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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…
Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
This short paper concerns discretization schemes for representing and computing approximate Nash equilibria, with emphasis on graphical games, but briefly touching on normal-form and poly-matrix games. The main technical contribution is a…
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…
Computing Nash equilibria of zero-sum games in classical and quantum settings is extensively studied. For general-sum games, computing Nash equilibria is PPAD-hard and the computing of a more general concept called correlated equilibria has…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
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…
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…
This paper presents a new primal-dual method for computing an equilibrium of generalized (continuous) Nash game (referred to as generalized Nash equilibrium problem (GNEP)) where each player's feasible strategy set depends on the other…
This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous…
While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares…
The Nash Equilibrium is a much discussed, deceptively complex, method for the analysis of non-cooperative games. If one reads many of the commonly available definitions the description of the Nash Equilibrium is deceptively simple in…
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…
We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for…
Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…
Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…