Algorithms for Loot Box Design

Loot boxes are a primary source of revenue in the video game industry. Loot boxes randomly “drop” items of differing value. To design a loot box, sellers must choose the loot box’s purchase price and drop rate (or drop probability) of each item. We show that, in general, the loot box design problem is NP-hard. By restricting the form of player utilities, we can solve the problem exactly in polynomial time when the number of items is fixed. Under different restrictions, we solve the problem approximately in polynomial time with fixed precision. Both restrictions are satisfied by a class of exponential utility functions. We solve a more generalized version of the model in an extension, at the cost of only being able to provide an approximation that runs in polynomial time when the number of items is fixed. Some of our results follow by relating loot box design to selecting prices for each item, and selling them directly.

Funding: This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) [Grant RGPIN-2020-06488], by the Social Sciences and Humanities Research Council of Canada (SSHRC) [Grant AWD-029333], and by the Singapore Ministry of Education [MOE Grant A-8000459-00-00].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.0026.