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POLIS Working Papers - Working paper n. 83

Dynamic inconsistency and different models of dynamic choice - a review

December 2006


Abstract

In this paper the problem of inconsistent dynamic choice is discussed, as considered in the literature, both under certainty in the context of changing preferences, and under risk and uncertainty in the case of preference orderings which violate expected utility theory.
The problem of inconsistent choice in a dynamic decision situation has been initially analysed in the literature in a context of certainty and related to the problem of preferences changing exogenously through time. Hammond (1976, 1977) generalises the analysis, but keeps it confined to a situation without risk or uncertainty, which he will introduce only later (Hammond 1988a,b; 1989). Hammond overcomes the distinction between exogenously and endogenously changing tastes, and concentrates the analysis on the essential aspect of the problem - that preferences get reversed over time. This implies considering dynamic choice in a general framework. The discussion on dynamic inconsistency under certainty brings about the definition of two different models of behaviour: the myopic approach and the sophisticated approach. In a context of choice under risk and uncertainty, dynamic inconsistency occurs when preference orderings over risky or uncertain outcomes violate Expected Utility Theory, particularly through violation of the Independence Axiom.
The problem of the dynamic inconsistency of non-expected utility agents is illustrated first through the arguments by Raiffa (1968). Raiffa frames the problem of inconsistent choice in a context of dynamic choice under risk, by showing that dynamic consistency is not compatible with the usual choices in an Allais paradox when this is considered as a decision problem in two stages. The two main models - Machina (1989) and McClennen (1990) - are then discussed, after having illustrated briefly the general theoretical debate on the justification of expected utility as a normative theory, in which the dynamic inconsistency argument and the two models are framed. Both arguments offer a similar - though formally different - solution to the problem of the dynamic inconsistency in this context, the resolute approach. Particular attention is given to McClennen's (1990) approach to the problem.
From the discussion it emerges that McClennen has given a formal and very complete model for sophisticated behaviour under risk and uncertainty. Other two approaches to this model of behaviour are discussed. Karni and Safra (1989b, 1990) elaborate a model of ‘behavioural consistency' which represents a solution to the problem of dynamic inconsistency with non-expected utility preferences, extending to risk and uncertainty the sophisticated approach. Dardanoni (1990) frames the problem and discusses the limits of sophisticated choice in this context.

JEL Classification numbers

D90, D81

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Monthly online jounal "POLIS Working Papers" - Registration n.591, 12/05/2006 - Tribunale di Alessandria
ISSN: 2038-7296


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