Imperfect-Recall Games: Equilibrium Concepts and Their Complexity

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...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Tewolde, Emanuel, Brian Hu Zhang, Oesterheld, Caspar, Zampetakis, Manolis, Sandholm, Tuomas, Goldberg, Paul W, Conitzer, Vincent
Format: Article
Language:English
Subjects:
Complexity
Decision theory
Game theory
Recall
Zero sum games
Online Access:Get full text
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Summary: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 P, PPAD, PLS, \(\Sigma_2^P\) , \(\exists\)R, and \(\exists \forall\)R.
ISSN:2331-8422