographic sites (i.e., Lille, Nancy, Luxembourg, Nantes), where each site can host transactions nodes (i.e., that send transactions to the network) and/or mining nodes. This ability to adapt the available Grid'5000 resources makes it possible to test various blockchain technologies and applications with heterogeneous configurations. For instance, for a given blockchain platform (e.g., Ethereum [START_REF] Wood | Ethereum: A secure, decentralised generalised transaction ledger[END_REF], [START_REF]Ethereum web site[END_REF]) we can assess the performance of the network while varying the number of mining nodes.

However, evaluating the performance of a blockchain application assuming a single parameter is too narrow because there is a multitude of parameters such as mining difficulty and Gas limit that potentially affect the general performance of the blockchain network. Moreover, some other parameters are inherited from the fact that we are dealing with distributed and decentralized systems, for example the number of participants, network topology, hardware configuration (e.g., CPU frequency, network bandwidth). Thus, an experiment management tool is necessary to control the various experimental parameters. The next section details our orchestration tool for conducting blockchain experiments on the Grid'5000 platform.

B. Blockchain orchestration tool

In the area of cloud computing, orchestration refers to the management of resources including placement and configuration of virtual machines, for example [START_REF] Wang | Scientific cloud computing: Early definition and experience[END_REF]. In our context, the blockchain orchestration tool automates the deployment of blockchain infrastructure (nodes, network) and smart contracts in a given environment. Here, we focus on two types of blockchain networks; the private and consortium ones. Because installing and managing a private blockchain environment includes significant manual work due to the many components that need to be installed, configured and monitored properly, we developed an orchestration tool to automate the blockchain infrastructure installation and deployment, and to provide a mean to control the whole life cycle of experiments.

The Grid'5000 platform offers different experiment management tools, such as experiment scheduling, resource allocation and node reconfiguration [START_REF] Cappello | Grid'5000: A large scale and highly reconfigurable grid experimental testbed[END_REF]. However, still there is no dedicated tool that can manage blockchain-based experiments. It was an important design goal to not reinvent the wheel by developing a completely new tool, but to extend the In the future, we plan to cover more blockchain platforms. Figure 2 depicts the architecture of the proposed framework. The Grid'5000 testbed (on the left) is interfaced with the Ruby-Cute module. The experiment management tool (on the right hand side) comprises the node reservation module that sends the reservation request to Ruby-Cute, which handles the resource reservations and operating system deployments. Once the resource are ready, a list of nodes (i.e., machine names) is forwarded to the blockchain deployment and configuration module, which has four main tasks to prepare the blockchain environment; Genesis file configuration setting, network initialization, miners startup, and finally configuration validation. Genesis file configuration: the genesis block is the starting block of the blockchain (block 0) and "genesis.json" is the file defining it. It looks like the "configuration" of the blockchain, as example we can set the level of difficulty to mine blocks or the Gas limit. Indeed, changing these parameters in the genesis file facilitates the creation of customized private blockchains. For instance, we can tune the "difficulty" parameter to control the speed of the block generation. Network initialization: it disseminates the genesis-file and the experiment scripts to the participating nodes. Then it initializes the blockchain client in each node. Once all nodes are running, it grabs the addresses of the nodes (e.g, enode://address:@IP:port) to construct the Static-nodes file which in-cludes the peers that all nodes should connect to in order to join the blockchain network. Miners startup: it runs all the nodes to start mining. So each node will gain some Ethers (in case of Ethereum blockchain), consumed later to deploy smart contracts and to send transactions to the network. Configuration validation: it deploys a smart contract and runs workloads. This task is essential to test the configuration of the blockchain and to make it ready and steady.

To summarize this section, we presented the functionality of the blockchain orchestration tool and how it can be used with Grid'5000 to provide a missing tool to control blockchain experiments. The next section elaborates a case study of a FinTech application. Our motivation is to show how the proposed orchestration tool and the Grid'5000 testbed can be used to evaluate the performance of the application over a large-scale testbed.

III. USE CASE: KYC SMART CONTRACT

Nowadays there is a huge number of banking transactions around the world. For instance, the Society for Worldwide Interbank Financial Telecommunication (SWIFT) has recorded 28.45 million financial transactions per day. Hence, to avoid transaction fraud it is vital to have proper techniques for verifying the identity of the parties involved in a payment transaction and also their rights to perform and/or receive a payment transaction.

The term 'Know Your Customer' (KYC) is widely used in the financial world by financial institutions and other regulated companies to identify their clients before doing financial business with them. The process of KYC is as follows: if a client needs to make a payment transaction from his/her bank account to another bank account through a payment provider, the payment provider does the KYC to validate the client's identity for instance by the client's name, from the bank where the money was transferred from. The client's name is then crosschecked with the name stated by the client. during the sign-up of the payment provider's service [START_REF] Mainelli | Sharing ledgers for sharing economies: an exploration of mutual distributed ledgers (aka blockchain technology)[END_REF]. Also the client's name may also be crosschecked against third-party databases like World-Check6 , which helps organizations fight financial crime.

A. Traditional KYC problems

Performing KYC is an easy task in countries that provide electronic services to verify a persons identity. However, if such services are not available to financial institutions it is risky to accept individuals as clients [START_REF] Geer | Method and system for identity and know your customer verification through credit card transactions in combination with internet based social data[END_REF]. Therefore, the KYC process performed when on-boarding a new client is timeconsuming and each financial institution must do its own KYC. For instance, when a client needs to open a bank account, the bank sends the client's information to the registries, which store the client's information in their databases and the customer becomes "KYC Compliant". This process is repeated every time the client needs to open a new bank account.

B. Blockchains to the rescue

Blockchain technology can solve many of the problems related to KYC like the on-boarding issue. The blockchain of the public distributed ledger can disseminate the client's information across many banks, once verified. Thus, a KYC once performed can be accessed by other financial institutions with unique authorization from the client. This will make the KYC process much easier, simpler, less time consuming and cost-effective. Second, the centralized databases-based KYC solutions also expose a vulnerability. While in blockchain, the KYC data is replicated across many various nodes, which makes it immutable and traceable, because of blockchain's append-only data structure [START_REF] Mainelli | Sharing ledgers for sharing economies: an exploration of mutual distributed ledgers (aka blockchain technology)[END_REF].

C. Blockchain-based KYC POC

This use case demonstrates how the blockchain can be used to serve the KYC process. Figure3 illustrates the use case of the KYC. The steps are explained as follows:

1) A client allows a bank to perform KYC by providing documents like identity card, financial situation, etc. 2) The bank will review and validate identity and financial information about the client and approve him/her as 'KYC Compliant'.

3) The bank adds KYC information and status to a blockchain platform to confirm it has been verified. 4) The bank give the client a token that can be used as a proof of his/her KYC status. 5) A third party can be given the authorization by the client to check his KYC status. 6) The intended bank can check the KYC information.

D. Blockchain KYC POC Implementation

To implement the blockchain KYC we used the Ethereum blockchain platform and the Solidity7 programming language to write the smart contract. The source code of the smart Fig. 3: The workflow of the KYC POC contract is available on Github8 Due to the storage limitation of blockchains, we use a Peer-to-Peer file system, the Inter-Planetary File System (IPFS), to store the KYC documents like identity card and passport [START_REF] Benet | Ipfs-content addressed, versioned, p2p file system[END_REF]. The main advantages of IPFS are: it provides a permanent and decentralized method of storing and sharing files and it has no single point-of-failure compared to centralized data storage systems. Therefore, IPFS is in use at: banks, legal archives, blockchain companies and smart contract applications [START_REF]Blockchains and the web: IPFS[END_REF]. In the KYC case, each file stored in IPFS is given a unique fingerprint (cryptographic hash), which will be stored in the KYC smart contract.

IV. EVALUATION AND EXPERIMENTAL RESULTS

As explained in section II the performance of a blockchainbased application is difficult to evaluate with respect to one single parameter, since there are many parameters that control the performance of the blockchain environment. In this section, we elaborate how the orchestration tool presented in SectionII-B facilitates the evaluations using the Grid'5000 testbed. The evaluation starts with reserving nodes, so as input to our orchestration tool we specify the number of nodes to be reserved per site and the duration of the experiments. Once the nodes are ready, our tool goes through the steps explained in II-B to deploy and to configure a private blockchain and setup the KYC application.

A scripted workload deploys the KYC smart contract and starts the workload generator. The workload simulates KYC client registration events as a Poisson distribution, as its widely used to simulate queues like the arriving of emails or calls [START_REF]Statistics: The poisson distribution[END_REF]. Our aim is to show how the proposed framework can be used to study the behavior of blockchain, with specific configurations, under massive KYC client registration requests.

For this experiment, we reserved 25 nodes scattered over five different geographic sites. The Gas-limit As shown in Figure 4, minimizing the number of mining nodes does not have a significant effect on the latency, because the workload is small. However, there is a trade-off between lowering the number of mining nodes and the security of blockchain network, because more mining nodes means more nodes validate the transactions.

Table II illustrates the results for tuning the Mean of the Poisson distribution (the shaded column) while other parameters are fixed. We also noticed that the latency does not change significantly if the delay between transactions varied from 500 ms to 10 ms. Thus, we plan to study the location of the nodes sending transactions to the network. For example, if the transactions are generated from Lille (north of France) and the mining nodes are located in Sophia (South of France). As the Grid'5000 infrastructure is well connected there is no issue to have it distributed, so we expect to get results that reflect the pure behavior of blockchain network protocol. We believe it will enrich our understanding of the application in question and of the employed blockchain.

V. RELATED WORK

Since Bitcoin [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF], blockchains have been gaining in popularity. They are used in vastly different areas, for example to perform payments as in Bitcoin, together with IoT devices as in [START_REF] Christidis | Blockchains and smart contracts for the internet of things[END_REF], or to allow users to implement smart contracts that are executed on the blockchain [START_REF] Wood | Ethereum: A secure, decentralised generalised transaction ledger[END_REF].

Although the public blockchain networks comprise several thousand nodes (Bitcoin and Ethereum), there is also a need for the private execution of blockchain transactions as mentioned in [START_REF] Li | Towards scalable and private industrial blockchains[END_REF]. For example, Multichain [START_REF] Multichain | [END_REF] is a permissioned blockchain, wherefore only participants who have been given the corresponding permissions can view or interact with the blockchain. Furthermore, [START_REF] Li | Towards scalable and private industrial blockchains[END_REF] proposes an approach with a system of interacting satellite chains with which it is possible to share transactions only with selected entities.

As discussed in [START_REF] Zheng | An overview of blockchain technology: Architecture, consensus, and future trends[END_REF], different blockchain variants share a common basis, the chain of blocks, but may differ greatly in other aspects, such as the consensus algorithm. The latter also impacts the performance of blockchains, for example the scalability [START_REF] Croman | On scaling decentralized blockchains[END_REF]. Consequently, Proof-of-Work blockchains in particular have been given consideration, especially with respect to improving the scalability. [START_REF] Eyal | Bitcoin-ng: A scalable blockchain protocol[END_REF] proposes a new blockchain protocol based on epochs and leaders that propose new blocks at a fast rate, while [START_REF] Poon | The bitcoin lightning network: Scalable off-chain instant payments[END_REF] and [START_REF]Raiden network[END_REF] use offblockchain payment channels.

In addition, research has been conducted on analyzing blockchains and providing tools to stress different blockchain components. On one hand, [START_REF] Pongnumkul | Performance analysis of private blockchain platforms in varying workloads[END_REF] analyzes the performance of private blockchains. To do this, they utilize a single machine located in a cloud and deploy either Hyperledger [START_REF]Hyperledger fabric web site[END_REF] or Ethereum blockchains. Due to the single machine setup, consensus mechanisms are not considered in that work. On the other hand, [START_REF] Dinh | Blockbench: A framework for analyzing private blockchains[END_REF] considers multiple layers within a blockchain system and proposes workloads that stress a target layer or the blockchain system as a whole. Multiple machines located in a cluster are used simultaneously, and the consensus algorithm is considered.

As opposed to these works, this paper provides an easy to use framework that distributes nodes to distant geographical sites, thus providing conditions that are similar to real blockchain networks that can be scattered either over a country, a continent or the world. Furthermore, the tool allows the configuration of the blockchain nodes. The proposed tool can be used for the following purposes. First, custom blockchain deployments can be tested, verified and adapted before being used in a production environment. Second, new implementations dealing with the performance of blockchains can be analyzed at a large scale. Third, measurements can be performed under varying conditions, such as the location of the nodes or the blockchain configuration, again, at large scale.

To achieve this, the tool proposed herein uses the Grid'5000 platform. Grid'5000 has been presented in [START_REF] Cappello | Grid'5000: A large scale and highly reconfigurable grid experimental testbed[END_REF] and is supported by multiple sites in France and one in Luxembourg.

VI. CONCLUSION

A blockchain experimentation framework is a valuable means for researchers and developers to further their understanding of the blockchain technology. Therefore, there is a pressing need for a highly reconfigurable and controllable environment to be able to experiment with blockchains extensively. In this paper, we proposed using the Grid'5000 a large scale distributed platform that can easily be controlled and reconfigured. In parallel, we present our orchestration tool that provides a means to control and manage private blockchain environments over Grid'5000. As a direct application of using this framework, the blockchain KYC application has been discussed. A POC has been implemented. We provided preliminary and basic results of how the framework (the testbed and the orchestration tool) can be used to conduct blockchain evaluation experiments on a large scale real environment.

As future work, we still have many open questions to answer; regrading the evaluation of blockchain environments from different aspects and more focus will be given to security and privacy issues of private blockchain applications. Also we need to take our orchestration tool a step further to support other common-known blockchain platforms like IBM Hyperledger. More advanced technology will be integrated in our orchestration framework, mainly the Ansible 9 automation technology.

Fig. 4 :

 4 Fig. 4: Tuning the number of mining nodes vs, the latency time to handle 100 clients registration

TABLE I :

 I KYC POC evaluation results (Tuning: number of mining nodes)

	# Nodes	# Mining nodes	Gas Limit	Mining difficulty	# Client	Mean Poisson (ms)	Latency (sec)
	25	25	0x8000000000000	0x5ffffff	100	10	383.48
	25	20	0x8000000000000	0x5ffffff	100	10	419
	25	18	0x8000000000000	0x5ffffff	100	10	413
	25	15	0x8000000000000	0x5ffffff	100	10	381.8
	25	13	0x8000000000000	0x5ffffff	100	10	418.72

TABLE II :

 II KYC POC evaluation results (Tuning: Mean Poisson distribution)

			# Nodes	# Mining nodes		Gas Limit		Mining difficulty	# Client	Mean Poisson (ms)	Latency (sec)
			25		25	0x8000000000000	0x5ffffff	100	500	376.1
			25		25	0x8000000000000	0x5ffffff	100	50	386.34
			25		25	0x8000000000000	0x5ffffff	100	10	383.48
		400
	Time duration (sec)	350
		300
		12	14	16	18	20	22	24	26
					Number of mining nodes

https://github.com/wshbair/Blockchain-Orechtration-Framework

https://www.grid5000.fr

https://github.com/ruby-cute/ruby-cute

http://www.rubydoc.info/github/ruby-cute/ruby-cute/Cute/G5K/API

https://www.swift.com/about-us/swift-fin-traffic-figures

https://risk.thomsonreuters.com

https://solidity.readthedocs.io/en/develop/

https://github.com/wshbair/Blockchain-Orechtration-Framework/KYC

VII. ACKNOWLEDGEMENTS

Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations. The present project is supported by the National Research Fund, Luxembourg under grant agreement number 11785982.


Is More Information Always Better? An Analysis Applied to Information-Based Policies for Environmental Protection

Keywords: Informational elasticity, Information provision, Information overload. JEL Classification Numbers: Q50, D80, K20

Environmental policy has intensively focused on information-based instruments that seek to change agents' behavior through information provision. This information provision is generally considered as likely to ultimately improve environmental quality. We suggest a new and complementary way to consider information-based instruments. We formalize the insight that information provision differs from information impact by introducing the concept of informational elasticity. We show that beyond an optimum level, an additional information load, regardless of the information quality, could do more harm than good. Indeed, some perverse effects could occur, resulting in a worse overall impact. Several policy and strategic implications such as the potential conflict with the normative right-to-know principle and the manipulation of 'information overload' are stressed.

I. Introduction

During the last two decades, environmental economists end other scientists turned their attention to information-based policies in response to dysfunctional markets. According to [START_REF] Tietenberg | Disclosure Strategies for Pollution Control[END_REF], the conceptual economic foundation for disclosure strategies is the Coase Theorem, which asserts that socially optimal risk sharing can be obtained if all stakeholders can negotiate at a very low cost.

Information asymmetries constitute an impediment to such private bargaining. Removing or at least attenuating such information asymmetries may enable to reach a Pareto-optimal outcome [START_REF] Kleindorfer | Informational Regulation of Environmental Risks[END_REF][START_REF] Case | The Law and Economics of Environmental Information as Regulation[END_REF]. In line with economists' arguments "preaching" the good impact of information provision, environmental policy has intensively focused on information-based instruments developed in order to support or replace existing instruments, i.e., command-and-control and market-based instruments. These informational policies encompass a broad range of instruments from mandatory disclosure programs such as the Toxic Release Inventory (TRI 1 ) in the USA or the New Economic Regulation Act in France to voluntary programs such as ecolabeling schemes 1 "The Toxics Release Inventory (TRI) is a publicly available Environmental Protection Agency (EPA) database that contains information on toxic chemical releases and other waste management activities reported annually by certain covered industry groups as well as federal facilities. This inventory was established under the Emergency Planning and Community Right-to-Know Act of 1986 (EPCRA) and expanded by the Pollution Prevention Act of 1990." (http://www.epa.gov/tri/, visited on November, 4 th , 2004).

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 3 implemented in numerous countries. A common feature of these informational approaches is their aim to change directly or indirectly the behavior of economic agents, such as consumers, insurers, investors and other stakeholders. According to Harrison and Antweiler (2001, p. 1), "informational strategies for environmental protection are predicated on the assumption that firms will respond to pressure from consumers, workers, investors, and communities armed with more complete information about those firms' environmental practices". By disclosing information, agents who have it can make informed decisions and better protect their interests, whatever they may be [START_REF] Paredes | Blinded by the Light: Information Overload and its Consequences for Securities Regulation[END_REF]. The potential for such an increasing role for disclosure strategies is reinforced by the continual decrease of the cost of information collection, aggregation and dissemination.

Several economic studies are devoted to the informational disclosure impact on the environment. For example, several recent empirical studies [START_REF] Hamilton | Pollution as News: Media and Stock Market Reactions to the Toxic Release Inventory Data[END_REF][START_REF] Konar | Information as Regulation: The Effect of Community Right to Know Laws on Toxic Emissions[END_REF][START_REF] Khanna | Toxic Release Information: A Policy Tool for Environmental Protection[END_REF] use TRI data to look at the effect of publicizing information on firms' stock market performance, which in turn influence firms' emissions. However, the results are mitigated. While some economists pointed out the good impact of information disclosure, some others stressed its uselessness (for comprehensive surveys of the growing literature, see Magat and Viscusi, 1992;[START_REF] Tietenberg | Disclosure Strategies for Pollution Control[END_REF][START_REF] Case | The Law and Economics of Environmental Information as Regulation[END_REF][START_REF] Esty | Environmental Protection in the Information Age[END_REF][START_REF] Mol | Environmental governance in the Information Age: the emergence of informational governance[END_REF]; see also [START_REF] Wynne | The Emperor's New Ecologos? A Critical Review of the Scientific Certification Systems Environmental Report Cards and the Green Seal Certification Mark Programs[END_REF] for an application to ecolabeling schemes). In this paper, we attempt to reconcile divergent views on the environmental effectiveness of information-based instruments, by suggesting a complementary way to consider them. This paper differs from several to date by formalizing the insight that information provision differs from information impact 2 . Access to information is not a substitute for abilities to process it.

Little attention has been paid to how information is used by the demand side. If deciders do not or can not process information effectively, information disclosure may be counterproductive [START_REF] Paredes | Blinded by the Light: Information Overload and its Consequences for Securities Regulation[END_REF] 3 . Another major point of this contribution is to consider that information overload can be 2 In line with Loewenstein (1999, p. 25) we attempt modestly to bring some "psychological insights to bear on economic phenomena".

Comment citer ce document : Bougherara, D., Grolleau, G., [START_REF] Bougherara | Is more information always better ? An analysis applied to information-based policies for environmental protection[END_REF]. Is more information always better ? An analysis applied to information-based policies for environmental protection. 4 instrumentalized in order to disadvantage rivals [START_REF] Hilke | Noisy Advertising and the Predation Rule in Antitrust Analysis[END_REF] or other agents, e.g., public authorities overwhelmed with huge quantities of true but useless information. Such a strategy is likely to increase transaction costs.

We introduce the concept of informational elasticity and show that beyond an optimum level, an additional information load, regardless of its qualitative dimensions, could do more harm than good.

Indeed, while providing more information, until information symmetry, is generally considered as likely to ultimately improve environmental quality, we argue that some adverse effects could occur, resulting in a worse overall impact than before information provision 4 . In some cases, information overload 5 may lead individuals to make worse decisions compared to a situation with less information. Let us briefly expose some examples stressing the relevance of studying such a topic.

When the Environmental Protection Agency (EPA, 1995 6 ) considered expanding the type of information that must be reported under the Toxic Release Inventory program, the Chemical Manufacturers Association (CMA) "stated that collecting and reporting volumes of use would not necessarily measure source reduction efforts. In addition to causing "information overload", the CMA claimed that collected materials accounting data would not be complete enough to produce an accurate picture of what was really happening inside a facility's many processes." The debate was clearly stated as follows: "A key public policy question is "How much information should the MIC control room of the Bhopal plant, at the time of the accident, the operators were extremely overloaded and found it "virtually impossible to look after the 70-odd panels, indicators and console and keep a check on all the relevant parameters" (Agarwal et. al., 1985, quoted by Meshkati, 1991).

4 More information may cause other unintended and negative effects such as increasing compliance costs and costs to process information, opportunity costs and chilling risk-taking [START_REF] Paredes | Blinded by the Light: Information Overload and its Consequences for Securities Regulation[END_REF].

5 "A useful way of thinking about the concept of information overload is that it arises when the incremental decreases in decision effectiveness due to additional information quantity are greater than the incremental increases in decision effectiveness due to the additional information quality" (Keller and Staelin, 1987, p. 202).

Comment citer ce document : Bougherara, D., Grolleau, G., [START_REF] Bougherara | Is more information always better ? An analysis applied to information-based policies for environmental protection[END_REF]. Is more information always better ? An analysis applied to information-based policies for environmental protection. 6 extensive discussion about information overload in the context of securities regulation). 8 " As stressed by the previous controversy, potential or real 'information overload' may also be used as an argument in order to avoid or weaken additional information-based policies Information provision may be legitimated on several grounds such as the public desire for transparency and access to information, the bureaucratic impetus for centrally available and reliable information and the rise in public concern about particular environmental hazards. A kind of 'technology push' may also partially explain the development of information-based policies [START_REF] Mclauchlan | Environmental Democracy and Stewardship through Land and Resource Information: The Case of the Land Gazette[END_REF][START_REF] Esty | Environmental Protection in the Information Age[END_REF]. Information provision is said to enable agents with environmental preferences to make fully informed decisions. Note that we analyze information provision from an economic efficiency viewpoint rather than from an ethical standpoint such as the so-called right-to-know principle. Assuming such restriction, we focus our attention on whether more information is always desirable or not.

The remainder of the paper is as follows. In next section we propose a diagrammatic description of information-based policies. We define the concept of informational elasticity and suggest some methods to measure it. In section III, we present a simple model that shows under which conditions more information may lead to perverse effects in terms of the expected environmental improvement.

Section IV presents policy implications that can be derived from our analysis. Section V concludes.

8 Another example about the risks of environmental information releases is developed in [START_REF] Mclauchlan | Environmental Democracy and Stewardship through Land and Resource Information: The Case of the Land Gazette[END_REF].

Comment citer ce document : Bougherara, D., Grolleau, G., [START_REF] Bougherara | Is more information always better ? An analysis applied to information-based policies for environmental protection[END_REF]. Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

7

II. Informational elasticity and the classification of information-based policies

"One cannot determine the effect of a law by simply looking at the law itself -at the conduct the law requires. Instead, one must determine how people will respond to the law." [START_REF] Coase | The Problem of Social Cost[END_REF] We provide a general description of information-based policies before introducing the concept of informational elasticity. Information-based policies involve the intervention of several agents. To make the exposition simple, we provide a diagrammatic view of the general mechanism sustaining those policies in figure 1. The Information Source is the party that holds private information to be delivered to the Information Provider. The latter gathers information, standardizes it and releases it to the Decider. The Decider is the target of the policy whose decision is to be influenced. The Decider usually takes decisions in a context more or less loaded with information 9 . Moreover, his decisions may vary in quality. Quality of decisions may be defined as the accurateness of the decider's behavior aimed at leading to a given impact depending on the quantity of information. The concept of decision quality or decision effectiveness and its operationalization has been extensively debated in the literature (see [START_REF] Jacoby | Information Load and Decision Quality: Some Contested Issues[END_REF][START_REF] Jacoby | Perspectives on Information Overload[END_REF][START_REF] Keller | Effects of Quality and Quantity of Information on Decision Effectiveness[END_REF] for discussions devoted to this question) 10 . The extensive review of this literature is out of scope of our contribution but we cannot omit the seminal work of [START_REF] Simon | Is more information always better ? An analysis applied to information-based policies for environmental protection[END_REF]. [START_REF] Simon | Is more information always better ? An analysis applied to information-based policies for environmental protection[END_REF] points out that individuals are boundedly rational and have limited cognitive abilities to store, process and interpret information.

Moreover they are vulnerable to several cognitive biases. Agents will satisfice rather than optimize.

They economize on cognitive efforts by adopting heuristics but are also subject to biases (Tversky 9 The context is a fuzzy and multidimensional concept used to characterize the informational environment. From a given point corresponding to the sum of past information released, this information environment can be considered as the number of impulses that compete to capture the attention of agents.

10 The notion of decision effectiveness in marketing literature has primarily been concerned with product choice made by prospective consumers under conditions of different informational loads. Information overload occurs when the prospective buyer is unable to complete the buying task successfully, as might be evidenced, for example, when an objectively inferior product choice is made by a high proportion of consumers under high load conditions. "The underlying cause of this phenomenon is assumed to be due to a "limited capacity" processing system, and that approaching this limit results in decisional errors" [START_REF] Owen | Clarifying the Simple Assumption of the Information Load Paradigm[END_REF].

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development ,10 (3),197198199200201202203204205206207208209210211212213 , 1974). Nevertheless, without purporting to resolve the question, we consider that decision quality can be viewed as the concordance between the ideal choice according to the agent's preferences among a set of available alternatives and the real choice achieved after information releases. Moreover, we consider that the operationalization of decision quality is far from easy and may include several items such as decision accuracy, time costs, uncertainty reduction and so on (Jacoby, 1984, p. 433).

[Insert Figure 1 here]

For ease of exposition, we distinguish several categories of agents, i.e., the information source, information provider and decider. Such distinctions are rather diagrammatic because the dividing line is frequently fuzzy in the real world. Sometimes the information source and the information provider are confounded such as in the New Economic Regulation Act. Moreover, the final decision can be influenced through several channels, more or less direct. Indeed, in several situations certain agents are the end-deciders, e.g., a pollutant firm, in the sense that they undertake the technical actions that will change the environmental quality. However, their decision more or less favorable to the environment can be influenced by intermediate deciders, such as investors. For example, investors may select firms where they want to invest according to their environmental performance. Therefore, they can push polluting firms to improve their environmental results by undertaking actions favorable to the environment. Lastly, note that a more complex model can enable us to take into account several feedback effects, e.g., when deciders influence the information collected and provided.

[Insert Table 1 here]

At this point, we introduce the informational elasticity ε , which measures the responsiveness of a given decider, namely the quality of its decisions, to a given change in the quantity of information released by the information provider. In the case of the Toxic Release Inventory, it measures the The operationalization of the variable 'information quantity' is not analyzed here. Obviously, this necessary task is far from easy and interested readers can usefully refer to [START_REF] Jacoby | Information Load and Decision Quality: Some Contested Issues[END_REF], [START_REF] Jacoby | Perspectives on Information Overload[END_REF] and [START_REF] Lurie | Decision Making in Information-Rich Environments: The Role of Information Structure[END_REF] for different methods potentially applicable to our example. In the case of the New Economic Regulation Act, the informational elasticity measures the quality of decisions of investors to a given change in the quantity of information released by firms through their annual report. Quality of decisions may then measure the ability of investors to process information and take the right action leading to an environmental improvement in accordance with their preferences. It refers to the comparison between the current decisions taken by the decider and the decision he would have taken if his processing abilities were infinite and information was complete. Of course, we implicitly postulate that the decider has eco-friendly preferences. Information provision should therefore entail a positive impact, i.e., an environmental improvement.

Using the conventional equation in the case of a continuous and derivable function, the informational elasticity ε is given by:

I I Q dQ D dD = ε (1)
I I Q Q Q - = ∆ ). Note that 0 > ∆ I Q
because we postulate an increase in the quantity of information released by the information provider.

Increasing the quantity of information is usually considered as a way to improve the quality of decisions ( 0 > ε ). However, in some cases, it may lead to a decrease in the quality of decisions. For example, [START_REF] Wynne | The Emperor's New Ecologos? A Critical Review of the Scientific Certification Systems Environmental Report Cards and the Green Seal Certification Mark Programs[END_REF] is rather skeptic about Environmental Report Cards that are labels listing the impact of a product for several environmental fields. The aim of report cards is to provide raw information without any judgment value to enable consumers' sovereign choice. However, such a huge amount of information may be difficult to process for consumers and decrease the quality of their decisions ( 0 < ε ). Informational elasticity may also be nil ( 0 = ε ). If prior perceptions of deciders correspond to the released information, the TRI may have no impact. [START_REF] Khanna | Toxic Release Information: A Policy Tool for Environmental Protection[END_REF] note that "the greater the prior environmental information that investors have about a firm, the smaller the impact of the provision of additional information on their stock market returns" 11 .

The classification of information-based policies according to their informational elasticity is particularly relevant for policy makers who aim at maximizing the efficiency of funds invested in such policies. This point is briefly developed in section IV. An empirical way to determine the environmental elasticity of information-based policies is to realize well-designed surveys to simulate the reaction of deciders to an increase in the release of information. Another way is to exploit data related to the impact of an information-based policy on behaviors. A third way to test this informational elasticity could be to achieve pilot studies in small areas where information is released and subsequent changes recorded. Finally, experiments enabling the control of the informational 11 Although we somewhat emphasized the investor in this section, we admit that he has no direct impact on the environment. His behavior is supposed to send a signal (through stock prices) to the firm, which is then supposed to take actions that impact the environment. Achieving a stronger connection in this regard may constitute a way to be closer to the realm.

Comment

III. An analytical framework

We are interested in determining the overall impact 12 (or policy effectiveness) I of a change in the release of information. I is a function of the quality of decisions made by the decider D which is itself a function of the quantity of information I Q and the informational load of the context in which decisions are made C13 so that we can write

)) ( ), ( (

I I Q C Q D I I =
. Thus, the total differential of

I is:         ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ = I I I I dQ Q C C D dQ Q D D

I dI

Equation (1) shows that the variation in the overall impact due to an increase in

I Q ( 0 > I dQ
) is the addition of two effects.

A Quality of Decisions Effect

The first term of (1),

I I dQ Q D D I ∂ ∂ ∂ ∂
, corresponds to the effect on I of a variation in the quality of decisions due to an increase in the quantity of information. The higher the quality of decisions is, the higher the overall impact is ( 0 > ∂ ∂

D I

). Therefore, the overall sign of the Quality of Decisions Effect 12 The higher the overall impact is, the lower the pollution is. This impact can be obviously associated with society's welfare by assuming that ceteris paribus, the society prefers a less polluted environment. Then,

Comment

I I dQ Q D dD ∂ ∂ = with          < < ∂ ∂ = = ∂ ∂ > > ∂ ∂ 0 if 0 0 if 0 0 if 0 ε ε ε I I I Q D Q D Q D
We use the psychological law of Yerkes-Dodson (1908) to determine the sign of the Quality of Decisions Effect. The essence of this law is the relationship between performance, e.g., quality of decisions and pressure, e.g., the information load (Leibenstein, 1997) 14 . If we visualize the quality of decisions on the ordinate and the quantity of information on the abscissa, the Yerkes-Dodson law may be represented by a roughly inverted-U curve (figure 2) 15 . As informational load increases, quality of decisions comes closer to maximization. Beyond some point informational load may be so high that decision-makers find it rather difficult to cope.

[Insert Figure 2 here]

A Context Effect 14 An inspiring source for our model is the so called 'Yerkes-Dodson law'. Although this point is out of scope of our paper, this 'law' is intuitively convincing and seems to benefit from a tradition of empirical support [START_REF] Broadhurst | The Interaction of Task Difficulty and Motivation: The Yerkes-Dodson Law Revisited[END_REF][START_REF] Duffy | Activation and Behavior[END_REF]. 15 Admitting that economic agents face information costs that may be increasing non-linearly with the number of choices or the number of information dimensions to evaluate may constitute an attempt to express the Yerkes-Dodson law in economic terms.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

13

The second term of (1), In sum, an adverse effect on the overall impact17 may appear each time negative effects exceed the positive one, if any (case c in table 2).

I I dQ Q C C D D I ∂ ∂ ∂ ∂ ∂ ∂ ,

[Insert table 2 here]

Our analysis shows that the Quality of Decisions Effect is determinant and must be sufficiently positive to overcome the negative effect of the context informational load. Its effect is crucial in determining the effect of information-based policies.18 16 We make an implicit assumption. Namely, as soon as information is released, the Context Effect becomes negative. We could have considered the case where the Context Effect is nil up to a threshold of the quantity of information. Above this threshold, the Context Effect becomes negative. To make things simple, we do not consider this case.

Presumably, what is considered noise (C) from the view of environmental problem may be 'useful' information seen in relation to other problems the agent solves (e.g., consumption optimization). Consequently, when capturing information overload, the model must take account of the welfare cost that environmental information provision has when it 'crowds out' attention given to other non-environmental (but for the agents welfare still important) problems.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

14

IV. Policy considerations for introducing information-based instruments

The policy implications developed are necessarily tentative. Introducing information-based policies can ultimately motivate polluters to reduce their emissions. Under a ceteris paribus clause, informational elasticity allows to compare different scenarios where the informational elasticity (and the subsequent environmental improvement) varies among sectors and/or among groups of deciders.

Computing the informational elasticity can guide policymakers in selecting sectors and/or deciders for which information based-instruments would make the most significant environmental improvement (environmental effectiveness) for a given amount of resources (economic efficiency).

More concretely, if we postulate that the ultimate aim of information provision is an overall environmental improvement (and not only ethical considerations such as the 'right to know'), is it better to provide information to investors, consumers or firms? Indeed the information design and dissemination varies according to the targeted agents and therefore the implied costs. Different users can be expected to become overloaded at different levels and to different extents, stressing the importance of tailoring disclosure [START_REF] Paredes | Blinded by the Light: Information Overload and its Consequences for Securities Regulation[END_REF]. Informational elasticity provides a partial reply to the previous question by indicating to what extent 1$ invested in information provision will change the targeted agents' behavior and therefore improve the environment quality. The empirical tests suggested in the second section can help policy designers to better allocate scarce resources and generate higher environmental improvement, or at least avoid some hidden perverse effects by introducing an information-based policy for an inappropriate sector or targeting less sensitive deciders. Our analysis does not conclude that policy makers have to ban information dissemination in certain circumstances, but stresses the possible need of complementary measures e.g., educating deciders or increasing their processing capacities19 . Information spillovers are likely to occur and where consumer choice is a function of the quantity of information as well as his/her decision-making environment or context. This formulation, then, would allow the "quality" of a consumer's decision to depend on both the quantity of information and the context. This is an important point as the same quantity of information can have different effects on the agent decision depending on the context in which the agent uses the information.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 15 information provision can affect more than the targeted population, e.g., consumers' information can also influence investors' decisions. These indirect effects should be integrated in a more complex model where they can strengthen or weaken the overall effectiveness of the information-based policy.

The model proposed above allows the integration of the effects of the informational context ex ante, i.e., the state of the information context before the introduction of the information-based instrument.

It can also be computed by simulating different scenarios of manipulation of this context by strategic agents. Indeed, some agents can provide additional information in order to overload information recipients. The potential effectiveness of an information-based instrument can be weakened by the strategic use of information overload, which may increase deciders' satisfaction but decrease the quality of their decisions [START_REF] O'reilly | Individuals and Information Overload in Organizations: Is More Necessarily Better?[END_REF]. Indeed, once the informational threshold of deciders is exceeded, additional information, regardless of its reliability, may generate some perverse effects, by decreasing the quality of decisions. Strategic agents can inundate or overload the targeted deciders of the information-based instruments by true but inappropriate information, making deciders less sensitive (or not sensitive at all and maybe counter-sensitive) to public provision of appropriate environmental information. Such information overload may be used to raise rivals' costs or lower rivals' revenues (Salop and Scheffman, 1998;See Hilke and Nelson, 1984 for an insightful application to 'noisy advertising'). For example, a strategic incumbent threatened by the launch of an ecolabeled product can raise switching costs of consumers by releasing additional information on the 'ecofriendliness' of the competitor 20 . Such questions generate product "fear, doubt and uncertainty"

(the so-called FUD strategy in computer markets) among consumers and may force the ecofriendly competitor to bear extra costs to convince consumers 21 .

20 Such strategy often relies on two mechanisms -rather difficult to disentangle -the use of information overload but also on the questioning of the competitor's reliability.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

16

According to Simon, "what information consumes is rather obvious: it consumes the attention of its recipients. Hence a wealth of information creates a poverty of attention, and a need to allocate that attention efficiently among the overabundance of information sources that might consume it 22 ."

Consequently, creating such a 'noisy informational context' may lead to 'anaesthetize' deciders.

Recently, the German Federal Environmental Agency has stressed the negative effects of huge amounts of environmental information aiming at influencing the consumer, among other impulses for attention: "The flood of other ecolabels also poses a problem for the first environmental label [Blue Angel]. A great deal of packaging is meanwhile emblazoned with half-a-dozen badges all of them courting the customer's favour. Attracting attention has become more difficult. (…) The average person is confronted daily with 3000 advertising impulses" (German Federal Environmental Agency, 2002 23 ). Indeed, once their attention is consumed by other information, it is not available for environmental information. Consequently, the multiplicity of ecolabeling schemes may generate a testable hypothesis for further research, i.e., "Has the increase in the number of competing eco-claims reduced their efficacy to influence consumer behaviour?" Such strategic behaviors can legitimize the intervention of public authorities to define and enforce 'rules of the game' [START_REF] North | Institutions, Institutional Change and Economic Performance, Political Economy of Institutions and Decisions[END_REF] aiming at regulating information release. Such rules can enter in conflict with other principles, based on ethical grounds such as the 'right to know' or the 'freedom of speech'. Training and education may improve processing abilities. Note that some groups or specific devices such as associations, experts, information systems or competitors may adopt counter strategies. Equipped with higher processing abilities they may decipher strategic complex information or reduce the information flows aiming at 'destabilizing' deciders.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 17

Although information overload may be counterproductive in terms of environmental performance, policy makers may legitimize such additional information releases on ethical grounds. More formally, all other things being equal, let us simply assume that the society welfare W results from exercising the right to know R and improving the environment I that are both function of the quantity of information , i.e.,

)) ( ), ( (

i i Q I Q R W . I I I I dQ Q I I W dQ Q R R W W ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ =
Up to a certain quantity of information released i.e., * I Q , the indirect effects of additional information on the society welfare are opposite, i. e.

0 0 < ∂ ∂ ∂ ∂ > ∂ ∂ ∂ ∂ I I Q I I W and Q R R W . If I I Q I I W Q R R W ∂ ∂ ∂ ∂ > ∂ ∂ ∂ ∂ , then 0 > dW
and releasing additional information is beneficial to the overall society welfare despite the detrimental effect of informational overload on the environment.

In other words, an information overload may be desirable if the society values more the right to know than the negative consequences that is to say, a reduced environmental effectiveness, resulting from this information overload.

Lastly, an important implication of limited information processing ability is that command-andcontrol can work better than information provision. For example, suppose that there were no regulation of food or drugs. To be sure he is not buying dangerous or ineffective products, the individual would have to do research about everything you buy. There would be a colossal wasteful duplication of effort as each individual tried to determine whether products are safe. Instead, individuals delegate basic decisions to the government that does not allow harmful food or drugs on the market. Consequently, the lives of individuals are greatly simplified. Consequently, command and control approaches in environmental regulation may reduce the set of alternatives among which 18 individuals choose and economize on transaction costs due to the non-processing of huge amounts of information for each every product.

V. Conclusion

We have introduced the concept of informational elasticity that may help policy makers in designing and implementing more effective information strategies for environmental protection. We have also showed that the information symmetry of 'walrasian' markets is not always desirable and how information-based instruments can generate some perverse effects on the environment. The considered source of the 'perverse effect' differs from the previous literature (mainly focused on asymmetric information), notably by introducing psychological considerations (limited processing capacities, divergence between desired information load for satisfaction and optimal performance) in the decision making process. In certain plausible circumstances, deliberate ignorance may be rational. Although we have focused our attention on information strategies for environmental protection schemes, the framework and the results are generic and can be easily applied to numerous similar situations.

Moreover, by postulating that policy makers seek to improve the environment, information-based policies can be more efficient and environmentally effective for certain sectors and/or deciders (positive and high information elasticity) than others. In other words, the selection of targeted sectors and/or deciders matters. To communicate effectively, it may be advantageous to limit the provided information. If the well-intentioned sender knows the recipient will not have time to read a 12-page report, he is better off writing a shorter report that focuses on the things that he considers the most important. In some cases, information-based instruments schemes can need complementary devices to achieve their promises such as decider education to process available information or devices susceptible to increase the informational threshold of targeted deciders24 .

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

19

The main results have been derived from a generic analytical framework and under very simplifying assumptions 25 . Many extensions can be analyzed such as the combination of other related effects mentioned above. Moreover, the model assumes a single decision-maker and a single channel of impact. In many cases information-based policies are expected to impact investors, consumers, voters (who might be persuaded to contact their legislator for protection), even employees (who might prefer to work for a "socially responsible" firm). This logic suggests that at least for some information-based policies many markets and many decision-makers could be involved. The model treats all information-based contexts as homogeneous. Two common settings are ecolabeling of consumer products -such as sustainably harvested wood -and TRI type reporting of pollution.

Obvious differences include the fact that the pollution setting involves an externality on a third-party, while the consumer product setting affects a direct consumer of the product. Also the type of information supplied is very different. In one case targeted to specific potential buyers and in the other supplied to the general public. By focusing on a specific informational strategy or policy tool between well-identified and characterized information emitter and recipient, further research may contribute to a better understanding of the economic mechanisms that may result in information overloading.

This paper has assumed the provision of uniform information from a quantitative viewpoint without really taking into account its qualitative and reliable dimensions. Indeed, information design matters.

Firms spend lots of money investigating exactly how to design and make their messages effective.

Moreover, information disclosure can be also considered as a device increasing the self-awareness Moreover, individuals may be reluctant to have less information available, regardless of the overall efficiency, because of a mental 'lock-in'. In short, suppressing information in order to improve decision effectiveness and economic efficiency may be unwelcome. It is worthwhile to note that some agents may legitimize their fight against the expansion of information-based policies by the likelihood of information overload and subsequent effects, such as the Chemical Manufacturers

Association advocating for a non-extension of the TRI 26 . The contribution has also considered homogeneous agents with the same processing abilities, but agents differ in their abilities 27 , opportunity costs and heuristics to process increasing information flows. Because of agents' differences, information overload and the optimal level of information is somewhat an agent specific phenomenon. If environmental information-based approaches produce an inhibiting level of information overload, they may only manage to engage an elite class, e.g., activists and bureaucrats.

Distinguishing subgroups inside a targeted population may help to provide more adequate amounts of information. Integrating the previous dimensions of information itself and information recipients, spillover effects, presence of information intermediaries and interactions with other public and private instruments will make the model closer to the real world. Extending this setting and testing it empirically constitutes a challenging topic for future research.

Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. ( 2007). Is more information always better ? An analysis applied to information-based policies for environmental protection.

  Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 9 quality of investors' decisions to a given change in the quantity of information released by the EPA.

  dD corresponds to the variation in the quality of decisions. For a discrete function, it is the difference between the quality of decisions after ( a D ) and before ( b D ) the release of information ( a change in the quantity of information released by the information provider.For a discrete function, it is the difference between the quantity of information after ( a I Q ) and before Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

  citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 11 context may bring insights on the estimate of the informational elasticity. These different ways are neither exhaustive nor mutually exclusive and can be combined to get better results.

  citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007. It may be positive, nil or negative. One important feature of our paper is to consider that the quality of decisions is a function of the quantity of information.

  is the indirect effect on I of an increase in the informational load of the context. Given that Q and C are thus measured in the same physical units, Indeed, every new piece of environmental information also increases the overall informational load of the decision maker proportionally. Finally, the more loaded the context is, the harder it is to process specific information among increasing flows of information, the lower the decision of quality is ( , the Context Effect is negative 16 .

  Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

Figure 27 Value

 27 Figure 2: The Yerkes-Dodson law

  Is there some minimum amount or type of information to which people have a moral or legal right? Is there an upper limit to the amount of information that people can use? At what point does the cost of collecting and providing access to information outweigh the value of the information use? Answers to these questions are likely to range widely, depending on one's philosophy of government and on the perceived value of an informed citizenry. Stakeholders in the TRI expansion debates have been observed to argue both sides of the issue: TRI provides too little information, on the one hand, and too much, on the other. Environmentalists and public health

	interest groups strongly support TRI expansion to include data on more chemicals, more industries,
	and more industrial processes. (…) Currently, some reportedly complain, TRI information gives
	people a false sense of understanding and power, but no real understanding, because TRI only reports
	releases, not the contextual information needed to evaluate potential effects of those releases on
	human health or the environment. (…) Others maintain that TRI expansion will provide too much
	data and overwhelm the public's ability to comprehend or use it. "Information overload" may be
	avoided, however, if data are well organized and made available in simple formats for viewing or
	manipulating." (CSR, undated 7 ). According to O'Rourke (2004, p. 25), "with hundreds of
	corporations now producing reports, a wide range of laws being implemented around the world, and
	dozens of nongovernmental initiatives on transparency and reporting emerging, there is staggering
	variation in what is reported, in what forms, and for which audiences. The Lawyers Committee for
	Human Rights reports over 2000 different indicators of labour standards used in corporate codes and
	monitoring systems. This range and variation in reporting can cause information overload and
	actually increase difficulties for comparing factories, brands, or countries. (…). CSR reporting is in
	fact in some danger now of reporting too much data that is not meaningful to critical stakeholders.
	The many audiences for CSR information are overwhelmed with information, and simultaneously
	over-stretched for time and resources to evaluate this information (see also Paredes, 2003 for an
	Comment citer ce document :
	Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An
	analysis applied to information-based policies for environmental protection. International Journal of
	Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 5 government provide?"

  the firm without being mediated through external pressures. Determining the optimal information load in a given context remains to do. Reducing the information may constitute a solution, but a question remains: what information to suppress and to which market participants?

	25 Economic theory typically considers specific economic agents. Producers are providing information about emissions
	(voluntarily or through legal compulsion). Information intermediaries may process and refine the raw data (e.g.,
	government agencies or NGOs). Stakeholders (consumers, workers, voters, investors) receive and process this refined

information, which influences particular decisions

(purchases, employment, voting intentions, and investments)

. It is possible to model each of these information flows and transmission mechanisms. Going further requires concretely modelling the heterogeneity of these agents, and finding suitable methods to aggregate their individual decisions into observable and measurable economic activities that result in an observable and measurable impact on the environment. Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 20 inside

General mechanism for information-based policies

  Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643

	Information-	Toxic Release	New Economic	European Ecolabel Advertising Campaign
	based policy	Inventory		Regulation Act		on Energy Savings
	Country Information Source	USA Firms	France Information Source Firms	Information Europe flows Firms	France -
	Information Provider	Environmental Protection Agency Information Provider Firms Report the locations Report on how the	Other information flows creating a French Agency for the Environment and The Energy more or less loaded context Labels on products Firms Benefits of saving energy
	Information	and quantities of chemicals stored on-	firm takes account of social and	of decisions pointing at the in terms of economic environmental saving and environmental
		site		environmental aspects	attributes	protection
	Deciders	Investors		Investors	Consumers	Households
	Decision	To hold or not companies accountable	Decider To invest or not in those firms	Impact To purchase or not Decisions To turn off the lights when ecolabeled products leaving the room
					Impact on the
	Impact	Impact on the decrease in chemical emissions	Impact on the quality of the environment	quality of the through a change in environment	Impact on energy savings
					consumption style
						25

International Journal of Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 24 Figure 1:

Table 1 : Some information-based policies in environmental regulation

 1 Comment citer ce document : Bougherara, D., Grolleau, G., Mzoughi, N. (2007). Is more information always better ? An analysis applied to information-based policies for environmental protection. International Journal of

Sustainable Development, 10 (3), 197-213. , DOI : 10.1504/IJSD.2007.017643 26

Noteworthy, several serious large-scale technological systems' accidents having grave consequences, such as those of Three Mile Island or Bhopal, and Chernobyl have been attributed to `operator error' caused by information overload. "In

EPA, 1995, Toxics Release Inventory (TRI) Program, Issues Paper #2, http://www.epa.gov/tri/programs/p3-ip2.htm, visited on October, 29th , 2004.

Congressional Research Service, Toxics Release Inventory: Do Communities Have a Right to Know More? III, http://www.ncseonline.org/NLE/CRSreports/pesticides/pest-9b.cfm, visited on October, 29 th , 2004.

C can be considered as the amount of competing information or "noise". Because of information overload, attention must be allocated selectively.

Note that we do not consider the overall impact from the decider viewpoint, but from the state viewpoint. The benevolent state wants to maximize the overall impact.

Note that while the overall impact on the environment is obviously the end objective for information-based policies, the mechanism through which information affects the environment constitutes the real object of interest (how do consumers/investors respond to information?). Indeed, information-based policies attempt to change individual behaviour.Thus, it may be natural to add a model which focuses more on individual behaviour. One possible direction is to model consumer choice as a function of both the quantity of information and the context. The context, then, affects the overall impact, but does not directly affect the decision of an individual. One suggestion is to think about setting up a problem

Technological devices such as information filters can be used to reduce the overall amount of information that a decider has to process.

A FUD strategy is "all about the promotion of inferior or overpriced products by casting shadows of doubt on the competition's product" (Angelakos, D., undated, FUD -A Marketing Strategy in the Computer Industry, http://members.hellug.gr/vyruss/computing/FUD_essay.html, visited onMarch, 24, 2005).

Herbert Simon, in Scientific American, September 1995, p. 201.

Federal Protection Agency, 2002, The Blue Angel Makes a Fresh Start -New Paths to Public Awareness, Umweltzeichen Newsletter, 5: 1-2.

Note that the information technology can be considered as an element of the problem because of 'technology-push' effect with a kind of self-enforcing mechanism and as an element of the solution by providing devices susceptible to help decision makers to process more information.


Christophe Chesneau
email: christophe.chesneau@unicaen.fr

Yogesh J Bagul
email: yjbagul@gmail.com

A Note on Some New Bounds for Trigonometric Functions Using Infinite Products

Keywords: Trigonometric function, Bernoulli inequality, infinite product, exponential bounds Mathematics Subject Classification(2010): 26D07, 33B10, 33B20

In this note, new sharp bounds for trigonometric functions are proved. We provide alternative proofs to existing results on exponential bounds, with some improvements, by using infinite products and the socalled Bernoulli inequality.

Introduction

The following two theorems have been proved by Yogesh J. Bagul [START_REF] Bagul | Inequalities involving circular, hyperbolic and exponential functions[END_REF]. The first result concerns bounds for cos(x).

Theorem 1. [2, Theorem 1] For x ∈ (0, 1), we have e -ax 2 < cos(x) < e -x 2 /2 , with a ≈ 0.6156265.

The second result is about bounds for sin(x)/x. Theorem 2. [2, Theorem 2] For x ∈ (0, 1), we have e -bx 2 < sin(x) x < e -x 2 /6 , with b ≈ 0.172604.

Our main interest is to provide tight and tractable lower bounds for cos(x) and sin(x)/x. The proofs of [2, Theorems 1 and 2] are based on the so-called l'Hospital's rule of monotonicity [START_REF] Anderson | Conformal Invarients, Inequalities and Quasiconformal maps[END_REF], with the use of non trivial derivative properties of involving functions.

In this paper, we first propose alternative proofs of these two results, with extensions, by the use of infinite product and the so-called Bernoulli inequality. Then new bounds for cos(x) and sin(x)/x defined with polynomial terms are proved. Their tightness are shown graphically.

Alternative proofs of existing bounds

The following version of the so-called Bernoulli inequality will be at the heart of our proofs. Proposition 1. [Bernoulli inequality] For u, v ∈ (0, 1), we have

1 -uv (1 -v) u .
We refer to [START_REF] Shi | Generalizations of Bernoulli's inequality with applications[END_REF]Theorem A] for the general version of the Bernoulli inequality (with less restriction on u and v). An elegant short proof for the considered version is given below.

Proof of Proposition 1. For u, v ∈ (0, 1) and k 1, we have u k u. It follows from the logarithmic series expansion that

ln(1 -uv) = - +∞ k=1 u k v k k u - +∞ k=1 v k k = uln(1 -v).
Composing by the exponential function, we obtain the desired inequality.

The following result is a slight generalization of [2, Theorem 1], but with a completely different proof.

Proposition 2. For α ∈ (0, π/2) and x ∈ (0, α), we have

e -βx 2 cos(x) e -x 2 /2 , with β = [-ln(cos(α))]/α 2 .
Proof of Proposition 2. The proof is centred around the infinite product of the cosine function: for all x ∈ R, we have

cos(x) = +∞ k=1 1 - 4x 2 π 2 (2k -1) 2 .
• Proof of the upper bound. Using the known inequality : e y 1 + y for y ∈ R and

+∞ k=1 1 (2k-1) 2 = π 2
8 , for x ∈ (0, π/2) (such that all the terms in the product are strictly positive), we have

cos(x) = +∞ k=1 1 - 4x 2 π 2 (2k -1) 2 +∞ k=1 exp - 4x 2 π 2 (2k -1) 2 = exp - 4x 2 π 2 +∞ k=1 1 (2k -1) 2 = exp - 4x 2 π 2 × π 2 8 = e -x 2 /2 .
• Proof of the lower bound. Using the infinite product expression of the cosine function and Proposition 1 (with respect to the considered u and v that satisfy u, v ∈ (0, 1)), for x ∈ (0, α), we have

cos(x) = +∞ k=1 1 - 4α 2 π 2 (2k -1) 2 x 2 α 2 +∞ k=1 1 - 4α 2 π 2 (2k -1) 2 x 2 /α 2 = +∞ k=1 1 - 4α 2 π 2 (2k -1) 2 x 2 /α 2 = (cos(α)) x 2 /α 2 = e -βx 2 , with β = [-ln(cos(α))]/α 2 .
By combining the obtained upper and lower bounds, we end the proof of Proposition 2. Proposition 3. For α ∈ (0, π) and x ∈ (0, α), we have

Note

e -γx 2 sin(x) x e -x 2 /6 , with γ = [-ln(sin(α)/α)]/α 2 .
Proof of Proposition 3. The proof is centred around the infinite product of the sinc function, i.e. sinc(x) = sin(x)/x for x = 0, the so-called Euler formula: for all x ∈ R -{0}, we have

sin(x) x = +∞ k=1 1 - x 2 π 2 k 2 .
• Proof of the upper bound. Using the inequality : e y 1 + y for y ∈ R and

+∞ k=1 1
k 2 = π 2 6
, for x ∈ (0, π), we have

sin(x) x = +∞ k=1 1 - x 2 π 2 k 2 +∞ k=1 exp - x 2 π 2 k 2 = exp - x 2 π 2 +∞ k=1 1 k 2 = exp - x 2 π 2 × π 2 6 = e -x 2 /6 .
• Proof of the lower bound. Using the infinite product expression of the sinc function and Proposition 1, for x ∈ (0, α), we have

sin(x) x = +∞ k=1 1 - α 2 π 2 k 2 x 2 α 2 +∞ k=1 1 - α 2 π 2 k 2 x 2 /α 2 = +∞ k=1 1 - α 2 π 2 k 2 x 2 /α 2 = sin(α) α x 2 /α 2 = e -γx 2 , with γ = [-ln(sin(α)/α)]/α 2 .
Note: Taking α = 1, we obtain γ = -ln(sin(1)) ≈ 0.1726037, and Proposition 3 becomes [2, Theorem 2].

Note: Similar results to Propositions 2 and 3 can be obtained with hyperbolic functions instead of trigonometric functions. Indeed, the following Bernoulli inequality exists: for u ∈ (0, 1) and v > 0, we have 1+uv (1+v) u (see [START_REF] Shi | Generalizations of Bernoulli's inequality with applications[END_REF]Theorem A]). Therefore, using the same arguments to the proofs of Propositions 2 and 3 with the infinite products for cosh(x) and sinh(x)/x, i.e. cosh(x)

= +∞ k=1 1 + 4x 2 π 2 (2k-1) 2 and sinh(x)/x = +∞ k=1 1 + x 2
π 2 k 2 , we establish that, for α > 0 and x ∈ (0, α),

• e θx 2 cosh(x) e x 2 /2 , with θ = [ln(cosh(α))]/α 2 , which is appeared in [3, Remark 2.1] and

• e ζx 2 sinh(x)/x e x 2 /6 , with ζ = [ln(sinh(α)/α)]/α 2 .

Polynomial bounds for trigonometric functions

This section is devoted to the proof of new sharp polynomial lower bounds or new proofs, for trigonometric functions.

Proposition 4. For x ∈ (0, π/2), we have

cos(x) 1 - 4x 2 π 2 π 2 /8 . (3.1)
Proof of Proposition 4. The proof combines the infinite product of the cosine function, Proposition 1 and

+∞ k=1 1 (2k-1) 2 = π 2 8
, but in a different way to the proof of Proposition 2. We have

cos(x) = +∞ k=1 1 - 4x 2 π 2 1 (2k -1) 2 +∞ k=1 1 - 4x 2 π 2 1/(2k-1) 2 = 1 - 4x 2 π 2 +∞ k=1 1/(2k-1) 2 = 1 - 4x 2 π 2 π 2 /8
.

We provide a graphical illustration of the bounds (3.1) in Figure 1.

(1 -4x 2 π 2 ) (π 2 8)
k 2 = π 2 6 : sin(x) x = +∞ k=1 1 - x 2 π 2 1 k 2 +∞ k=1 1 - x 2 π 2 1/k 2 = 1 - x 2 π 2 +∞ k=1 1/k 2 = 1 - x 2 π 2 π 2 /6 1
.

In the following Corollary, we give tight upper bound for cos(x).

Corollary 1. For x ∈ (0, π) we have

cos(x) 1 + 3π 2 π 2 + 6 1 - x 2 π 2 (π 2 +6)/6 -1 . (3.3)
Proof of Corollary 1. Using (3.2) and integrating we have

x 0 sin(t) dt x 0 1 - t 2 π 2 π 2 /6 t dt which turns into -cos(x) -1 - 3π 2 π 2 + 6 1 - x 2 π 2 (π 2 +6)/6 - 1
proving desired result.

The upper bound of Corollary 1 can be seen in Figure 2. Note: Similar results to Propositions 4 and 5 can be obtained with hyperbolic functions instead of trigonometric functions. Indeed, using the following Bernoulli inequality: for u ∈ (0, 1) and v > 0, we have 1 + uv (1 + v) u and the infinite products for cosh(x) and sinh(x)/x, we prove that, for x > 0,

• cosh(x)

1 + 4x 2 /π 2 π 2 /8 ,

• sinh(x)/x 1 + x 2 /π 2 π 2 /6 .

:

  Taking α = 1, we obtain β = -ln(cos(1)) ≈ 0.6156265, and Proposition 2 becomes [2, Theorem 1]. Proposition 3 below gives a generalization of [2, Theorem 2].

Figure 1 :- x 2 π 2 π 2 / 6 . ( 3 . 2 )

 122632 Figure 1: Graphs of the functions in (3.1) for x ∈ (0, π/2).

Figure 2 :

 2 Figure 2: Graphs of the functions in (3.3) for x ∈ (0, π).