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 various selection theories. We present all relevant techniques underlying homotopy algorithms. We give detailed expositions of the Lemke-Howson algorithm and the Van den ElzenTalman 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. JEL Classification Codes: C62, C63, C72, C73.

• Type: Conference
• Year: 2007
• Where: DAGSTUHL
• Authors: P. Jean-Jacques Herings, Ronald Peeters
• Keywords: Compute, DAGSTUHL 2007, Game-theoretic Equilibria, Nash Equilibria, Software Engineering