AI 中文总结
该研究构建了含内生偏好演化的连续时间随机选择理论，通过行为表示刻画随机选择，证明相关定理并建立McKean-Vlasov系统的存在性与弱唯一性，统一了多类相关内容。
AI 中文摘要
我们构建了一种具有内生偏好演化的连续时间随机选择理论。与动态随机效用不同，观测到的行为会通过潜在偏好状态的条件分布影响未来偏好，从而产生内生分布反馈。我们证明该反馈具有可观测的行为含义，并通过由同期选择和延续行为构成的行为表示来刻画随机选择。该表示可从随机选择中识别，得出将结构偏好动态与可观测行为关联的刚性结果，且能精确刻画分布依赖效用在何种情况下可在行为上约化为动态随机效用。我们进一步证明了一个行为不可能性定理：表现出行为分布反馈的随机选择阵列不存在动态随机效用表示。在概率层面，我们为具有条件律反馈的潜在条件McKean-Vlasov系统建立了存在性与弱唯一性。该结构在单一连续时间模型内统一了内生信息、潜在偏好动态、行为识别与随机选择。
英文摘要
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.
Comments65 pages
