  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.
