Slides of the talks: here
Andrea Attar (Toulouse School of Economics, CNRS): Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms (with E. Campioni, T. Mariotti and A. Pavan)
Abstract: We study the design of market information in competing-mechanisms games. We show that private disclosures, whereby principals asymmetrically inform agents of how their mechanisms operate, have two effects. First, they raise principals’ individual payoff guarantees, protecting them against their competitors’ threats. Second, they support equilibrium payoffs that cannot be supported via standard mechanisms. These results challenge the folk theorems a` la Yamashita (2010) and the canonicity of universal mechanisms of Epstein and Peters (1999). We propose a new approach to competing- mechanism games retaining key elements of classical mechanism-design theory while exploiting private disclosures to simplify the description of equilibrium communication.
Gorkem Celik (ESSEC Business School): Informative Certification: Screening vs. Acquisition (with Roland Strausz)
Abstract: We consider a monopolistic certifier providing two types of certification services to a seller with private information about the quality of her goods. The certifier can use certification as a screening device, disclosing soft information about the seller’s private information. Additionally, the certifier can use certification as a device of information acquisition, disclosing hard information about the good’s quality. Despite being costless, we show that, optimally, the certifier provides non-maximal information-acquisition, while offering maximal screening, revealing all private information. Thus, monopolistic certification exhibits no economic distortions as a screening device, but exhibits distortions as an information acquisition device, providing too little hard information. While feasible and costless, full information acquisition is suboptimal as it requires excessive information rents. Consequently, market inefficiencies remain due to market uncertainty but not due to private information.
Claude d’Aspremont (CORE, UCLouvain): Bayesian mechanism design: Old and new beliefs
Penélope Hernández (University of Valencia): Coordinating Through Platforms: Private Signals in Social Networks (with Julian Chitiva)
Abstract: Platforms play a crucial role in facilitating coordination among users by providing information that supports day-to-day decision-making. This coordination is vital in various real-world contexts, including fashion, politics, and other social dynamics. Users interact through networks structured by diverse relationship types, such as work environments, sports groups, and familial ties. While these links shape network interactions, individual idiosyncrasies can remain independent of the network’s structure. Additionally, platforms enable users to share private signals with their peers, enhancing the overall information available for decision-making. Consequently, users base their decisions on a combination of the platform-provided information, messages from other users, and their intrinsic preferences, which collectively influence their utility. The users’ utility function comprises two key components: (1) alignment with their preferred action, determined by their private type and the state of the world, and (2) the desire for coordination with others. We characterize the (unique) equilibrium action in an n-player game with private information, focusing on the final stage where users utilize platform messages and a communication network to form decisions. The equilibrium action of user i comprises six components. First, it includes the direct effect of the message that user i is aware of. Second, it encompasses the direct effect of the expected message that is unknown to user i. Third, it involves the indirect effect of the messages that influence the perception of the types of users, including user i, who disclose the message to them. Fourth, it considers the perception of the types of users who do not disclose the message to the user i. Finally, the equilibrium action incorporates the type of user i. This framework provides a comprehensive understanding of the interplay between private signals, network structure, and platform-mediated information in user decision-making.
Ron Holzman (Technion): The minimax property in infinite two-person win-lose games.
Abstract: We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we prove that a game satisfies the minimax property along with all its subgames if and only if none of its subgames is isomorphic to the ``larger number game." This generalizes a recent theorem of Hanneke, Livni and Moran.
Ehud Kalai (Northwestern University): Resilience in Strategic Analysis - Applications
Abstract: Analysis of equilibrium concepts of 𝑛-person strategic games (fixed n>2), reveals a hierarchy based on levels of resilience. At the bottom is Nash eqm (NE), representing the strategy profiles of resilience 0. At the top is dominant strategy eqm (DSE), representing the strategy profiles of resilience 𝑛-1. But knowledge of all resilience levels provide deeper strategic insights, than focusing solely on Nash & DSE. Illustration: Improved Implementation theory. As illustrated in 𝑛-prisoner dilemmas, high resilience eqm concepts enable robust unique implementation, even when DSE doesn’t exist.
Marie Laclau (HEC Paris, CNRS): A belief-based approach to signaling (joint with F. Koessler and T. Tomala)
Abstract: In this paper, we provide a geometric characterization of the set of interim equilibrium payoffs in a general class of signaling games. To obtain a tractable characterization, we use the belief based approach found in the literature on repeated games with incomplete information, cheap talk and Bayesian persuasion. This approach avoids to specify the prior, the strategies of the sender and receiver, and the belief system. The key ingredient is to consider Bayes-plausible belief distributions that are incentive-compatible for the sender. Geometrically, this leads to a constrained convexification of the graphs of the interim value correspondences. Our characterization extends the analogous result for sender-receiver cheap talk games. We illustrate the results with some classical signaling games. We derive the best equilibrium payoff for the sender when his preferences are type-independent. For zero-sum preferences, we obtain an explicit formula for the ex-ante equilibrium payoff and establish a simple condition for the uniqueness of interim equilibrium payoffs.
Qianjun Lyu (University of Bonn): Complete Contracts under Incomplete Information (with Gregorio Curello and Yimeng Zhang)
Abstract: We study a moral hazard model in which the output is stochastically determined by both the agent's hidden effort and an uncertain state of the world. We investigate how the contractibility of the ex-post realization of the state affects the principal's incentive to provide information. While detailed information allows the principal to better tailor the effort levels to the revealed states, coarser information enables the principal to base payments on the ex-post observation of states, thereby designing incentive schemes more effectively. Our main result establishes that when the state is contractible, full information is never optimal; however, when the state is not contractible, under certain conditions, full information is optimal.
Roger Myerson (University of Chicago): Dual reduction and elementary games with senders and receivers.
https://home.uchicago.edu/~rmyerson/research/eldual2023notes.pdf
Abstract: Consider the incentive constraints that define the incentive-compatible mechanisms of a senders-receivers game. Duals of these linear constraints form Markov chains on the senders' type sets and the receivers' action sets. The minimal nonempty absorbing sets of these Markov chains can be interpreted as the types and actions in a dual-reduced game. Any incentive-compatible mechanism of a dual-reduced game induces an equivalent incentive-compatible mechanism for the original game. We say that a game is elementary if all nontrivial incentive constraints can be satisfied as strict inequalities in incentive-compatible mechanisms. Any senders-receivers game can be reduced to an elementary game by iterative dual reduction. The set of games with transitive dual solutions is dense.
Heinrich Nax (University of Zurich): Evolutionary cooperative games: my PhD journey with Françoise (ex ante and ex post)
Abstract: In this talk, I will take a fresh look at what turned out to be the key paper from my doctoral thesis on the evolutionary foundations of the assignment game, and embed it into my ongoing research on the double auction with a focus on theory and closely related experiments. I will also speak about my expectations for academia and how working with Francoise has shaped my journey.
Indrajit Ray (Cardiff Business School): Any Outcome can be a Trading Equilibrium in a Market (with Manipushpak Mitra and Souvik Roy)
Abstract: We characterise the conditions for “trading” equilibrium outcomes in a strategic market game. We then find testable restrictions of a data set consisting of a finite set of traders and their period buying and selling vectors of a market obtained over discrete time periods. We prove that any such observable data is rationalizable as a trading equilibrium of a corresponding market game if and only if utility functions of all traders are “regular” utility functions.
Jérôme Renault (Toulouse School of Economics): A Folk theorem for finitely repeated games with public monitoring (with Johannes Hörner)
Abstract: We provide the Folk theorem for finitely repeated games with public signals, with a small variation of the usual assumptions for finitely repeated games with perfect observation, and for discounted repeated games with public signals. Our proof uses using standard recursive methods and assumes the existence of a public correlation device. Three counterexamples show that our assumptions are tight.
Anna Rubinchik (University of Porto): From Arbitrary Pairwise Comparisons to the Finest Ordered Partition of Alternatives (with Susana Furtado)
Abstract: Data regarding individual or collective choices is typically incomplete and rarely consistent. Our goal is to identify a rationalizable basis of observed choice, thereby addressing one of the fundamental questions of economic theory. Given any possible pairwise comparisons of choice items in a finite set, we propose an efficient algorithm to construct the finest partition of the set that admits a strict total order. Our basic algorithm applies when the data is complete and free of preference reversals, without requiring the comparisons to be transitive. We extend the algorithm to the case of incomplete pairwise comparisons, thus, essentially, eliminating the usual assumptions on choice behavior that are traditionally required for its rationalization. This extension can also accommodate preference reversals and indifference. Applications include recovering most informative rational preference relations from individual choice data, as well as constructing well-behaved social welfare correspondences based on majority voting outcomes.
Andrés Salamanca (Ca'Foscari University of Venice): Some advances in the theory of values for cooperative games with incomplete information.
Abstract: This survey offers a concise overview of recent advancements and open challenges in the study of value-like solution concepts for cooperative games with incomplete information. Modeling cooperation among players with asymmetric information presents numerous conceptual difficulties. In particular, it is not possible to derive an analog of the characteristic function as defined under complete information. Even if such a derivation were possible, the resulting (possibly NTU) characteristic function would not fully account for all relevant informational and strategic externalities. Although Myerson’s seminal work [Cooperative games with incomplete information, Int. J. Game Theory, 13, 1984] made significant progress in developing a general framework for defining and analyzing solution concepts for cooperative games with asymmetric information—the virtual utility approach—many questions and conceptual challenges remain unresolved. This survey selectively highlights recent achievements addressing some of these open problems, with an emphasis on contributions from my own research.
Stephan Semirat (Université Grenoble Alpes): Optimal equilibrium in single-peaked, single-crossing cheap talk games: a dynamic programming approach
Abstract: We consider information transmission between a sender, who has finitely many ordered types, and a receiver, who must choose a decision in a real interval. The payoff functions of both players, which depend on the sender's type and the receiver's decision, are assumed to be single-peaked and to satisfy the single-crossing property. To identify the ex-ante optimal (pure) equilibrium for the sender (or the receiver), we propose a dynamic programming approach. The formulation generalizes techniques used for optimal clustering of one-dimensional data.
Sylvain Sorin (Sorbonne University): Recent advances in 2-person 0-sum stochastic games.
Roland Strausz (Humboldt University): Mediated Renegotiation (with Andrea Attar and Lorenzo Bozzoli)
Abstract: We develop a new approach to contract renegotiation under informational frictions. Specifically, we consider mediated mechanisms which cannot be contingent on any subsequent offer, but can generate a new source of asymmetric information between the contracting parties. Taking as a reference the canonical framework of Fudenberg and Tirole (1990), we show that, if mediated mechanisms are allowed, the corresponding renegotiation game admits only one equilibrium allocation, which coincides with the second-best one. Thus, the inefficiencies typically associated to the threat of renegotiation may be completely offset by the design of more sophisticated trading mechanisms.
Peter Vida (CY Cergy Paris University and Corvinus University of Budapest): Unmediated communication in games with (in)complete information: the 4-player case (with Helmuts Azacis and Marie Laclau)
Abstract: We show that essentially every correlated equilibrium of any finite game with complete information with four players can be implemented as a perfect Bayesian equilibrium of an extended game, in which before choosing actions in the underlying game, players exchange cheap talk messages. In particular, we improve on the results of Barany 1992 and Gerardi 2004. Our result generalizes to sequential equilibria and to games with incomplete information, i.e. to the set of regular communication equilibria.
Rajiv Vohra (Brown University): Nash Bargaining with Coalitional Threats (with Debraj Ray)
Abstract: We study bargaining in the spirit of Nash’s axiomatic approach when coalitions as well as individuals have outside options. As in Nash, our solution maximizes the product of payoffs net of individual disagreements, but coalitional threats appear as conventional constraints and are not netted out from payoffs. An exploration of this key asymmetry forms the central theme of the paper. Additionally, we extend our solution to a setting in which coalitional threats are endogenously constrained by threats from subcoalitions. We use the resulting characterization to uncover a connection between our solution and an ethic based on “pragmatic egalitarianism.”
Bernhard von Stengel (London School of Economics): Extensive-Form Correlated Equilibrium