Related papers: Small Support Equilibria in Large Games
We consider sequences of games $\mathcal{G}=\{G_1,G_2,\ldots\}$ where, for all $n$, $G_n$ has the same set of players. Such sequences arise in the analysis of running time of players in games, in electronic money systems such as Bitcoin and…
There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
Real-world games, which concern imperfect information, multiple players, and simultaneous moves, are less frequently discussed in the existing literature of game theory. While reinforcement learning (RL) provides a general framework to…
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
Establishing the existence of exact or near Markov or stationary perfect Nash equilibria in nonzero-sum Markov games over Borel spaces is a challenging problem with limited positive results. Motivated by problems in multi-agent and Bayesian…
We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather…
Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…
We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…
This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the {\em best response policy}, which was proposed by Kearns et al. \cite{kls} as a way to represent all…
This article explores the minimum approximation ratio for Nash equilibrium in bi-matrix games, focusing on the Tsaknakis and Spirakis (TS) methods. The previous SOTA, TS algorithm, achieved an approximation ratio of 0.3393, but efforts to…
This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game as $n\rightarrow\infty$? Previous work on this…
Nash equilibrium (NE) is a central concept in game theory. Here we prove formally a published theorem on existence of an NE in two proof assistants, Coq and Isabelle: starting from a game with finitely many outcomes, one may derive a game…
We analyze the robustness of (pure strategy) Nash equilibria for network games against perturbations of the players' utility functions. We first derive a simple characterization of the margin of robustness, defined as the minimum magnitude…
This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash…
Algorithm design and analysis is a cornerstone of computer science, but it confronts a major challenge. Proving an algorithm's performance guarantee across all inputs has traditionally required extensive and often error-prone human effort.…
We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study…
This paper makes progress towards learning Nash equilibria in two-player zero-sum Markov games from offline data. Specifically, consider a $\gamma$-discounted infinite-horizon Markov game with $S$ states, where the max-player has $A$…