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Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players' payoffs, as in games, but also the other players' strategy sets. The solution…
We propose an algorithm for computing approximate Nash equilibria of partially observable games using Monte-Carlo tree search based on recent bandit methods. We obtain experimental results for the game of phantom tic-tac-toe, showing that…
In this paper, we consider stochastic monotone Nash games where each player's strategy set is characterized by possibly a large number of explicit convex constraint inequalities. Notably, the functional constraints of each player may depend…
The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We…
This paper is an exposition of algorithms for finding one or all equilibria of a bimatrix game (a two-player game in strategic form) in the style of a chapter in a graduate textbook. Using labeled "best-response polytopes", we present the…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
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…
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…
A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…
Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios…
Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a…
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…
We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree $d\geq 1$. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
We study equilibrium finding in polymatrix games under differential privacy constraints. Prior work in this area fails to achieve both high-accuracy equilibria and a low privacy budget. To better understand the fundamental limitations of…
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the…
The problem of finding pure strategy Nash equilibria in multiagent concurrent games with finite-horizon temporal goals has received some recent attention. Earlier work solved this problem through the use of Rabin automata. In this work, we…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer…
We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our primary method employs a version of the double oracle, iteratively adding strategies…