Research

We consider a decision maker who first chooses a costly information structure, and then chooses an action after receiving a signal. The choice of action is observed, but the choice of information is not. Due to the unobservability of the acquired private information, the choice of action appears random from an outside analyst’s point of view. We show that, given only stochastic choice from menus of actions, an analyst can identify the agent’s taste (risk attitude), prior belief, and information cost function. In addition, we discuss the behavioral implications of our model that are weaker than some key properties of random expected utility models because of the endogeneity and hence menu-dependence of private information. Finally, we provide necessary and sufficient conditions for stochastic choice to be rationalized by our model.

Consider an agent who, before making a choice, privately learns information about an uncertain, objective state of the world through a technology of sequential experiments. We consider two cases of learning costs. In the first, the agent discounts future payoffs geometrically. In the second, she incurs a constant flow cost of time. We show that if the observable data consist only of the joint distributions over chosen actions and decision times, an analyst can uniquely identify the discount factor in the first case and the flow cost of time in the second case, besides identifying the agent’s prior belief and taste. Moreover, we show how an analyst can recover the agent’s ex-ante welfare in both cases. Our approach does not rely on any knowledge about the underlying sequential experiment.

Consider an agent who decides whether to employ an information structure to learn about a payoff-relevant state of the world before making a decision. Information is costly either because (1) the agent has to wait a fixed amount of time for the availability of the information structure and is impatient, or because (2) she has to pay a fixed and menu-independent cost to use the information structure. For each menu of options the analyst observes random choice from the menu and whether the agent acquires the information. We give an axiomatic characterization of when this random choice is consistent with either of the cases (1) or (2). We also show how the analyst can identify the information structure the agent can employ, as well as its costs.

In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random but do not conform to expected utility theory. In the first, non-uniqueness obtains even if all preferences are confined to the betweenness class (Dekel, 1986) and are suitably monotone. The second example illustrates random choice behavior consistent with random expected utility that is also consistent with random non-expected utility. On the other hand, we find that if risk preferences conform to weighted utility theory (Chew, 1983) and are monotone in first-order stochastic dominance, random choice again uniquely identifies the distribution of preferences. Finally, we argue that, depending on the domain of risk preferences, uniqueness may be restored if joint distributions of choice across a limited number of feasible sets are available.

This paper addresses a revealed preference analysis for choice under risk, given that choice data contain only finitely many observations. Conditions on data are identified that are necessary and sufficient for the data to be consistent with maximization of a betweenness preference, which is a generalization of expected utility theory. Such consistency is equivalent to the existence of many supporting hyperplanes, one for each observation, that can be extended to a complete indifference map for some betweenness preference consistent with data. The derived conditions employ novel geometric arguments the intuition for which is clarified in numerous figures using the three-outcome simplex. Because they describe the exhaustive testable implications of betweenness preference maximization, they provide a more stringent test than what is used in the experimental literature, which is to check for direct violations of the key axiom.

We revisit the random expected utility mode in Gul and Pesendorfer (2006). In the model, the probability that a specific lottery is chosen equals the probability that the realized preference ranks this lottery as optimal. Meanwhile, in their model, choice from any feasible set of lotteries is single-valued; that is, it is summarized by a probability distribution over that set. To rationalize single-valued random choice, a random preference must have a property that, in any feasible set, the optimal lottery is unique with probability 1. This rules out some cases, for example, where only finitely many preferences are possible. In this note, choice from a feasible set is modeled instead as a random set: a probability distribution over all nonempty subsets. This allows choice to be both random and multi-valued, and so imposes no restriction on the distribution of preferences. We characterize the random expected utility model where two lotteries can be indifferent with positive probability. We also characterize the random subjective expected utility model when choice objects are Anscombe-Aumann acts.