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 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 FIXPa-complete. Towards our results for two-player games we devise a new perturbation of the strategy space of an extensive form game which in particular gives a new proof of existence of quasi-proper equilibria for general n-player games.
|Title of host publication||Fundamentals of Computation Theory : 23rd International Symposium, FCT 2021 Athens, Greece, September 12–15, 2021 Proceedings|
|Number of pages||13|
|Place of Publication||Cham|
|Publication status||Published - 2021|
|Series||Lecture Notes in Computer Science|