Optimal design of lottery with cumulative prospect theory
For sellers designing lotteries, this provides the first optimal design under a realistic behavioral model (CPT) for multi-outcome lotteries, though the problem is domain-specific.
This paper designs a lottery that maximizes seller profit when buyers follow cumulative prospect theory (CPT), overcoming the nonconvexity of CPT by reformulating as a three-level optimization problem. It proposes a linear-time algorithm for the optimal lottery and an efficient algorithm for settings with ticket price constraints, marking the first study to use CPT for lotteries with more than two outcomes.
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.