Coherent Decision Analysis With Inseparable Probabilities and Utilities

by Robert F. Nau (Journal of Risk and Uncertainty 10 71-91, 1991)

Abstract: This paper explores the extent to which a decision maker's probabilities can be measured separately from her utilities by observing her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of ``belief gambles'' which reveal probabilities distorted by marginal utilities for money, and a set of ``preference gambles'' which reveal utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decision maker's problem: her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books).

Key words: coherence, subjective probability, state-dependent utility, small worlds, risk neutral probabilities, noncooperative games, arbitrage, Dutch books

Comments: Besides exploring the consequences of inseparable probabilities and utilities for decision analysis, this paper presents a Bayesian theory of the 1-person game whose natural generalization is the Bayesian theory of n-person noncooperative games originally developed in the paper "Coherent Behavior in Noncooperative Games" (with McCardle) and extended to the case of non-risk-neutral players in "Arbitrage-Free Correlated Equilibria." (See also the description this paper in my research summary.)