Optimizing Free-to-Play Multiplayer Games with Premium Subscription

We consider the optimal operating policies of a free-to-play multiplayer game with a premium subscription to maximize its lifetime operating profit. Accounting for social comparisons between free and premium players, we model the game attracting or losing players with a hybrid of the Bass diffusion model and the replicator equation in evolutionary game theory. Leveraging optimal control theory, we characterize optimal dynamic pricing and advertising policies and show that the developer should prioritize initial growth through aggressive advertising, while postponing the introduction of a premium subscription. Surprisingly, the optimal subscription price may start high and gradually decrease. We further show that the developer should strengthen social-comparison effects, that payment-based matchmaking can be an effective monetization driver, and that our main findings remain robust when allowing individual in-game item purchases/partial premium subscription. These findings are potentially instructive for game developers adopting the premium subscription model.