A simplicial algorithm for computing proper Nash equilibria of finite games

Stationary Point;Game Theory;Nash Equilibrium

Intersection theorems on the simplotope

Stationary Point;Econometrics;Optimization

A simplicial algorithm approach to Nash equilibria in concave games

In this paper we demonstrate a new method for computing approximate Nash equilibria in n-person games. Strategy spaces are assumed to be represented by simplices, while payoff functions are assumed to be concave. Our procedure relies on a simplicial algorithm that traces paths through the set of strategy profiles using a new variant of Sperner's Lemma for labelled triangulations of simplotopes, which we prove in this paper. Our algorithm uses a labelling derived from the satisficing function of Geanakoplos (2003) and can be used to compute approximate Nash equilibria for payoff functions that are not necessarily linear. Finally, in bimatrix games, we can compare our simplicial algorithm to the combinatorial algorithm proposed by Lemke and Howson (1964).simplicial algorithm, Nash equilibria, strategy labelling

Homotopy Methods to Compute Equilibria in Game Theory

This paper presents a complete survey of the use of homotopy methods in game theory.Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by variousselection theories. We present all relevant techniques underlying homotopy algorithms.We give detailed expositions of the Lemke-Howson algorithm and the Van den Elzen-Talman algorithm to compute Nash equilibria in 2-person games, and the Herings-Vanden Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibriain general n-person games.operations research and management science;

Computing economic equilibria by variable dimension algorithms: State of the art

Economics

Simplicial algorithms for solving the nonlinear complementarity problem on the simplotope

Operational Research

Finding a Nash equilibrium in noncooperative N-person games by solving a sequence of linear stationary point problems

Game Theory;Nash Equilibrium