Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in 'Great Expectations. Part I' is a universal decision rule, in the sense that it can represent essentially all other decision rules.

Modica and Rustichini [Theory and Decision 37, 1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information...

Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices $v$, if the player were to reach vertex...

Given a finite game with common payoffs (i.e. the players have completely common interests), we show that the problem of determining whether there exists a joint strategy where each player nets at least k is NP-complete.

Logical characterizations of the common prior assumption (CPA) are investigated. Two approaches are considered. The first is called frame distinguishability and is similar in spirit to the approaches considered in the economics literature. Results similar to those obtained in the economics...

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...