Homotopy methods to compute equilibria in game theory

P.J.J. Herings*, R.J.A.P. Peeters

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


This paper presents a 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 the 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. We explain how the main ideas can be extended to compute equilibria in extensive form and dynamic games, and how homotopies can be used to compute all nash equilibria.
Original languageEnglish
Pages (from-to)119-156
Number of pages38
JournalEconomic Theory
Issue number1
Publication statusPublished - 1 Jan 2010

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