Related papers: Properties and applications of dual reduction

The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…

Discretely-constrained Nash-Cournot games have attracted attention as they arise in various competitive energy production settings in which players must make one or more discrete decisions. Gabriel et al. ["Solving discretely-constrained…

In this paper we introduce the discontinuous universal feedback for the problem of Nash equilibrium in two person non-zero sum differential game. We assume that there exist functions satisfying some conditions analogous to the infinitesimal…

In the Eisert protocol for 2 X 2 quantum games [Phys. Rev. Lett. 83, 3077], a number of authors have investigated the features arising from making the strategic space a two-parameter subset of single qubit unitary operators. We argue that…

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…

We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…

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 theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…

We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our…

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,…

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…

The generalized Nash equilibrium problems play a significant role in modeling and analyzing several complex economics problems. In this work, we consider jointly convex generalized Nash games which were introduced by Rosen. We study two…

This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…

Following the ideas laid out in Myerson (1996), Hofbauer (2000) defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that…

If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…