Abstract
Ambiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior.
Highlights
In dynamic-choice problems under uncertainty, the decision maker updates his preferences and his beliefs as new information arrives, taking optimal actions in each period
Dynamic Consistency (DC), requires that an action plan is optimal when evaluated with the updated preferences of a later period if and only if it is optimal when evaluated with the preferences of an earlier period
We show that Ellsberg preferences, Consequentialism and an axiom we call Conditional Preference imply that DC and value of information are violated
Summary
In dynamic-choice problems under uncertainty, the decision maker updates his preferences and his beliefs as new information arrives, taking optimal actions in each period. We show that a weakening of the “if” direction of DC characterizes the Bayesian updating of the beliefs revealed by potential trading behavior (and are not necessarily part of the utility representation of preferences) They are called “subjective beliefs” by Rigotti et al (2008) (RSS), who identify them for a wide variety of models with convex preferences over monetary acts, making our approach very general. In a companion paper (Galanis 2021), we show that the economic content of subjective beliefs extends to dynamic and multi-agent environments Their Bayesian updating is the minimum requirement which ensures that there is no speculative trade, generalising the result of Milgrom and Stokey (1982). If information is (weakly) valuable for each agent, public information is (weakly) not valuable, generalising the result of Hirshleifer (1971) and Schlee (2001) in competitive risk-sharing environments without aggregate uncertainty
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