Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs

We find that over time, the qualitative behavior of prices and associated number of users is the same, while advertising behaves in the opposite manner. If the costs of switching business models are considerable and/or the “addictiveness” of the game is low, history-dependent solutions emerge, where different initial situations result in different long-run business strategies. An intermediate level of game addictiveness can lead to thresholds in which the firm is indifferent between two distinct initial business strategies, even though both converge to the same strategy in the long run.