提出非线性效用下的概率决策框架，统一解释多种时间偏好现象
Function-coherent gambles
- 基于连续线性泛函定义函数一致性赌局，放宽线性效用限制
- 证明可接受赌局的表征定理，为非恒定贴现提供理论支撑
- 适用于超指数、状态依赖等复杂时间偏好，适合行为决策研究者
理想的赌局框架为模糊概率理论提供了基础，但严重依赖线性效用假设。本文提出函数一致性赌局，一种在保持基本理性性质的同时容纳非线性效用的推广。我们建立了函数一致性的核心公理，并证明了接受赌局可通过连续线性泛函表征的表示定理。该框架被用于分析各种形式的跨期贴现，包括双曲型、准双曲型、尺度依赖型和状态依赖型贴现。我们展示了这些替代恒定指数贴现的模型如何被整合进函数一致性框架。这种统一处理为在不确定性下的跨期决策中建模复杂的时间偏好模式提供了理论基础，弥合了规范理论与实际观察行为之间的差距。
原文摘要 · Abstract (English)
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates non-linear utility while preserving essential rationality properties. We establish core axioms for function-coherence and prove a representation theorem that characterizes acceptable gambles through continuous linear functionals. The framework is then applied to analyze various forms of discounting in intertemporal choice, including hyperbolic, quasi-hyperbolic, scale-dependent, and state-dependent discounting. We demonstrate how these alternatives to constant-rate exponential discounting can be integrated within the function-coherent framework. This unified treatment provides theoretical foundations for modeling sophisticated patterns of time preference within the desirability paradigm, bridging a gap between normative theory and observed behavior in intertemporal decision-making under genuine uncertainty.
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