Related papers: Counting derangements and Nash equilibria
This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. 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…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black…
In this article we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with $2n$ players. We consider a set of games with generic payoff parameters, with the only requirement…
Economists were content with the concept of the Nash equilibrium as game theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed that finding a Nash equilibrium is most likely a computationally hard problem, a result…
Computing Nash equilibrium in multi-agent games is a longstanding challenge at the interface of game theory and computer science. It is well known that a general normal form game in N players and k strategies requires exponential space…
We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash…
We introduce a general representation of large-population games in which each player s influence ON the others IS centralized AND limited, but may otherwise be arbitrary.This representation significantly generalizes the class known AS…
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…
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 consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…
Computing equilibria of games is a central task in computer science. A large number of results are known for \emph{Nash equilibrium} (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form…
We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…
Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game…
We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure…
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…
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 present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…
The computational study of equilibria involving constraints on players' strategies has been largely neglected. However, in real-world applications, players are usually subject to constraints ruling out the feasibility of some of their…