  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.
