The Computational Complexity of Trembling Hand Perfection and Other Equilibrium Refinements

Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, Troels Bjerre Sørensen

Abstract: The king of refinements of Nash equilibrium is trembling hand perfection. We show that it is NP-hard and Sqrt-Sum-hard to decide if a given pure strategy Nash equilibrium of a given three-player game in strategic form with integer payoffs is trembling hand perfect. Analogous results are shown for a number of other solution concepts, including proper equilibrium, (the strategy part of) sequential equilibrium, quasi-perfect equilibrium and CURB.