TL;DR
This paper develops a comprehensive theoretical framework for dynamic stochastic utility with finite choice sets, providing characterizations and identities applicable over arbitrary finite time horizons.
Contribution
It introduces new characterizations and mathematical identities for dynamic stochastic utility with finite choice sets, including cases with full support over preferences.
Findings
Characterization of stochastic utility with three-element choice sets
Mathematical identities for joint, marginal, and conditional sums
Extension to stochastic utility without cardinality restrictions
Abstract
I study dynamic random utility with finite choice sets and exogenous total menu variation, which I refer to as stochastic utility (SU). First, I characterize SU when each choice set has three elements. Next, I prove several mathematical identities for joint, marginal, and conditional Block--Marschak sums, which I use to obtain two characterizations of SU when each choice set but the last has three elements. As a corollary under the same cardinality restrictions, I sharpen an axiom to obtain a characterization of SU with full support over preference tuples. I conclude by characterizing SU without cardinality restrictions. All of my results hold over an arbitrary finite discrete time horizon.
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Taxonomy
TopicsEconomic theories and models · Decision-Making and Behavioral Economics · Game Theory and Voting Systems