Algorithmic rationality: Game theory with costly computation

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevertheless, we can use the framework to provide psychologically appealing explanations of observed behavior in well-studied games (such as finitely repeated prisoner’s dilemma and rock-paper-scissors). Furthermore, we provide natural conditions on games sufficient to guarantee that equilibria exist. ∗Minor updates in September 2011. An extended abstract of this paper appeared in the 1st Innovations in Computer Science Conference, 2010. Halpern is supported in part by NSF grants ITR-0325453, IIS-0534064, IIS0812045, and IIS-0911036, and by AFOSR grants FA9550-08-1-0438 and FA9550-09-1-0266, and ARO grant W911NF09-1-0281. Pass is supported in part by a Microsoft Research Faculty Fellowship, NSF CAREER Award CCF-0746990, AFOSR Award FA9550-08-1-0197, and BSF Grant 2006317.