INTRODUCTION

Traditionally, the problem for the theory of two-person games has been to establish the solution to an ideal type of interdependent choice situation characterized by the following background condition.

(1) Common knowledge. There is full common knowledge of (a) the rationality of both players (whatever that turns out to mean), and (b) the strategy structure of the game for all players, and the preferences that each has with respect to outcomes.

The force of this condition is that if a player i knows something that is relevant to a rational resolution of i's decision problem, then any other player j knows that player i has that knowledge. This is typically taken to imply (among other things) that one player cannot have a conclusive reason, to which no other player has access, for choosing in a certain manner. That is, there are not hidden arguments for playing one way as opposed to another.

In addition, one invariably finds that the analysis proceeds by appeal to the following (at least partial) characterization of rational behavior for the individual participant.

(2) Utility maximization. Each player's preference ordering over the abstractly conceived space of outcomes and probability distributions over the events that condition such outcomes can be represented by a utility function, unique up to positive affine transformations, that satisfies the expected-utility principle.

(3) Consequentialism. Choice among available strategies is strictly a function of the preferences the agent has with respect to the outcomes (or disjunctive set of outcomes) associated with each strategy.