Solution Concepts in A-Loss Recall Games: Existence and Computational Complexity

Imperfect recall games represent dynamic interactions where players forget previously known information, such as history of played actions. The importance of imperfect recall games stems from allowing a concise representation of strategies compared to perfect recall games where players remember all information. However, most of the algorith-mic results are negative for imperfect recall games – a Nash equilibrium (NE) does not have to exist and computing a best response or a maxmin strategy is NP-hard. We focus on a subclass of imperfect recall games, called A-loss recall games, where a best response can be found in polynomial time. We derive novel properties of A-loss recall games, including (1) a sufficient and necessary condition for the existence of NE in A-loss recall games, (2) example where both NE and maxmin require irrational numbers for rational input, and (3) NP-hardness of problems related to finding maxmin strategies and existence of a NE strategy.