Bell, D.E.
(1979).
*A utility function for time streams having interperiod dependencies.*
Behavioral Science 24 (3) 208-213. 10.1002/bs.3830240306.

## Abstract

A utility function that is separable over time cannot accurately reflect the preferences of a decision maker whose attitude toward risk in a given period of a time stream depends on the particular outcome in the previous and/or following period. In this paper we use conditional utility independence to give assumptions that do allow such preferences to be quantified. For a T-period time stream the result requires the assessment of T - 1 two-period utility functions and one scaling constant. If stationarity assumptions are appropriate, only one two-period utility function and two constants are required. MANY FACTORS serve to complicate the evaluation of alternative strategies that have impacts over time. Principal among them are the necessity of making tradeoffs between consequences in different periods and the uncertainty of the outcomes as to their magnitude and timing. These issues may be resolved with a von Neumann-Morgenstern utility function [10]. Such a utility function serves as a preference (or value) function in that it provides an ordering over certain outcomes and, in addition, its expectation provides a preference function over uncertain outcomes. The difficulties associated with this approach arise when the number of time periods is large, for the dimensionality of the utility function is equal to the number of time periods. The assessment of a one-dimensional (or one-attribute) utility function is relatively easy and that of a two-dimensional utility function still practical. However, without major simplifying assumptions, the assessment of high-dimensional utility functions is impractical. The problem is to find reasonable assumptions that reduce the assessment of the utility function to a manageable level without losing the flexibility to reflect the decision maker's true preferences accurately, and without losing the property of the utility function as a useful evaluator of uncertain outcomes.

Item Type: | Article |
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Research Programs: | System and Decision Sciences - Core (SDS) |

Depositing User: | Romeo Molina |

Date Deposited: | 01 Dec 2016 12:56 |

Last Modified: | 27 Aug 2021 17:28 |

URI: | https://pure.iiasa.ac.at/14046 |

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