Homotopy Methods to Compute Equilibria in Game Theory

Abstract:     
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 various selection 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-Van den Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibria in general n-person games.

Number of Pages in PDF File: 38

Keywords: Homotopy, Equilibrium computation, Non-cooperative games, Nash Equilibrium

JEL Classification: C62, C63, C72, C73

working papers series