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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: December 21, 1999; revised version: December 27, 2000
Rights and permissions
About this article
Cite this article
Herings, PJ., Peeters, R. A differentiable homotopy to compute Nash equilibria of n-person games. Econ Theory 18, 159–185 (2001). https://doi.org/10.1007/PL00004129
Issue Date:
DOI: https://doi.org/10.1007/PL00004129