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Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes…
We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…
This paper deals with the complexity of the problem of computing a pure Nash equilibrium for discrete preference games and network coordination games beyond $O(\log n)$-treewidth and tree metric spaces. First, we estimate the number of…
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…
Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…
The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
This short paper concerns discretization schemes for representing and computing approximate Nash equilibria, with emphasis on graphical games, but briefly touching on normal-form and poly-matrix games. The main technical contribution is a…
The use of game theoretic models has been quite successful in describing various cooperative and non-cooperative optimization problems in networks and other domains of computer systems. In this paper, we study an application of game…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak…
The goal in this paper is to approximate the Price of Stability (PoS) in stochastic Nash games using stochastic approximation (SA) schemes. PoS is amongst the most popular metrics in game theory and provides an avenue for estimating the…
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…
In this work we present a hierarchical framework for solving discrete stochastic pursuit-evasion games (PEGs) in large grid worlds. With a partition of the grid world into superstates (e.g., "rooms"), the proposed approach creates a…