基于累积前景理论的彩票最优设计
Optimal design of lottery with cumulative prospect theory
AI总结：
本文基于累积前景理论，研究了在买家决策遵循该理论框架下，如何设计最大化卖家利润的彩票，并提出了线性时间算法和适用于更广泛场景的高效算法。
摘要：
彩票是卖方和买家之间的一种常见赌博形式。设计彩票需要一个模型来描述买家在面对不确定结果时的决策过程。累积前景理论（CPT）是一种描述性模型，能够捕捉人们对极端事件的过度估计倾向以及对收益和损失的不同态度。在本研究中，我们设计了一个彩票，以在买家的决策遵循CPT框架时最大化卖方的利润。主要困难在于CPT框架的非凸性，我们通过将问题重新表述为三级优化问题并刻画其最优解来克服这一困难。基于分析，我们提出了一种线性时间算法来计算最优彩票。此外，我们还提出了一种适用于更广泛场景的高效算法，该场景包含彩票价格约束。这是首次将CPT框架应用于设计具有超过两个结果的最优彩票。
英文摘要：
Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that captures people's propensity to overestimate extreme events and their different attitudes toward gains and losses. In this study, we design a lottery that maximizes the seller's profit when the buyers' decision-making adheres to the CPT framework. The main difficulty is the nonconvexity of the CPT framework, which we overcome by reformulating the problem as a three-level optimization problem and characterizing its optimal solution. Based on the analysis, we propose a linear-time algorithm that computes the optimal lottery. Furthermore, we present an efficient algorithm applicable to a broader setting with a ticket price constraint. This is the first study to employ the CPT framework in designing an optimal lottery with more than two outcomes.
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