English

On the computational complexity of evolution

Computational Complexity 2015-06-16 v2 Computer Science and Game Theory

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.

Cite

@article{arxiv.1506.00095,
  title  = {On the computational complexity of evolution},
  author = {Ioannis Avramopoulos},
  journal= {arXiv preprint arXiv:1506.00095},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T09:44:18.324Z