Managing the Release of Consumable Digital Goods in Freemium Games

A common practice for freemium games is to launch with a simple and intuitive design and release premium features over time in the form of in-app purchases (IAPs) to monetize players.We propose an optimal control model that yields insights into the optimality and economic justification of such an approach. Through analytically characterizing the game life cycle and optimal release pattern of IAP for certain structured instances, we characterize when games optimally launch with an initial period free of IAPs in order to maximize the growth of its player-base and later exploit this player-base for generating revenue by releasing IAPs. This strategy balances the tradeoff between the effects of IAP release on acquiring and retaining players with the revenuegenerating potential of selling IAPs. Our model also admits comparative statics results on how exogenous factors, such as the social nature of the game, influence the optimal time of initial IAP release. In a numerical study, we show that a game can be permanently free if it generates revenues outside of player purchases, say through advertising revenue. We also consider the possibility of an operating loss during the free period due to per-player operating costs. We show the length of the loss period (while the game is totally free) and the magnitude of loss depends on exogenous factors, including the strength of word-of-mouth.