Optimal design of lottery with cumulative prospect theory
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916023409573888 |
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| author | Akiyama, Shunta Obara, Mitsuaki Kawase, Yasushi |
| author_facet | Akiyama, Shunta Obara, Mitsuaki Kawase, Yasushi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00822 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal design of lottery with cumulative prospect theory Akiyama, Shunta Obara, Mitsuaki Kawase, Yasushi Computer Science and Game Theory Theoretical Economics 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. |
| title | Optimal design of lottery with cumulative prospect theory |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2209.00822 |