A Note on the Complexity of P � Matrix LCP and Computing an Equilibrium

It is proved that if it is NP-hard to solve the linear complemen-tarity problemwith P-matrix or to compute a Nash-equilibrium point in a 2-player game, then NP = coNP.

[1]  Mihalis Yannakakis,et al.  How easy is local search? , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).