Related papers: Computation of Cournot-Nash equilibria by entropic…
A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization…
It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…
We investigate the convergence properties of a continuous-time optimization method, the \textit{Mean-Field Best Response} flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions…
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network…
This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…
In this paper, we investigate the impact of introducing relative entropy regularization on the Nash Equilibria (NE) of General-Sum $N$-agent games, revealing the fact that the NE of such games conform to linear Gaussian policies. Moreover,…
We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…
In this paper we consider continuity of the set of Nash equilibria and approximate Nash equilibria for parameterized games. For parameterized games with unique Nash equilibria, the continuity of this equilibrium mapping is well-known.…
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…
This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…
We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…
We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…
We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots, f_N$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$ \dot u_j(t)=-\nabla_{x_j}f_j(u(t)) $$ $(j=1,\dots, N)$ are…
We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
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…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
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…