Gacha Game: Selling a Unit Good to a Prospect Theory Consumer

Abstract

This paper considers the design problem of selling a unit good to a prospect theory buyer, with non-negative constraints on the realized price. When the value is private and the reservation value is 0, it is optimal for the seller to use a post binary random price mechanism, where he charges a large price that may exceed the buyer's actual value and gives a full refund with some probability. When the reservation value is positive, the seller may provide infinite menus to different types of buyers. Each menu consists of a binary random price and a (potentially) interior probability of getting the good. If the buyer is naive about her dynamic inconsistent preference caused by probability weighting, the seller can potentially gain more profit from a dynamic pricing process. When the buyer's value is public, the generically unique optimal dynamic pricing strategy is to sell a ``lucky chest'' that delivers the good with some constant probability in each period. Until she finally gets the good, the buyer always naively believes she will try her luck just one last time.