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In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such solutions have been limited to specific, largely symmetric or…
This paper introduces constrained correlated equilibrium, a solution concept combining correlation and coupled constraints in finite non-cooperative games. In the general case of an arbitrary correlation device and coupled constraints in…
A game has approximate equilibria if for every $\epsilon >0$ there is an $\epsilon$-equilibrium. We show that there is a stochastic game that lacks approximate equilibria. This game has finitely many players and actions, their payoffs are…
We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection…
We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum Bayesian games with continuous types and finite actions under the conditions that the utility functions and the prior type distributions are continuous concerning the…
We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…
In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently"…
In this paper, we study multi-agent network games subject to affine time-varying coupling constraints and a time-varying communication network. We focus on the class of games adopting proximal dynamics and study their convergence to a…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
In this work, we provide a structural characterization of the possible Nash equilibria in the well-studied class of security games with additive utility. Our analysis yields a classification of possible equilibria into seven types and we…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…
We consider continuous-time equilibrium seeking in monotone aggregative games with coupling constraints. We propose semi-decentralized integral dynamics and prove their global convergence to a variational generalized aggregative or Nash…
We consider normal-form games with $n$ players and two strategies for each player, where the payoffs are i.i.d. random variables with some distribution $F$ and we consider issues related to the pure equilibria in the game as the number of…
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…
In a discrete space and time framework, we study the mean field game limit for a class of symmetric $N$-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct…
We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.