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We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
Lipschitz games, in which there is a limit $\lambda$ (the Lipschitz value of the game) on how much a player's payoffs may change when some other player deviates, were introduced about 10 years ago by Azrieli and Shmaya. They showed via the…
We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixed-strategy Nash equilibrium in tree-structured graphical multi-hypermatrix games (GMhGs). GMhGs are generalizations of normal-form…
An open problem in linear quadratic (LQ) games has been characterizing the Nash equilibria. This problem has renewed relevance given the surge of work on understanding the convergence of learning algorithms in dynamic games. This paper…
We study the repeated congestion game, in which multiple populations of players share resources, and make, at each iteration, a decentralized decision on which resources to utilize. We investigate the following question: given a model of…
We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
Learning and equilibrium computation in games are fundamental problems across computer science and economics, with applications ranging from politics to machine learning. Much of the work in this area revolves around a simple algorithm…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information…
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
This paper investigates the challenge of learning in black-box games, where the underlying utility function is unknown to any of the agents. While there is an extensive body of literature on the theoretical analysis of algorithms for…
We consider the problem of computing stationary points in min-max optimization, with a particular focus on the special case of computing Nash equilibria in (two-)team zero-sum games. We first show that computing $\epsilon$-Nash equilibria…
Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…
Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given…
The distributed computation of Nash equilibria is assuming growing relevance in engineering where such problems emerge in the context of distributed control. Accordingly, we present schemes for computing equilibria of two classes of static…