Assortment optimization for online video games

We consider an assortment optimization problem for a class of online video games where the in-game virtual store has a unique structure with two sections: Featured and Just For You (JFY). All customers (players) are offered the same Featured section assortment, whereas the JFY section is used for personalized recommendations. We model customer choice under a constrained mixture-of-nested-logit model and propose different solution methods for the resulting assortment optimization problems. First, we introduce a novel mixed-integer nonlinear programming (MINLP) formulation. Numerical experiments show that the MINLP formulation generally obtains optimal solutions efficiently, using a variety of instances derived from conversations with our industry partner to mimic the environment found in their video game stores. In addition, we propose three approximate solution methods with theoretical performance guarantees: a fully polynomial time approximation scheme, a mixed-integer linear programming formulation, and a heuristic algorithm. To understand the impact of a shared Featured section, we analyze the distribution of display capacity between the Featured and JFY sections. Our numerical experiments highlight that the Featured section plays a critical role in balancing revenue and customer utility. To validate our use of a mixture-of-nested-logit model, we further conduct a simulation study based on ground-truth instances that are independent of the underlying structure of the consumer choice models we consider. The results indicate that our nested structure yields superior performance in terms of both capturing customer behavior and simulation revenue, compared with the mixture-of-multinomial logit model and the current practice of our industry partner. Overall, our paper is the first to study assortment optimization for the gaming industry under discrete choice models; it is also the first to devise both exact and approximate solution approaches for the constrained mixture-of-nested-logit model. Our results provide guidance for effective management of assortments in online video game stores and offer an “assortment” of solution approaches, allowing practitioners to choose one that best suits their environment.