Computational Complexity of Computing a Quasi-Proper Equilibrium

TL;DR

This paper investigates the computational difficulty of finding quasi-proper equilibria in finite extensive form games, establishing complexity results and providing efficient algorithms for special cases.

Contribution

It proves PPAD-completeness for symbolic computation in two-player games and FIXP_a-completeness for approximations in n-player games, with a polynomial algorithm for zero-sum cases.

Findings

PPAD-complete for two-player symbolic quasi-proper equilibrium

Polynomial-time algorithm for zero-sum games

FIXP_a-complete for approximations in n-player games

Abstract

We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasi-proper equilibrium is $\mathrm{PPAD}$-complete for two-player games. For the case of zero-sum games we obtain a polynomial time algorithm based on Linear Programming. For general $n$-player games we show that computing an approximation of a quasi-proper equilibrium is $\mathrm{FIXP}_a$-complete.