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

A. Seidl, J.P. Caulkins, R.F. Hartl, Peter Kort

Research output: Contribution to journalArticleScientificpeer-review


This paper addresses the problem of a video game producer who starts out with a subscription-based business model but considers when, if ever, to switch to a free-to-play model, which price discriminates between typical users, who play for free, and heavy users who pay for acquiring extra features. The videogame producer has the possibility to advertise the game, where advertising costs are quadratic. Furthermore, he can influence the outflow of players by pricing.

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.
Original languageEnglish
Pages (from-to)700-715
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - Jun 2018



  • OR in entertainment
  • optimal control
  • multi-stage modeling
  • history-dependence
  • videa games business model

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