Imperfect-Recall Games: Equilibrium Concepts and Their Complexity
Imperfect-Recall Games: Equilibrium Concepts and Their Complexity
Emanuel Tewolde, Brian Hu Zhang, Caspar Oesterheld, Manolis Zampetakis, Tuomas Sandholm, Paul Goldberg, Vincent Conitzer
Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence
Main Track. Pages 2994-3004.
https://doi.org/10.24963/ijcai.2024/332
We investigate optimal decision making under imperfect recall, that is, when an agent forgets information it once held before. An example is the absentminded driver game, as well as team games in which the members have limited communication capabilities. In the framework of extensive-form games with imperfect recall, we analyze the computational complexities of finding equilibria in multiplayer settings across three different solution concepts: Nash, multiselves based on evidential decision theory (EDT), and multiselves based on causal decision theory (CDT). We are interested in both exact and approximate solution computation. As special cases, we consider (1) single-player games, (2) two-player zero-sum games and relationships to maximin values, and (3) games without exogenous stochasticity (chance nodes). We relate these problems to the complexity classes PPAD, PLS, Σ_2^P, ∃R, and ∃∀R.
Keywords:
Game Theory and Economic Paradigms: GTEP: Noncooperative games