On the computational complexity of evolution

Abstract

It is well-known that the problem of recognizing an ESS in a symmetric bimatrix game is coNP-complete. In this paper, we show that recognizing an ESS even in doubly symmetric bimatrix games is also coNP-complete. Our result further implies that recognizing asymptotically stable equilibria of the replicator dynamic in this class of games is also a coNP-complete problem.

I am withdrawing the claim that NP = coNP. The community working on the hardness of nonlinear optimization problems uses the term "NP-hard" to mean hardness under Turing (rather than Karp) reductions and does not distinguish between "NP-hard" and "coNP-hard" problems. Therefore, my proof that NP = coNP has a flaw in its argument. The rest of the results are correct though