COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1342

A Derivation of Expected Utility Maximization in the Context of a Game

Itzhak Gilboa
Tel-Aviv University and Cowles Foundation, Yale University
David Schmeidler
Tel-Aviv University and The Ohio State University

December 2001

A decision maker faces a decision problem, or a game against nature. For each probability distribution over the state of the world (nature's strategies), she has a weak order over her acts (pure strategies). We formulate conditions on these weak orders guaranteeing that they can be jointly represented by expected utility maximization with respect to an almost-unique state-dependent utility, that is, a matrix assigning real numbers to act-state pairs. As opposed to a utility function that is derived in another context, the utility matrix derived in the game will incorporate all psychological or sociological determinants of well-being that result from the very fact that the outcomes are obtained in a given game.

Keywords: Expected utility, ultimatum game

JEL Classification: D70