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

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