🤖 AI Summary
This study addresses the inability of traditional dynamic random utility models to capture endogenous feedback from behavior to preferences. It proposes a continuous-time stochastic choice theory that formalizes this feedback through the joint distribution of latent preferences and observable choices: current actions influence the evolution of future preferences via conditional distributions. The work innovatively introduces a behavioral representation in which preferences depend on the distribution of past choices, thereby establishing a rigid link between preference dynamics and observed behavior. It further demonstrates that, in the presence of such distributional feedback, the standard dynamic random utility representation no longer holds. By leveraging a conditional McKean–Vlasov system and integrating behavioral identification with continuous-time stochastic process analysis, the paper establishes existence and weak uniqueness of the model solution, providing a unified framework for identifying endogenous information, preference evolution, and stochastic choice.
📝 Abstract
We develop a continuous-time stochastic choice theory with endogenous preference evolution. Unlike dynamic random utility, observed behavior affects future preferences through the conditional distribution of latent preference states, generating endogenous distributional feedback. We show that this feedback has observable behavioral implications and characterize stochastic choice by a behavioral representation consisting of contemporaneous choice and continuation behavior. This representation is identified from stochastic choice, yields a rigidity result linking structural preference dynamics to observable behavior, and characterizes exactly when distribution dependent utility is behaviorally reducible to dynamic random utility. We further prove a behavioral impossibility theorem: stochastic choice arrays exhibiting behavioral distributional feedback admit no dynamic random utility representation. On the probabilistic side, we establish existence and weak uniqueness for the underlying conditional McKean-Vlasov system with conditional law feedback. The structure unifies endogenous information, latent preference dynamics, behavioral identification, and stochastic choice within a single continuous-time model.