Optimal design of lottery with cumulative prospect theory

Shunta Akiyama, Mitsuaki Obara and Yasushi Kawase

Papers from arXiv.org

Abstract: 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.

Date: 2022-09
New Economics Papers: this item is included in nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2209.00822 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2209.00822

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().