Limited Lookahead in Imperfect-Information Games
This addresses strategic decision-making in games with hidden information, which is incremental by extending limited lookahead from perfect- to imperfect-information settings.
The paper tackles the problem of how to act against an opponent with limited lookahead in imperfect-information games, characterizing computational hardness and designing algorithms for optimal commitment strategies, with experimental results showing the limited-lookahead player often achieves game value under certain conditions.
Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one should act when facing an opponent whose lookahead is limited. We study this for opponents that differ based on their lookahead depth, based on whether they, too, have imperfect information, and based on how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard, NP-hard, or inapproximable. We proceed to design algorithms for computing optimal commitment strategies---for when the opponent breaks ties favorably, according to a fixed rule, or adversarially. We then experimentally investigate the impact of limited lookahead. The limited-lookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium---but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths.