Related papers: Settling the complexity of computing approximate t…

We prove that computing a Nash equilibrium of a two-player ($n \times n$) game with payoffs in $[-1,1]$ is PPAD-hard (under randomized reductions) even in the smoothed analysis setting, smoothing with noise of constant magnitude. This gives…

In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…

We prove that finding an epsilon-Nash equilibrium in a succinctly representable game with many players is PPAD-hard for constant epsilon. Our proof uses succinct games, i.e. games whose payoff function is represented by a circuit. Our…

We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several…

We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As…

We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\delta>0$, an…

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…

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…

This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed…

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.

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 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…

Computing Nash equilibrium in multi-agent games is a longstanding challenge at the interface of game theory and computer science. It is well known that a general normal form game in N players and k strategies requires exponential space…

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was…

We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…

We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…

In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an $\eps$-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size $O(\log n)$ in the random…

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…

We study the randomized query complexity of approximate Nash equilibria (ANE) in large games. We prove that, for some constant $\epsilon>0$, any randomized oracle algorithm that computes an $\epsilon$-ANE in a binary-action, $n$-player game…

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…