提出非加性序列动态下的函数一致博弈框架，解决长期决策中的收益累积问题。
Function-Coherent Gambles with Non-Additive Sequential Dynamics
- 引入对数域非线性组合算子，模拟重复博弈的乘积型收益增长
- 保持时间平均增长率，解决经典期望值与实际长期收益不一致的问题
- 适用于有非平稳奖励动态的金融、行为经济学等场景
理想的博弈框架为模糊概率理论提供了严谨基础，但依赖于线性效用的合理性公理。在前期工作中，我们提出了函数一致博弈以适应非线性效用。然而，在重复博弈中，尤其是复利式收益的跨期选择中，标准的可加组合公理无法正确刻画长期评估。本文通过放松可加组合公理，引入一种在对数域中聚合重复博弈的非线性组合算子，该算子保持了时间平均（几何）增长率，解决了遍历性问题。我们证明了该算子的关键代数性质，讨论其对一致性、风险评估及表示的影响，并提供了若干说明性例子。该方法弥合了期望值与时间平均之间的差距，统一了规范性理论与实证观察到的非平稳奖励动态。
原文摘要 · Abstract (English)
The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate non-linear utility. However, when repeated gambles are played over time -- especially in intertemporal choice where rewards compound multiplicatively -- the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。