This paper concerns individual choice among from which the individual will later choose a single object. In particular, it concerns relations on opportunity sets which satisfy preference for flexibility, a set is at least as good as all of its subsets, but which may not satisfy revealed preference, the union of two sets may be strictly preferred to each one taken separately. A representation theorem is given which rationalizes such choice behavior as being as if the individual is uncertain about future tastes. IN MANY PROBLEMS of individual choice, the choice is made in more than one stage. At early stages, the individual makes decisions which will constrain the choices that are feasible later. In effect, these early choices amount to choice of a subset of items from which subsequent choice will be made. This paper concerns choice among such opportunity sets, where the individual has a desire for flexibility which is irrational if the individual knows what his subsequent preferences will be.

Joel S. Demski, David M. Kreps, Models in Managerial Accounting, Journal of Accounting Research, Vol. 20, Supplement: Studies on Current Research Methodologies in Accounting: A Critical Evaluation (1982), pp. 117-148

Sequential equilibria comprise consistent beliefs and a sequentially ra tional strategy profile. Consistent beliefs are limits of Bayes ratio nal beliefs for sequences of strategies that approach the equilibrium strategy. Beliefs are structurally consistent if they are rationaliz ed by some single conjecture concerning opponents' strategies. Consis tent beliefs are not necessarily structurally consistent, notwithstan ding a claim by Kreps and Robert Wilson (1982). Moreover, the spirit of structural consistency conflicts with that of sequential rationali ty. One avoids these difficulties by weakening structural consistency to allow convex combinations of opponents' strategies, but this intr oduces correlation into the strategies that justify out-of-equilibriu m beliefs.

Games in which one party conveys private information to a second through messages typically admit large numbers of sequential equilibria, as the second party may entertain a wealth of beliefs in response to out-of-equilibrium messages. By restricting those out-of-equilibrium beliefs, one can sometimes eliminate many unintuitive equilibria. We present a number of formal restrictions of this sort, investigate their behavior in specific examples, and relate these restrictions to Kohlberg and Mertens' notion of stability.

Finite horizon sequential decision problems with a temporal von NeumannMorgenstern criterion are analyzed. This criterion, as developed in [7], is a generalization of von Neumann-Morgenstern (expected) utility of the vector of rewards, wherein an individual's preferences concerning the timing of the resolution of uncertainty are taken into account. The preference theory underlying this criterion is reviewed and then extended in natural fashion to yield preferences for strategies in sequential decision problems. The main result is that value functions for sequential decision problems can be defined by a dynamic programming recursion using the functions which represent the original preferences, and these value functions represent the preferences defined on strategies. This permits citation of standard results from the dynamic programming literature, concerning the existence of (memoryless) strategies which are optimal with respect to the given preference relation.

We consider dynamic choice behavior under conditions of uncertainty, with emphasis on the timing of the resolution of uncertainty.Choice behavior in which an individual distinguishes between lotteries based on the times at which their uncertainty resolves is axiomatized and represented, thus the result is choice behavior which cannot be represented by a single cardinal utility function on the vector of payoffs.Both descriptive and normative treatments of the problem are given and are shown to be equivalent.Various specializations are provided, including an extension of "separable" utility and representation by a single cardinal utility function.

To ensure that individual actors take certain actions, community enforcement may be required. This can present a rules-versus-discretion dilemma: it can become impossible to employ discretion based on information that is not widely held, because the wider community is unable to verify how the information was used. Instead, actions may need to conform to simple and widely verifiable rules. We study when discretion in the form of exceptions to a simple rule can be implemented, if the information is shared by the action taker and a second party, who is able to verify for the larger group that an exception is warranted. In particular, we compare protocols where the second party excuses the action taker from taking the action ex ante with protocols where the second party instead forgives a rule-breaking actor ex post.

[We propose a new criterion for equilibria of extensive games, in the spirit of Selten's perfectness criteria. This criterion requires that players' strategies be sequentially rational: Every decision must be part of an optimal strategy for the remainder of the game. This entails specification of players' beliefs concerning how the game has evolved for each information set, including informaiton sets off the equilibrium path. The properties of sequential equilibria are developed; in particular, we study the topological structure of the set of sequential equilibria. The connections with Selten's trembling-hand perfect equilibria are given.]