Related papers: Approximate Well-supported Nash Equilibria below T…
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 consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…
In this work, we provide a structural characterization of the possible Nash equilibria in the well-studied class of security games with additive utility. Our analysis yields a classification of possible equilibria into seven types and we…
This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Lasserre type Moment-SOS relaxations are used to solve them.…
In 1975 the first author proved that every finite tight two-person game form $g$ is Nash-solvable, that is, for every payoffs $u$ and $w$ of two players the obtained game $(g;u,w)$, in normal form, has a Nash equilibrium (NE) in pure…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
An heuristic approach to compute strong Nash (Aumann) equilibria is presented. The method is based on differential evolution and three variants of a generative relation for strong Nash equilibria characterization. Numerical experiments…
The Nash Equilibrium (NE), one of the elegant and fundamental concepts in game theory, plays a crucial part within various fields, including engineering and computer science. However, efficiently computing an NE in normal-form games remains…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
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…
Nash equilibrium (NE) is a central concept in game theory. Here we prove formally a published theorem on existence of an NE in two proof assistants, Coq and Isabelle: starting from a game with finitely many outcomes, one may derive a game…
We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent…
We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs…
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…
Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…
Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…
This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from…
We consider $\epsilon$-equilibria notions for constant value of $\epsilon$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that…