Decision theory with moral hazard and statedependent preferences

Abstract

Introduction Scope and example In the theory of utility , as presented in modern terms by von Neumann and Morgenstern (1947) and their followers, one starts from a set of prizes, say the finite set B with elements b q , q = 1,…, t . One then defines probability mixtures of prizes, by means of numerical probability vectors β on B , and observes the preferences of a decision-maker among such probability mixtures. When these preferences satisfy three simple axioms (complete order, independence and continuity – see Section 3 below), there exists a real-valued function u on B , called utility, such that preferences among probability mixtures of prizes are isomorphic with expected utilities. That is, the mixture β is preferred to the mixture if and only if In the theory of games against nature , as presented in modern terms by Savage (1954) and his followers, one starts from a set of alternative, mutually exclusive states of the world, say the finite set S with elements s 1 ,…, s n . Using, as before, a set B of prizes (‘consequences’), acts f , f ′,…, are defined as mappings of S into B – that is, as state distributions of prizes (instead of the probability distributions of prizes considered in utility theory). One then observes the preferences of a decision-maker among acts.

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