Gacha Game: When Prospect Theory Meets Optimal Pricing

TL;DR

This paper explores optimal pricing strategies for selling goods to buyers with prospect theory preferences, revealing different mechanisms based on buyer sophistication and inconsistency, including loot boxes and insurance options.

Contribution

It introduces the first analysis of optimal pricing under prospect theory with probability weighting, distinguishing mechanisms for naive and sophisticated buyers.

Findings

Naive buyers are best served by loot box mechanisms.

Sophisticated buyers benefit from insurance-based mechanisms.

Optimal mechanisms depend on buyer's awareness of their own inconsistency.

Abstract

I study the optimal pricing process for selling a unit good to a buyer with prospect theory preferences. In the presence of probability weighting, the buyer is dynamically inconsistent and can be either sophisticated or naive about her own inconsistency. If the buyer is naive, the uniquely optimal mechanism is to sell a ``loot box'' that delivers the good with some constant probability in each period. In contrast, if the buyer is sophisticated, the uniquely optimal mechanism introduces worst-case insurance: after successive failures in obtaining the good from all previous loot boxes, the buyer can purchase the good at full price.