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 action spaces, bounded payoffs, Polish type spaces, and nested information admit a Bayesian equilibrium.

This paper investigates the strategic and welfare properties of endogenous population partitioning (secession) within large-population anonymous games featuring strategic heterogeneity. We consider a continuum-player framework with a binary action space where players are categorized either as fol- lowers, who experience positive network externalities from conformity, or as contrarians, who seek distinctiveness via anti-conformism. We fully characterize the set of Nash equilibria and establish con- ditions under which costless secession yields structural Pareto improvements. We demonstrate that in any strategically mixed society, every mixed-strategy Nash equilibrium admits a Pareto-improving se- cession. With finitely many types, secession systematically mitigates coordination frictions, enhancing both individual payoffs and aggregate utility. Furthermore, we characterize social planner configura- tions optimizing weighted aggregate utility, establishing a formal mathematical isomorphism between optimal jurisdictional design and the theory of Bayesian persuasion solved via concavification. Finally, we derive the structural conditions governing migration stability when subgroups can unilaterally re- locate across distinct societies.

Characterizing and explicitly computing equilibria of undiscounted dynamic games have been a challenge for many years. In this paper, we study quitting games, which are stopping games where the terminal payoff does not depend on the stage of termination. We adapt the recursive approach of Abreu et al. (Econometrica 58(5):1041–1063, 1990) to characterize a certain subset of the set of subgame-perfect ε -equilibrium payoffs. Our approach is based on the novel representation of strategy profiles through absorption paths, which was developed in Ashkenazi-Golan et al. (Math Program 203(1–2):735–762, 2024), and our characterization focuses on absorption paths in which exactly one player randomizes between quitting and continuing at any point in time. Since quitting games form a special case of both stopping games and stochastic games, our approach may be useful in studying more general classes of these games.

We introduce a new type of games, called “opportunity-hunting games,” in which two players compete to discover an uncertain event (“opportunity”) that occurs at an unobserved and random point in time. Players can inspect whether the event has already occurred again and again, but each inspection is costly. Varying the parameters of the model spans the range from games where competition between the players to be the first to identify the opportunity is the dominant force, to games in which free riding on the other player’s effort is the dominant force. We characterize the game’s unique symmetric Markov perfect equilibrium. (JEL C72, C73)

We study the value of information in predicting the evolving state of a finite Markov chain. At each stage, a decision maker chooses a state and observes only whether the current state of the chain matches her choice; the resulting information is used to make a prediction on the state at the final stage of the problem. We show that, when the chain starts from an invariant distribution, the optimal terminal value is non-decreasing with the number of observations and converges at a uniform exponential rate. We introduce the predictive learning index, which measures whether all attainable informational value is extracted after finitely many observations, and show that both finite and infinite indices may occur. In contrast, for nonstationary initial distributions, the value may strictly decrease with the horizon.

In many institutional settings, k items are selected with the goal of representing the underlying distribution of claims, opinions, or characteristics in a large population. We study environments with two adversarial parties whose preferences over the selected items are commonly known and opposed. We propose the Quantile Mechanism: one party partitions the population into k disjoint subsets, and the other selects one item from each subset. We show that this procedure is optimally representative among all feasible mechanisms, and illustrate its use in jury selection, multi-district litigation, and committee formation.

We study two-player zero-sum repeated games with incomplete information on one side, where the payoff function is tail measurable (and not necessarily the long-run average payoff). We show that the maxmin value equals the concavification of the value function of the non-revealing game. In addition, we provide an example demonstrating that, under tail-measurable payoffs, the value of the game may fail to exist.

We study a strategic experimentation game with exponential bandits, in which experiment outcomes are private. The equilibrium amount of experimentation is always higher than in the benchmark case where experiment outcomes are publicly observed. In addition, for pure equilibria, the equilibrium amount of experimentation is at least socially optimal, and possibly higher. We provide a tight bound on the degree of over-experimentation. The analysis rests on a new form of encouragement effect, according to which a player may hide the absence of a success to encourage future experimentation by the other player, which incentivizes current experimentation.

We study multiplayer Blackwell games, which are repeated games where the payoff of each player is a bounded and Borel-measurable function of the infinite stream of actions played by the players during the game. These games are an extension of the two-player perfect-information games studied by David Gale and Frank Stewart (1953). Recently, various new ideas have been discovered to study Blackwell games. In this paper, we give an overview of these ideas by proving, in four different ways, that Blackwell games with a finite number of players, finite action sets, and tail-measurable payoffs admit an ε-equilibrium, for all ε>0.

We study multi-player games with perfect information and general payoff function, where the set of stages is the set of non-positive integers {…,-2,-1,0}. We define two related equilibrium concepts: one considering only deviations at finitely many stages and another considering all deviations. We show that (i) The sets of equilibrium plays coincide for the two equilibrium concepts, provided that at least two players are active along each infinite play. (ii) In win-lose games, the game has an equilibrium if the winning sets have Borel-rank at most 2, and we provide a counter-example showing that this is no longer true for Borel-rank 3. (iii) In general non-zero-sum games, the game has an equilibrium if the payoff functions are continuous, for example, with reversed-time 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.

We study dynamic decision-making scenarios where the decision maker has several consultants at her disposal, and at every period, chooses between taking an action or getting information on the underlying state through one of the consultants. We explore the optimal strategy, and find that if one of the consultants discloses the state with a positive probability, this consultant will be used in all optimal strategies, provided the consultation cost is sufficiently small.

We analyze a two-period principal-agent model in which the principal faces a budget constraint, and the agent's private costs of performing tasks across the two periods may be correlated. We examine the optimal design of the reward scheme and the cost correlation structure. Our findings reveal that when the budget is low, the optimal reward scheme employs \textit{sufficient performance targeting}, rewarding the agent's first performance. Conversely, when the principal's budget is high, the focus shifts to \textit{sustained performance targeting}, compensating the agent's second performance. Introducing a negative cost correlation proves particularly beneficial in both scenarios: it increases the likelihood of the agent performing at least once under low budgets and balances the agent's total costs to facilitate consistent performance under high budgets. However, the optimal cost correlation structure can be more elaborate, especially for intermediate budget levels. Our results offer valuable insights for real-world applications, such as research funding allocation.

In this note, we propose an alternative definition of strategies and histories in opportunity hunting games, as introduced in Eilat, Neeman and Solan (2025). The advantage of the formulation presented here is that it encompasses a broader class of strategies than the inertial strategies analyzed in Eilat, Neeman and Solan (2025), including those that allow for a countably infinite number of inspections within finite time intervals. Although the definitions of histories and strategies in this broader setting are more subtle, we show that the main results continue to hold. This demonstrates that the findings in Eilat, Neeman and Solan (2025) are robust to environments in which players have access to a richer strategy space.

An absorbing game is a stochastic game with a single nonabsorbing state. Such a game is called recursive if all players receive a payoff of 0 in the nonabsorbing state, and positive if all payoffs in absorbing states are positive. An action profile is nonabsorbing if, when it is played, the game remains in the nonabsorbing state with probability 1. The set of nonabsorbing action profiles can be partitioned into the connected components of an undirected graph, whose vertices are these profiles, with two vertices joined by an edge whenever the corresponding profiles differ in the action of a single player. A connected component is said to be rectangular if it is the Cartesian product of subsets of the players' action sets. We prove that every positive recursive absorbing game whose nonabsorbing components are all non-rectangular admits an undiscounted equilibrium payoff.

We investigate a two-period Bayesian persuasion game, where the receiver faces a decision, akin to a one-armed bandit problem: to undertake an action, gaining noisy information and a corresponding positive or negative payoff, or to refrain. The sender's objective is to dissuade the receiver from taking action by furnishing information about the payoff. Our findings describe the optimal strategy for the amount and timing of information disclosure. In scenarios where the sender possesses knowledge of the receiver's first-period action or observes a noisy public signal correlated with it, the optimal strategy entails revealing information in the second period. If this alone proves to be insufficient to dissuade the receiver from acting, supplementary information is provided in the first period. In scenarios where information must be provided without conditioning on the receiver's first-period action, the optimal strategy entails revealing information exclusively in the first period.

We are given a bounded Borel-measurable real-valued function on a product of countably many Polish spaces, and a product probability measure. We are interested in points in the product space that can be used to approximate the expected value of this function. We define two notions. A point is called a weak ϵ-approximation, where ϵ≥0, if the Dirac measure on this point, except in finitely many coordinates where another measure can be taken, gives an expected value that is ϵ-close to the original expected value. A point is called a strong ϵ-approximation if the same holds under the restriction that in those finitely many coordinates the measure is equal to the original one. We prove that both the set of weak 0-approximation points and the set of strong ϵ-approximation points, for any ϵ>0, have measure 1 under the original measure. Finally, we provide two applications: (i) in Game Theory on the minmax guarantee levels of the players in games with infinitely many players, and (ii) in Decision Theory on the set of feasible expected payoffs in infinite duration problems.