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arXiv · 2209.00822

Optimal design of lottery with cumulative prospect theory

Shunta Akiyama·Mitsuaki Obara·Yasushi Kawase
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Abstract

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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Shunta Akiyama, Mitsuaki Obara, Yasushi Kawase. 2022-09-02. Optimal design of lottery with cumulative prospect theory. https://doi.org/10.1145/3811815

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