Economic Theory

, Volume 18, Issue 1, pp 159–185 | Cite as

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

  • P. Jean-Jacques Herings
  • Ronald J.A.P. Peeters
Symposium Articles

Summary.

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.

Keywords and Phrases: Computation of equilibria – Noncooperative game theory – Tracing procedure. 
JEL Classification Numbers: C63, C72. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • P. Jean-Jacques Herings
    • 1
  • Ronald J.A.P. Peeters
    • 1
  1. 1.Department of Economics, Universiteit Maastricht, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS (e-mail: P.Herings@algec.unimaas.nl) NL

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