Related papers: Communication complexity of Nash equilibrium in po…

We study the problem of computing approximate Nash equilibria (epsilon-Nash equilibria) in normal form games, where the number of players is a small constant. We consider the approach of looking for solutions with constant support size. It…

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…

We propose a type of non-cooperative game, termed multi-cluster aggregative game, which is composed of clusters as players, where each cluster consists of collaborative agents with cost functions depending on their own decisions and the…

We show that the problem of finding an {\epsilon}-approximate Nash equilibrium in an anonymous game with seven pure strategies is complete in PPAD, when the approximation parameter {\epsilon} is exponentially small in the number of players.

In this work, we investigate an application of a Nash equilibrium seeking algorithm in a social network. In a networked game each player (user) takes action in response to other players' actions in order to decrease (increase) his cost…

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear…

We prove that computing an $\epsilon$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $\epsilon$. Our result holds for 3-sparse games, which is tight given that 2-sparse…

We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash…

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…

Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…

The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium…

We study the computational complexity of decision problems about Nash equilibria in $m$-player games. Several such problems have recently been shown to be computationally equivalent to the decision problem for the existential theory of the…

Contrary to the customary view that the celebrated Nash-equilibrium theorem in Game Theory is paradigmatic for non-cooperative games, it is shown that, in fact, it is essentially based on a particularly strong cooperation assumption.…

Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks…

We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games…

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 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…