A differentiable homotopy to compute Nash equilibria of n-person games

P.J.J. Herings*, RJAP Peeters

*Corresponding author for this work

    Research output: Contribution to journalArticleScientificpeer-review


    The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines a unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples.

    Original languageEnglish
    Pages (from-to)159-185
    Number of pages27
    JournalEconomic Theory
    Issue number1
    Publication statusPublished - Jun 2001


    • computation of equilibria
    • noncooperative game theory
    • tracing procedure


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