Gacha Game Analysis and Design

Gacha game is a special opaque selling approach, where the seller is selling gacha pulls to the buyer. Each gacha pull provides a certain probability for the buyer to win the gacha game reward. The gacha game has been enthusiastically embraced in numerous online video games and has a wide range of potential applications.In this work, we model the complex interaction between the seller and the buyer as a Stackelberg game, where the sequential decision of the buyer is modeled as a Markov Decision Process (MDP). We define the whale property in the context of gacha games. Then, we show that this is the necessary condition to achieve optimal revenue. Moreover, we provide the revenue-optimal gacha game design and show that it is equivalent to the single-item single-bidder Myerson auction.We further explore two popular multi-item gacha games, namely, the sequential multi-item gacha game and the banner-based multi-item gacha game. We also discuss the subsidies in the gacha game and demonstrate how subsidies may encourage the buyer to engage in grinding behavior. Finally, we provide a case study on blockchain systems as gacha games.