SOME ALGORITHMIC QUESTIONS ABOUT NASH EQUILIBRIA

One of the most central results in Algorithmic Game Theory is that computing a (mixed) Nash equilibrium for a strategic game is PPAD - complete, even if there are only two players. This result emerged out of a sequence of breakthrough papers in the last few years. What happens if one is looking for an output Nash equilibrium that satisfies some additional properties? For several natural properties, the problem becomes NP-complete. In this note, we host a detailed exposition for a proof of one such result; the proof is originally due to Conitzer and Sandholm [8].