This chapter studies normal form games of a special kind. It studies games played by very knowledgeable causal expected-value maximizers. These games are defined, and theorems concerning their resolutions are developed.

Hyperrational games are in several dimensions highly idealized objects that, while approached, are probably never realized. I am interested in the theory of these objects, but not for the light it promises to cast on actual games, or as a source of prescriptions for actual games. Rather, I think that this theory, and especially the part to do with problems of hyperrational games, can contribute to explanations and understandings of real agents and cultures, and can contribute justifications of such aspects of culture as coercive institutions. Also, though this is no part of my motivation, some scholars may take an interest in the theory because of the grist it can seem to provide for criticisms of Bayesian rationality.

THE CONCEPT OF A HYPERRATIONAL NORMAL-FORM GAME

I begin with conditions for normal-form games in a certain strict or ideal sense, and then proceed to conditions specific to hyperrational games.

Axiom 1. In a pure strategy game, each of finitely many players has as an option exactly the members of a finite set of strategies.

Axiom 2. Each player in a game has an expected value for each possible interaction of strategies.