Related papers: Finding Nash Equilibria of Two-Player Games
We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this…
We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The…
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…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
This article introduces a class of $Nash$ games among $Stackelberg$ players ($NASPs$), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a…
In this paper, we propose an equilibrium-seeking algorithm for finding generalized Nash equilibria of non-cooperative monotone convex quadratic games. Specifically, we recast the Nash equilibrium-seeking problem as variational inequality…
In this paper we consider the problem of finding a Nash equilibrium (NE) via zeroth-order feedback information in games with merely monotone pseudogradient mapping. Based on hybrid system theory, we propose a novel extremum seeking…
We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph $G(n,p)$. Our focus is on 2-player symmetric games with 2 strategies played between the incident members of…
A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to…
We derive sublinear-time quantum algorithms for computing the Nash equilibrium of two-player zero-sum games, based on efficient Gibbs sampling methods. We are able to achieve speed-ups for both dense and sparse payoff matrices at the cost…
We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically distributed given some hidden…
We evaluate the best-response (BR) algorithm for lattice convex-quadratic games, where the players have nonlinear objectives and unbounded feasible sets. We provide a sufficient condition that if certain interaction matrices (the product of…
In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…
We study the query complexity of finding the set of all Nash equilibria $\mathcal X_\star \times \mathcal Y_\star$ in two-player zero-sum matrix games. Fearnley and Savani (2016) showed that for any randomized algorithm, there exists an $n…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…