Galit Ashkenazi-Golan (LSE)
Title: When Slow and Steady Wins the Race
Abstract: We explore continuous multiagent gradient learning dynamics with the speed of learning as a strategic choice.
Each player is maximizing the discounted reward along the learning trajectory.
We shed light on the different effects that the learning speed has, provide some theoretical results, numerical approximations and simulations.
For example, we go into the different considerations involved in answering the question: do you always want to learn as fast as possible, when the game is prisoner's dilemma?
Charles Bertucci (CEREMADE, CNRS, Université Paris-Dauphine)
Title: Mixed equilibria, incomplete information and correlated equilibria in mean field games
Abstract: The purpose of this talk is to illustrate how we can translate some basic game theory concepts into the language of partial differential equations which is used to characterize equilibria of mean field games. I will focus on the concepts of mixed strategies/equilibria, incomplete information and correlated equilibria. Part of this talk is still work in progress.
Francis Bloch (PSE)
Title: Bonacich Pricing: Search Frictions and Price Competition in Networks
Abstract: We analyze price competition in a two-sided network connecting firms with markets. We suppose that consumers search for goods under uniform linear waiting costs and characterize demand under search frictions as a linear function of prices. We compute equilibrium prices of firms as a function of the two-sided network, study the effect of entry on prices and consumer welfare, and contrast uniform and discriminatory prices.
Pierre Cardaliaguet (Paris Dauphine University)
Title: Differential and Mean Field Games
Abstract: In this talk I will first present basic aspects of differential games (games in continuous time in which players control a state which evolves according to a (stochastic) differential equation) and of mean field games (differential games with infinitely many small players). Then I will discuss more advanced aspects of these topics, such as differential games and mean field games with imperfect information.
Nicolò Cesa-Bianchi (Università degli Studi di Milano)
Title: Regret, Games, and Boosting: a Reverie of Gambles and Bounds (with Marco Bressan, Nataly Brukhim, Emmanuel Esposito, Shay Moran, Yishay Mansour, Maximilian Thiessen).
Abstract: We revisit the celebrated result connecting regret minimization, boosting, and the minimax theorem. Our main result is a more general characterization of the frontier between boosting and random guessing.
Roberto Cominetti (Universidad Católica de Chile) Near-Optimal Sample Complexity for MDPs via Anchoring
Title: Near-Optimal Sample Complexity for MDPs via Anchoring
Abstract: We present a model-free algorithm to compute $\varepsilon$-optimal policies for average reward Markov decision processes, in the weakly communicating setting. Given a generative model, our procedure combines a recursive sampling with Halpern's iteration, achieving a sample and time complexity $\widetilde{O}(\|h\|_{sp}^{2}/\varepsilon^{2})$. To our knowledge, this is the best complexity for model-free algorithms and matches the known lower bound up to a factor $\|h\|_{sp}$. Although the complexity bound involves the unknown span seminorm $\|h\|_{sp}$ of a bias vector, the algorithm requires no prior knowledge and implements a stopping rule that guarantees finite termination.
John Levy (University of Glasgow)
Title: Bayesian Equilibrium Existence by Cutting a Continuum of Cakes Which Aren't Really Cakes (with Eilon Solan, Royi Jacobovic)
Abstract: A Bayesian game is said to have nested information if the players are ordered, and each player knows the types of all players that follow her in that order.
We prove that all multiplayer Bayesian games with finite actions spaces,
bounded payoffs, Polish type spaces, and nested information admit a Bayesian equilibrium. This talk will focus on the step of moving from epsilon-equilibrium existence to exact-equilibrium existence, by selecting among limits of the former as epsilon goes to 0 using Mertens' measurable "measurable selection" theorem.
János Flesch (Maastricht University)
Title: Games with an infinite past
Abstract: "We define a model of multi-player dynamic games with the main feature that the set of stages is the set of non-positive integers {...,−2,−1,0}. In such a game, there is no initial position, and if the current stage is n, then all the infinitely many stages ...,n − 2,n − 1 are past stages and the remaining finitely many stages n+1,...,−2,−1,0 are future stages. We assume that the game has perfect information: at each stage n, depending on the infinite sequence (..., a_{n−2},a_{n−1}) of past actions, one of the players is active and chooses the action a_{n} from a finite action set. The payoff to each player is a bounded function of the resulting infinite play (...,a_{−1},a_{0}).
We define two related equilibrium concepts: one only taking deviations at finitely many stages into account and another taking all deviations into account. Our main results are as follows: (i) The sets of equilibrium plays coincide for the two equilibrium notions, provided that at least two players are active along each infinite play. (ii) For zerosum win-lose games (where each infinite play is either a win for player 1 or a win for player 2), the game has an equilibrium if the winning sets are Borel measurable and have rank at most 2, and we provide a counter-example that shows that this is no longer true for rank 3. (iii) In general non-zerosum games, the game has an equilibrium if the payoffs are continuous, for example, for reversed-discounted payoffs. The challenge for all these results is that not all strategy profiles admit a consistent infinite play, hampering the use of backward induction arguments."
Françoise Forges (Paris Dauphine University)
Title: Strategic communication
Abstract: A selective survey of models and results on strategic communication (1966-2025)
Stephan Gaubert (INRIA and École polytechnique)
Title: The competitive spectral radius of families of nonexpansive mappings
Abstract: We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpansive operator depending on the actions of both players. This generalizes to the two-player (and non-linear) case the notion of joint spectral radius of a family of invertible matrices, as well as the notion of lower spectral radius. We show that the value of this game does exist, and we characterize it in terms of an infinite dimensional non-linear eigenproblem. This provides a two-player analogue of Mañe’s lemma from ergodic control. This also extends to the two-player case results of Kohlberg and Neyman (1981), Karlsson (2001), and Vigeral and the author, concerning the asymptotic behavior of nonexpansive mappings (generalizations of the Wolff-Denjoy theorem). We also show that the value of the game admits a dual characterization when the nonexpansive maps are quasi-isometries, or when they are order preserving and positively homogeneous self-maps of a cone equipped with Funk’s and Thompson’s metrics. We finally discuss computational aspects.
This is based on arXiv:2410.21097, with Marianne Akian and Loïc Marchesini, and on a followup work with Ian Morris, 2505.22468
Fabien Gensbittel (TSE)
Title: Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition
Abstract: We prove the existence of a Markov-perfect equilibrium in randomized stopping times for a model of the war of attrition in which the underlying state variable follows a homogenous linear diffusion. The proof uses the fact that the space of Markovian randomized stopping times can be topologized as a compact absolute retract, which in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markov-perfect equilibrium.
Hugo Gimbert (CNRS)
Title: Deciding the Existence of an Almost-Surely Winning Strategy in a Zero-Sum Stochastic Games with Signals
Abstract: Stochastic games with signals are a pervasive model of competitive decision making under imperfect information. We review several results about the decidability of the following decision problem: does player I has an almost-surely winning strategy.
Olivier Gossner (CNRS, LSE, École polytechnique)
Title: : High order information design
Abstract: Fixing game data we ask: 1/ what distributions of outcomes can be implemented under common certainty of rationality by some information structure? and 2/ given such an implementable distribution, how can we construct a corresponding information structure? We answer these questions by showing that all distributions are implementable by information structures described by Markov processes that generate arbitrarily high level beliefs. We conclude that the (closure of) the set of implementable distributions is a convex polyhedron.
Hari Govindan (University of Rochester)
Title: Axiomatic Equilibrium Selection: The Case of Generic Extensive-Form Games.
Abstract: A solution concept that is a refinement of Nash equilibria selects for each finite game a nonempty collection of closed and connected subsets of Nash equilibria as solutions. We impose three axioms for such solution concepts. The axiom of backward induction requires each solution to contain a quasi-perfect equilibrium. Two invariance axioms posit that solutions of a game are the same as those of a game obtained by the addition of strategically irrelevant strategies and players. Stability, as defined by Mertens, satisfies these axioms; and any solution concept that satisfies them must, for generic extensive-form games, select from among its stable outcomes. A strengthening of the two invariance axioms provides an analogous axiomatization of components of equilibria with a nonzero index.
Michael Greinecker (ENS Paris-Saclay, CEPS)
Title: Sequential Equilibria in a Class of Infinite Extensive Form Games
Abstract: Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form but is not defined for extensive-form games in which a player can choose among a continuum
of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium.
Josef Hofbauer (University of Vienna)
Title: On sustainable and learnable equilibria
Abstract: I will present some results and open problems on sustainable and learnable equilibria.
Johannes Horner (TSE, CNRS)
Title: Separating the Wheat from the Chaff
Abstract: This paper considers a three-player game between a judge and two players, one of whom is an expert, who knows the state of the world, and the other is a quack, who doesn't. The judge doesn't know which player is an expert, but receives a noisy signal of the state of the world? The judge must pick one of the players, and would like to pick the expert. Both players would like to be picked. How should the players posture, and how should the judge decide?
Philippe Jehiel (PSE & UCL)
Title: Evolutionary Stable Analogy-Based Expectation Equilibria
Abstract: We develop an evolutionary approach to endogenize the choice of analogy partitions in the analogy-based expectation equilibrium (Jehiel, 2005) in environments consisting of multiple (possibly many) symmetric normal-form games with identical action spaces and a categorization (or analogy partition) with more classes comes with a higher fitness cost. In an evolutionarily stable analogy-based expectation equilibrium (ESABEE), we require that analogy partitions and strategies satisfy two conditions: (i) given an analogy partition, the associated strategy is a best response to the corresponding analogy-based expectations; and (ii) analogy partitions that arise with positive probability induce the highest overall fitness among all possible partitions. We show that an ESABEE (possibly involving distributions over analogy partitions) always exists in finite environments, and we establish that they are the steady states of dynamic systems in which analogy partitions are reproduced proportionally to their fitness in each period (as in the replicator dynamics), and strategies are adjusted by moving in the direction of the best responses induced by the partitions (as in belief-based learning models). We illustrate the concept using a family of Hawk-Dove games, for which we establish quite generally that some mixing across analogy partitions must arise when there are many such games, and note several properties that ESABEE must satisfy in such applications such that assigning positive probabillity to coarse partitions irrespective of the fitness costs associated with having finer partitions. We also consider an investment application in which the decision maker observes his cost type and need to form expectations about the benefit which can take multiple values and we assume that the decision maker can use at most k categories. We characterize when the first-best can be obtained as an ESABEE, and we contrast the analysis with that obtained with rational expectations and an optimal information partition about the benefit realization (as in Dow, 1991) or an optimal information partition about the state (allowing for the case in which the decision maker would not be informed of his cost type) as in the information design literature.
Marie Laclau (HEC-CNRS)
Title: A belief-based approach to signaling
Abstract: We provide a geometric characterization of the set of interim equilibrium payoffs in the general class of costly signaling games. Our characterization offers a unified, belief-based framework to study both cheap talk and costly signaling, with or without transparent motives. The key ingredient is the analysis of Bayes-plausible belief distributions and signal-contingent interim values that are incentive-compatible for the sender. Geometrically, this leads to a constrained convexification of the graphs of the interim value correspondences. We apply and illustrate the results in a class of intimidation games. We also derive the sender’s best equilibrium payoff under transparent motives. Finally, we compare the equilibrium outcomes to those arising when the sender can commit to a signaling strategy.
Rida Laraki (UM6P)
Title: On the Relationship Between The Strategic Stability of Nash Equilibria and Their Fixed Point Index
Abstract: This talk investigates the relation between some strategic features of mixed Nash equilibria and their fixed point index in finite games. We present new results that deepen our understanding of how equilibrium structure relates to index theory:
A mixed Nash equilibrium x is isolated with index +1 if and only if it can be made the unique equilibrium of a larger game, constructed by adding strategies that are strictly inferior responses to x. This settles an open question posed explicitly by Hofbauer (2003) and implicitly by Myerson (1996).
A Nash component admits an equilibrium of index +1 in its neighbourhood under every perturbation of any strategically equivalent game if and only if the component itself has a positive index.
For any finite game, any selection of equilibria from each Nash component, and any assignment of indices ±1 to these equilibria such that their sum equals the index of the component, there exists a perturbation of a strategically equivalent game whose equilibria approximate the selected ones and preserve the assigned indices.
These results bridge equilibrium refinement, index theory, and robustness to strategic perturbations, offering new insights into the structure and stability of Nash equilibria.
Lucie Ménager (Université Paris Panthéon Assas)
Title: The Cost of Knowing: Firms Testing vs Consumer Feedbacks
Abstract: Firms selling products of uncertain quality face a trade-off in how they learn about their products' safety. They can either conduct laboratory tests before market launch, which are costly but contain no reputational risk, or test in the field, i.e., learn from consumer feedbacks, where revenues are generated but bad outcomes can trigger severe financial and reputational losses. We develop a theoretical model in which firms choose between these two modes of experimentation. We show that, in the absence of regulation, firms may prefer to experiment in the field despite the potential harm to consumers, as doing so avoids upfront costs and delays. We analyze how regulatory interventions, such as mandatory lab testing or liability for harm, affect equilibrium outcomes. Our findings highlight a moral hazard problem in unregulated markets and provide guidance for designing policies that align corporate incentives with consumer safety.
Abraham Neyman (Hebrew University of Jerusalem)
Title: 60 Years of Tension in the Big Match: Patience, Sunk Costs, and Strategic Complexity
Abstract: The Big Match has long served as a central example in the theory of stochastic games, illustrating the tension between patience, the sunk-cost principle, and strategic complexity. I will present results from two recent papers on the limitations of public-memory strategies in the Big Match.
In earlier work, we established that private-finite-memory strategies and public–O(log n)-memory strategies—namely, strategies that use only O(log n) public memory states within the first n stages—suffice, even if they employ time-independent action selection, to achieve ε-optimality in all sufficiently long finite-horizon games, while no public-finite-memory strategy does.
Our recent results sharpen these bounds. We prove that (a) public–o(log n)-memory strategies that employ time-independent action selection, and (b) public–o((log log n)/(log log log n))-memory strategies, which allow time-dependent action selection, both fail to secure, for every ε > 0, a payoff above ε in the Big Match with {0,1} payoffs, for a wide range of n-stage games and λ-discounted games.
Marc Quincampoix (LMBA, Université de Brest)
Title: Generalized differentiation in Wasserstein space and multiagent control problem (with Rossana Capuani, Antonio Marigonda).
Abstract: Several concepts of generalized differentiation in Wasserstein space have been proposed in order to deal
with the intrinsic nonsmoothness arising in the context of optimization problems in Wasserstein spaces.
We introduce a concept of admissible variation encompassing some of the most popular definitions as
special cases. This enables us to define a generalized differentiation in Wasserstein space that we show
to coincide in the smooth case to several other differentiation concepts already existing in the literature.
The relevance of such new concept of variation lies in the fact that it enables us to define sub/super
differentials to study viscosity solutions to Hamilton Jacobi Bellman equations. We will investigate an
optimal multiagent control problem where this concept is used and we will obtain a comparison theorem
for the corresponding Hamilton Jacobi equation.
Miquel Oliu Barton (Université de Paris-Nanterre)
Title: 15 Years of Stochastic Games
Abstract: In this talk I will present the theory of stochastic games, and discuss a selection of recent developments over the past 15 years.
Panayotis Mertikopoulos (CNRS, Université Grenoble Alpes)
Title: Online learning in games: Limits, limit sets, and limitations
Abstract: In this talk, I will discuss a range of results concerning the long-run behavior of online learners that are involved in an unknown repeated game (that is, when any given player is not necessarily aware of the other players' actions or objectives). The talk will focus on a widely studied family of online learning methods known as "regularized learning", and we will pay special attention to the information available to the players—from full information, to bandit, payoff-based feedback. In this general context, I will describe a series of results characterizing the possible outcomes of the process, from convergence to a Nash equilibrium, to sets of pure strategies that are (minimally) closed under better replies.
Jérôme Renault (TSE)
Title: Limit value in dynamic games
Abstract:
Ludovic Renou (QMUL)
Title: Designing Information for Learning
Abstract: We characterize what a principal learns when they incentivize agents to experiment with information only
Marco Scarsini (LUISS University)
Title: Nonatomic games
Abstract: Nonatomic games are used as an approximation of finite normal-form anonymous games with many players. In this talk I will survey the theory of nonatomic games, focusing on some relevant classes, such as congestion games. I will examine the concept of Wardrop equilibrium and some recent extensions of it. In particular, I will relate solution concepts of nonatomic games to solution concepts of finite games and I will show in which sense nonatomic games approximate finite anonymous games with many players.
This survey does not aim at being exhaustive and is unapologetically biased.
Elon Solan (Tel Aviv University)
Title: Uniform Equilibria in Stochastic Games with and without Public Correlation Device
Abstract: I will discuss the concept of uniform equilibrium in multiplayer stochastic games, with and without a public correlation device. I will survey old and new results on the existence of such equilibria.
Sylvain Sorin (Sorbonne University)
Title: Equilibria: structure, degree, index and dynamics
Abstract: This is a survey talk on some properties of the set of equilibria.
We will recall the structure theorem (Kohlberg and Mertens), degree and index (Demichelis and Germano, Govindan and Wilson) and dynamical properties (Demichelis and Ritzberger).
We will discuss few examples and present some extensions.
Tristan Tomala (HEC Paris)
Title: Linking mechanisms with few messages
Abstract: We study a sender-receiver problem where there the sender communicates about a series of states to a receiver who takes a series of actions. Our model has two distinctive features. First, the set of messages that the sender uses has a fixed size which is possibly smaller than the number of states and than the number of actions. Second, the receiver's strategy is fixed beforehand, and the sender reacts optimally to it. This represents the interaction between a rational player and a fixed decoding algorithm. Our goal is to characterize the empirical join distributions of states and actions which are achievable, given the incentives of the sender and the message limitations.
Xavier Venel (LUISS University)
Title: Price-Only Contracts with Censored Demand Observations: A repeated game approach
Abstract: In many supply-chain scenarios, precise demand data is rarely available, and retailers must rely on incomplete information shaped by past operational decisions. Typically, retailers can only access sales data, observing demand only when it is not larger than the inventory level.
Consequently, inventory decisions impact not only current profits but also the quality of data available for future planning.
We study a repeated game with incomplete information modeling a two-tier supply chain where demand is uncertain and partially observed (censored). In this setting, a supplier provides a single product to a retailer, who faces uncertain market demand over a selling horizon of $T$ periods. Each period, the supplier incurs a production cost per unit and sets the wholesale price. The retailer, facing a newsvendor problem, chooses the order quantity based on the wholesale price before demand is realized. If the demand exceeds the order quantity, the unmet demand is lost and cannot be observed, resulting in censored demand data. We assume that both the retailer and the supplier observe the sales.
We prove the existence of Markov Perfect Equilibria in the special case where the demand is a Weibull distribution with a gamma-prior. In the special case of an exponential demand, we provide a characterization and we prove uniqueness.
Bernhard von Stengel (LSE)
Title: Maximal Numbers of Nash Equilibria in Bimatrix Games
Abstract: Quint and Shubik (1997) conjectured that a non-degenerate n-by-n game has at most 2^n-1 Nash equilibria in mixed strategies. The conjecture is true for n<5 but false for n>5. We answer it positively for the remaining case n=5, which had been open since 1999. The problem can be translated to a combinatorial question about the vertices of a pair of simple n-polytopes with 2n facets. We introduce a novel obstruction based on the index of an equilibrium, which states that equilibrium vertices belong to two equal-sized disjoint stable sets of the graph of the polytope. This bound is verified directly using the known classification of combinatorial types of dual-neighborly polytopes in dimension 5 with 10 facets. Non-neighborly polytopes are analyzed with additional combinatorial techniques where the bound is used for their disjoint facets. We also give new tight bounds for some non-square bimatrix games.
Jörgen Weibull (Stockholm School of Economics)
Title: Detection stable equilibria
Abstract: If a player expects others to adhere to a certain Nash equilibrium, what is then the player’s incentive to use his or her equilibrium strategy, rather than some other best reply if such exist? The question is particularly pertinent for equilibria in mixed strategies. We analyze this question for finite two-player games and formulate an incentive criterion, “detection stability”, for players to stick to their equilibrium strategies. All equilibria of strictly competitive games are detection stable. Detection stable equilibria (DSE) also exist in potential games. We characterize DSE as subgame perfect equilibria of a “spying game” and show that in generic games with independent payoffs an equilibrium is a DSE if and only if it is pure. We also show that detection stability is logically independent of other refinements, and relate DSE to commitment-robust equilibria (Rosenthal, 1991) and informationally robust equilibria (Robson, 1994).