Communication and Information in Games on Networks – CIGNE

The first task is devoted to the study of dynamic interactions with communication networks. We characterize equilibria in games with exogenous communication networks, and construct communication protocols with desirable properties in order to generate correlation via decentralized cheap talk. The second task is devoted to the study of dynamic interactions with information networks. We first study exogeneous information networks by considering non-Bayesien learning in networked economies, and by studying dynamic games where information about distant players is imperfect and given by a delay depending on a network. Then, we study endogenous information networks by considering a model of opinion formation and lobbying.

In the article Interactive Information Design, F. Koessler, M. Laclau and T. Tomala study an information design problem with several senders, who have some pieces of information which can be independent or correlated. The setup is extended in a dynamic way in a particular setting (so called rectangular games). L. Renou (with M. Makris) also studies a dynamic information design problem in the article Information Design in Multi-Stage Games. In the article Unmediated Communication in Games with Complete Information: the 4-Player Case, M. Laclau and P. Vida show that every correlated equilibrium of a finite game with four players with complete information can be implemented as a perfect Bayesian equilibrium of an extended game, where players can communicate costlessly before choosing an action. In the article Best-Response in Pure Public Good Games on Networks, M. Faure (with S. Bervoets) studies the best-response dynamics in public games on networks. M. Faure (with S. Bervoets and M. Bravo) also obtained results in the article Learning and Convergence to Nash in Games with Continuous Action Spaces. X. Venel studies with A. Mandels a model of opinion and lobbying in Dynamic Competition on Social Networks. In Games with incomplete information : the dependent case, M. Oliu-Barton (with F. Gensbittel) establishes a reccurence formula to build optimal strategies in zero-sum repeated games with incomplete information on both sides, in the general case (the dependent case).

An important project is related to sender-receiver games in networks : a sender owns some private information about the state of the nature, and a receiver, who may be far form the sender in a communication network, takes a decision which affects all the agents in the network (and the utilities of all agents, sender, receiver and intermediaries, depend on the state of the nature). Sequential rationality is imposed. The project aims at characterizing the networks for which all communication equilibria of the Sender-Receiver game without intermediaires can be obtained.

1. M. Laclau and T. Tomala, Repeated Games with Public Deterministic Monitoring, Journal of Economic Theory (à paraître) : www.sciencedirect.com/science/article/pii/S0022053117300285 2. D. Condorelli, A. Galeotti, L. Renou, Bilateral Trading in Networks, The Review of Economic Studies (à paraître) : www.restud.com/paper/bilateral-trading-in-networks/ 3. J. Renault and X. Venel, Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces, Mathematics of Operations Research (à paraître) : pubsonline.informs.org/doi/abs/10.1287/moor.2016.0814 4. M. Oliu-Barton, The Splitting Game: Value and Optimal Strategies, Dynamic Games and Application (à paraître) : www.researchgate.net/publication/313817514_The_Splitting_Game_Value_and_Optimal_Strategies

The ever growing importance of social medias, Internet and big data, is radically transforming the world we live in; we live in an ever more connected world with access, at a click, to vast amount of information and multiple channels of communication (social forums such as Facebook, blogs, comments on websites, etc). The aim of this research project is to understand the long-run implications of repeated and frequent interactions in networked economies/organizations, where the possibilities of communication among agents as well as the information they get are given by networks.

Some disciplines have a long tradition of studying networks, such as physics, biology or sociology. Recently, computer scientists have considerably developed the study of communication networks. In economics, the subject is more recent, but major advances have been accomplished regarding for instance strategic formation of networks, peer effects and influence, trust and enforcement, bargaining, buyer-seller networks, informal insurance, diffusion of information, etc. Yet, many aspects of networks are still to be understood, in particular regarding the strategic use of communication and information in long-term networked interactions. This is the main focus of this research proposal.

A central question in Game Theory is how privately informed players use optimally their information. In order to take advantage of his private information, a player has to use it, and thus has to reveal some of it. This trade-off is even more intricate if players have the opportunity to communicate with each others about the information they obtain. Indeed, players may have incentives to misreport or fabricate information (e.g., to spread false rumors), to conceal their information to others, etc.

Information and communication are closely related concepts. The role of communication is to transmit information, and a communication network models the flow of information transmission. For instance, through public forums, one can transmit information about what others did in the past to a large audience. The more connected one is, the more diffuse the information is. (Think about a food blogger with a large number of followers reviewing a restaurant.) As another instance, in repeated interactions with incomplete information, in which players may not know their opponents’ preferences, nor the choices available to them, communication allows the players to share confidential and private information.

However, communication and information are distinct concepts. On the one hand, communication is about transmitting and sharing information among players, and this information can be (strategically) manipulated by the players. On the other hand, the information structure of a game--which can be depicted by a network structure in some situations--specifies what players know and observe: this is non manipulable information (for instance, players may know their own preferences or monitor their opponents' moves).

This research project aims at analyzing the strategic use of communication and information in dynamic games where interaction, communication or information possibilities revolve around networks. To this end, we intend to emphasize the role of communication networks on the one hand and of information networks on the other. The reason is first due to the previous distinction between these two notions. Second, we aim at disentangling the effects of each network structure (i.e., information or communication). Finally, even if both networks appear in real-life applications, they might not be the same.