论文标题
彩票的最佳设计与累积前景理论
Optimal design of lottery with cumulative prospect theory
论文作者
论文摘要
彩票是卖方和多个买家之间赌博的一种流行形式，其盈利设计是卖方的主要兴趣。设计彩票需要对买方的决策过程进行建模，以确定不确定的结果。这种决策的最有前途的描述模型之一是累积前景理论（CPT），它代表了人们对收益和损失的态度，及其对极端事件的高估。在这项研究中，我们设计了一个彩票，当买家遵循CPT时，可以最大化卖方的利润。派生的问题是非概要和受约束的，因此，直接表征其最佳解决方案是一项挑战。我们通过将问题重新定义为三级优化问题来克服这一困难。重新制定使我们能够表征最佳解决方案。基于此特征，我们提出了一种算法，该算法在线性时间内相对于彩票的数量计算最佳彩票。此外，我们为票价受到限制的更一般环境提供了有效的算法。据作者所知，这是使用CPT框架设计最佳彩票的第一项研究。
A lottery is a popular form of gambling between a seller and multiple buyers, and its profitable design is of primary interest to the seller. Designing a lottery requires modeling the buyer decision-making process for uncertain outcomes. One of the most promising descriptive models of such decision-making is the cumulative prospect theory (CPT), which represents people's different attitudes towards gain and loss, and their overestimation of extreme events. In this study, we design a lottery that maximizes the seller's profit when the buyers follow CPT. The derived problem is nonconvex and constrained, and hence, it is challenging to directly characterize its optimal solution. We overcome this difficulty by reformulating the problem as a three-level optimization problem. The reformulation enables us to characterize the optimal solution. Based on this characterization, we propose an algorithm that computes the optimal lottery in linear time with respect to the number of lottery tickets. In addition, we provide an efficient algorithm for a more general setting in which the ticket price is constrained. To the best of the authors' knowledge, this is the first study that employs the CPT framework for designing an optimal lottery.
