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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…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a…
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 a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed…
Motivated by the fact that in many game-theoretic settings, the game analyzed is only an approximation to the game being played, in this work we analyze equilibrium computation for the broad and natural class of bimatrix games that are…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
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 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…
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…
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…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
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…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
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 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…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…