Related papers: An Efficient Optimal-Equilibrium Algorithm for Two…
In large-scale games, approximating the opponent's strategy space with a small portfolio of representative strategies is a common and powerful technique. However, the construction of these portfolios often relies on domain-specific…
We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and…
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…
A long-standing open problem in algorithmic game theory asks whether or not there is a polynomial time algorithm to compute a Nash equilibrium in a random bimatrix game. We study random win-lose games, where the entries of the $n\times n$…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
We examine the problem of the existence of optimal deterministic stationary strategiesintwo-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions.We show that the existenceof such…
Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm…
Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…
In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…
Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. In this paper, we consider the notion of…
This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…
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…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
We present a simple primal-dual algorithm for computing approximate Nash-equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold'em Poker). Our algorithm is numerically stable,…
We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the…
For common notions of correlated equilibrium in extensive-form games, computing an optimal (e.g., welfare-maximizing) equilibrium is NP-hard. Other equilibrium notions -- communication (Forges 1986) and certification (Forges & Koessler…
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
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 study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…