Related papers: Regular Potential Games
Computing the Nash equilibrium (NE) for N-player non-zerosum stochastic games is a formidable challenge. Currently, algorithmic methods in stochastic game theory are unable to compute NE for stochastic games (SGs) for settings in all but…
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…
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…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random…
We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…
We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…
We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…
Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
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…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for games with a continuum of players with both attractive and…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…
We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…