Problem definition: Games are the fastest-growing sector of the entertainment industry. Freemium games are the fastest-growing segment within games. The concept behind freemium is to attract large pools of players, many of whom will never spend money on the game. When game publishers cannot earn directly from the pockets of consumers, they employ other revenue-generating content, such as advertising. Players can become irritated by revenue-generating content. A recent innovation is to offer incentives for players to interact with such content, such as clicking an ad or watching a video. These are termed incentivized (incented) actions. We study the optimal deployment of incented actions. Academic/practical relevance: Removing or adding incented actions can essentially be done in real-time. Accordingly, the deployment of incented actions is a tactical, operational question for game designers. Methodology: We model the deployment problem as a Markov decision process (MDP). We study the performance of simple policies, as well as the structure of optimal policies. We use a proprietary data set to calibrate our MDP and derive insights. Results: Cannibalization—the degree to which incented actions distract players from making in-app purchases—is the key parameter for determining how to deploy incented actions. If cannibalization is sufficiently high, it is never optimal to offer incented actions. If cannibalization is sufficiently low, it is always optimal to offer. We find sufficient conditions for the optimality of threshold strategies that offer incented actions to low-engagement users and later remove them once a player is sufficiently engaged. Managerial implications: This research introduces operations management academics to a new class of operational issues in the games industry. Managers in the games industry can gain insights into when incentivized actions can be more or less effective. Game designers can use our MDP model to make data-driven decisions for deploying incented actions.

An important problem in single-player video game design is how to sequence game elements within a level (or “chunk”) of the game. Each element has two critical features: a reward (e.g., earning an item or being able to watch a cinematic) and a degree of difficulty (e.g., how much energy or focus is needed to interact with the game element). The latter property is a distinctive feature in video games. Unlike passive services (like a trip to the spa) or passive entertainment (like watching sports or movies), video games often require concerted effort to consume. We study how to sequence game elements to maximize overall experienced utility subject to the dynamics of adaptation to rewards and difficulty and memory decay. We find that the optimal design depends on the relationship between rewards and difficulty, leading to qualitatively different designs. For example, when the proportion of reward-to-difficulty is high, the optimal design mimics that of more passive experiences. By contrast, the optimal design of games with low reward-to-difficulty ratios resembles work-out routines with “warm-ups” and “cool-downs.” Intermediate cases may follow the classical “mini-boss, end-boss” design where difficulty has two peaks. Numerical results reveal optimal designs with “waves” of reward and difficulty with multiple peaks. Level designs with multiple peaks of difficulty are ubiquitous in video games. In summary, this paper provides practical guidance to game designers on how to match the design of single-player games to the relationship between reward and difficulty inherent in their game’s mechanics. Our model also has implications for other interactive services that share similarities with games, such as summer camps for children. This paper was accepted by Jeanette Song, operations management. Funding: This work was supported by the National Natural Science Foundation of China [Project 72201210] and Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2020-06488]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2022.4665 .

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