Buyers often search across sellers to learn which product best fits their needs. We study how sellers manage these search incentives through their disclosure strategies (e.g., product trials, reviews, and recommendations) and ask how competition affects information provision. If sellers can observe the beliefs of buyers or can coordinate their strategies, then there is an equilibrium in which sellers provide the “monopoly level” of information. In contrast, if buyers’ beliefs are private, then there is an equilibrium in which sellers provide full information as search costs vanish. Anonymity and coordination thus play important roles in understanding how advice markets work.
We provide a theory of random intertemporal choice. Agents exhibit stochastic choice over consumption due to preference shocks to discounting attitudes. We first demonstrate how the distribution of these preference shocks can be uniquely identified from random choice data. We then provide axiomatic characterizations of some common random discounting models, including exponential and quasi-hyperbolic discounting. In particular, we show how testing for exponential discounting under stochastic choice involves checking for both a stochastic version of stationarity and a novel axiom characterizing decreasing impatience.
We propose a novel model of stochastic choice: the single-crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single-crossing property. We offer a characterization of SCRUMs based on two easy-to-check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single-peaked and single-dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.
We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter’s perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent’s beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well-calibrated or rational.
We provide a foundation for beliefs within the classic revealed preference methodology that allows for state-dependent utilities. Suppose an agent is Bayesian and signals affect beliefs but not tastes. Under these two assumptions, an analyst who only observes the agent's pre-signal preferences and post-signal random choice can uniquely identify all of the following: (1) the agent's ex-ante prior, (2) the agent's signal structure and (3) the agent's state-dependent utilities.
We introduce a model of random ambiguity aversion. A group of agents with heterogeneous levels of ambiguity aversion choose from a set of options. An analyst does not observe this heterogeneity but observes aggregate choice that is probabilistic or random . We characterize a model where the analyst can uniquely identify the distribution of ambiguity aversion from random choice. Moreover, the analyst can also assess when one population is more ambiguity averse than another. The model also applies to a single agent receiving independent shocks to ambiguity aversion. More generally, we analyze the stochastic properties of non-linearity in models of random utility maximization.
We consider a model where agents have heterogeneous beliefs about state persistence. Equilibrium trading behavior is ordered if agents can be ranked according to the degree of disposition effect (i.e. they buy when prices fall and sell when prices rise) that they exhibit. We show that trading behavior is ordered if and only if beliefs in the population can be ordered via a single parameter measuring persistence. Agents who believe that states are less persistent exhibit the disposition effect while those who believe that states are more persistent exhibit the opposite behavior (i.e. a form of the house-money effect).