Imperfect-Recall Games: Equilibrium Concepts and Their Complexity
This work addresses the challenge of optimal decision-making for agents with memory limitations, such as in team games with limited communication, but it is incremental as it builds on existing game theory frameworks.
The paper tackles the problem of finding equilibria in extensive-form games with imperfect recall, analyzing the computational complexity of three solution concepts (Nash, multiselves EDT, multiselves CDT) across various game types, and relates these problems to complexity classes such as P, PPAD, and Σ₂ᴾ.
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, $Σ_2^P$ , $\exists$R, and $\exists \forall$R.