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

P. Jean-Jacques Herings and Ronald Peeters

Economic Theory, 2001, vol. 18, issue 1, 159-185

Abstract: 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: Computation; of; equilibria; -; Noncooperative; game; theory; -; Tracing; procedure. (search for similar items in EconPapers)
JEL-codes: C63 C72 (search for similar items in EconPapers)
Date: 2001-04-11
Note: Received: December 21, 1999; revised version: December 27, 2000
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Citations: View citations in EconPapers (18)

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