Dynamic Inconsistency in Choice and Different Models of Dynamic Choice – A Review

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 introduces 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. Then we discuss the two main models in this context, Machina (1989) and McClennen (1990), 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 models offer a similar - though formally different - solution to the problem of dynamic inconsistency in this context. Particular attention is given to McClennen’s (1990) approach: the resolute approach. From the above discussion it emerges that McClennen also offers a formal and very complete model for sophisticated behaviour under risk and uncertainty. Therefore, we discuss other two approaches to this model of behaviour: Karni and Safra (1989b,1990), whoelaborate 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; and Dardanoni (1990), who frames the problem and discusses the limits of sophisticated choice in this context.