Optimal design of lottery with cumulative prospect theory

TL;DR

This paper develops a linear-time algorithm for designing optimal lotteries that maximize seller profit under the cumulative prospect theory, capturing realistic buyer decision behaviors.

Contribution

It introduces a novel reformulation of the nonconvex CPT-based lottery design problem as a three-level optimization, enabling efficient solution methods.

Findings

Proposed a linear-time algorithm for CPT-based lottery design.

Extended the algorithm to settings with ticket price constraints.

First study to apply CPT to lotteries with more than two outcomes.

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.