Dynamic Random Choice

Abstract

I provide an axiomatization of stochastic utility over two periods, stating testable necessary and sufficient conditions under which an agent's choice behavior under exogenous menu selection can be modeled by a pair of random utility functions. Although static random utility is characterized by a single axiom, Block-Marschak nonnegativity, I demonstrate that an additional notion of marginal consistency is needed for the two-period axiomatization. In particular, when each period's choice set has size three, I restate the characterization using the simpler axiom of stochastic regularity. I conclude by stating several corollaries, including an axiomatization of stochastic utility with full support and an axiomatization of n-period stochastic utility.

Nonparametric Analysis of Dynamic Random Utility Models

“…However, the primitive in both Li (2021) and Chambers et al (2021) differs from ours in the general setup. Importantly, in our setup the domain of classical consumer choice is endowed with a primitive order (i.e., the vector order), and preference revelation respects that primitive order.…”

“…Recent interest in DRUM in finite abstract discrete choice space has provided partial characterizations of it when the primitive is the joint distribution of choices across time and with full menu variation. Li (2021) provides an axiomatic characterization of DRUM for two time periods and full menu variation. Chambers, Masatlioglu and Turansick (2021) consider correlated choice which is the joint distribution of choice on a pair of menus, the choice may be made by a group instead of a single decision maker.…”

“…Another difference is that we deal with a continuum of choices, and limited observability of menus and histories. Finally, Li (2021) and Chambers et al (2021) assume comprehensive menu variation that allows them to provide a characterization analogous to Block and Marschak (1960) exploiting the nested structure of menus under the set containment. In contrast to them, choice sets in our setup are not nested, so we cannot use the characterizations in Li (2021) and Chambers et al (2021).…”

“…Finally, Li (2021) and Chambers et al (2021) assume comprehensive menu variation that allows them to provide a characterization analogous to Block and Marschak (1960) exploiting the nested structure of menus under the set containment. In contrast to them, choice sets in our setup are not nested, so we cannot use the characterizations in Li (2021) and Chambers et al (2021). Aguiar and Kashaev (2021) studies a panel setup as well but uses a first-order-conditions approach to deal with some forms of dynamic preferences.…”