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

Highlights

• We analyze different business models in the video game industry.

• The willingness of players to pay for content determines the optimal business model.

• Switching from subscription to free-to-play can be optimal.

• We find solution paths that double back and cross themselves in the state space.

• This dramatic result stems from the irreversibility of switching to free to play.

Abstract

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.

Introduction

The growing availability of computing devices (e.g. consoles, personal computers, and especially smartphones) and network access has made the video-game industry one of the fastest growing industries. Video games sales in the United States alone in 2015 were estimated to be over $16 billion¹ and worldwide around $61 billion.² Furthermore it is estimated that the market for video games will pass the $100 billion revenue checkpoint by the end of 2017.³ Growth in the sales of mobile games are particularly strong, see Marchand and Hennig-Thurau (2013).

The classical business model is to charge for each copy of the game sold. This is still very common, particularly with games for computers and consoles, with Grand Theft Auto V being a prominent example. However, other business models are made possible by the fact that the marginal costs of producing additional copies are extremely low after the firm has incurred the considerable expense of producing the game, see e.g. Shapiro and Varian (1999). In the market for mobile games, for instance, it is not unusual to generate revenues instead by advertising and franchising; Angry Birds being a notable example.

The two business models we analyze in the present paper are particularly relevant for multi-player games: the subscription-based business model in which all users pay a monthly fee, and a free-to-play (freemium) business model, in which only enthusiastic players, which we call “heavy users”, pay for extra features they acquire. These features can be additional content or in-game items that help the player advance in the game. Hamari (2015) found that the willingness of users to pay for content is positively associated with their use intentions and a general positive attitude towards in-game purchases, and that players may purchase more if they cannot enjoy the game fully without doing so. The advantage of the subscription-based model is that every player generates revenue. The advantage of the free-to-play model is that new players are attracted more easily as they do not have to pay for the basic content of the game.

It is common for many games, but perhaps particularly for multi-player games, that new customers are recruited by existing customers, compare also e.g. Shapiro and Varian (1999), Rogers (2003), and our model accounts for these network effects in the sense that new players are attracted by a large existing user base because of positive word-of-mouth effects.

The present model distinguishes two categories of players based on their willingness to pay for additional content. In particular, we consider “heavy users”, who are willing to pay for additional content in the free-to-play model, and “light users” who are not. Note that often only a minority of players is willing to pay for content; however, if the total number of users is sufficiently large, the resulting revenues can still become huge.⁴

We suppose that the firm starts out with the subscription-based model and considers switching to the free-to-play model, not the opposite, for two reasons. First, that seems to be the general tendency in this industry, as is reflected in the following quote from an article in the Economist about the video-games industry:⁵

“the future of video games, and of gaming profits, is in mobile, where games are usually given away, and where their creators make money by selling extra features to the most enthusiastic players.”

An example of a developer that changed from subscriptions to microtransactions is San Francisco-based Three Rings Design. They launched Puzzle Pirates in 2003 as a subscription-only game, but in 2005 a microtransaction version was launched called Doubloons. Other examples include EverQuest, Star Wars: The Old Republic, Aion: The Tower of Eternity, and The Lord of the Rings Online.

Second, switching from free-to-play to a subscription-based business model requires charging for something that customers used to receive for free. That can be exceedingly unpopular, perhaps in part because of the psychological concept of “loss aversion”, see Kahneman and Tversky (1984). The resulting massive loss of users, particularly light users, could be fatal to word of mouth recruitment and the product or firm’s reputation more generally.

The Economist (2011) reports that the video-game industry is moving toward more-and-more differentiated markets as the industry becomes increasingly fragmented. This suggests that firms are not so much competing head-to-head just on price as in commodity markets; after all, from the consumers’ perspective, the primary cost of playing video games is the time invested, not the money spent. Instead, firms seek to dominate a particular niche and choose the balance of advertising, brand image, business model, and of course also price that comprises the ideal business model for that niche. For this reason we refrain from analyzing a strategic game where different firms are competing over the same point in product space. We instead design an optimal control model with a single firm operating in a particular segment of the broader video-game market. This firm chooses price, advertising, and its business model to maximize the present value of its discounted cash flow stream. Advertising is a big thing in this industry, since, as games have become a mainstream pastime, advertising expenses have become enormous),⁶ with most of the spendings done postrelease, see Marchand and Hennig-Thurau (2013).

By applying multi-stage methods from optimal control, see Tomiyama (1985), Tomiyama and Rossana (1989), Makris (2001), we obtain some interesting managerial insights. In the model developed below, it is optimal for firms to persist in the subscription-based strategy for some time if initially the number of “light users” is relatively large. On the other hand, if the total number of users is relatively low, the firm should switch to free-to-play immediately.

Also, within either phase or business model, when the number of users is increasing that boon should be exploited by trimming advertising budgets and increasing prices. This means raising the subscription fee in the subscription phase, and increasing the unit price for additional content in the free-to-play phase. Overall, advertising is higher in the free-to-play phase because when light users are able to play for free, there are more of them, and that makes advertising more effective.

The present paper also extends the literature on history-dependent solutions in multi-stage models, see e.g. Caulkins, Feichtinger, Grass, Hartl, Kort, Seidl, 2013a, Caulkins, Feichtinger, Hartl, Kort, Novak, Seidl, 2013b, Moser, Seidl, and Feichtinger (2014). In particular, so-called Skiba or DNSS⁷ curves are detected, see e.g. Skiba (1978), Wagener (2003), Grass, Caulkins, Feichtinger, Tragler, and Behrens (2008), Zeiler, Caulkins, Grass, and Tragler (2010), Caulkins et al. (2015), where the firm is indifferent between different options concerning when to switch from one business model to another, including the possibilities of switching immediately to free-to-play, switching in finite time, or switching in infinite time (i.e. never).

If switching costs are considerable and/or the level of game addiction is low, we observe a fairly classic form of history dependence in the sense that it depends on the initial situation whether in the long run it is optimal to pursue a subscription or a free-to-play business model.

However, a more interesting form of history-dependence can arise when the level of game addiction is neither too high, nor too low. Then it turns out that the firm can be indifferent between either starting out with the subscription business strategy and switching to free-to-play after some time, or beginning with free-to-play immediately. That is, the firm can be indifferent between initially employing either of the two qualitatively different business models, but still always ends up with the same strategy and the same total discounted profit.

Furthermore, by extending considerations made in Caulkins et al. (2013a), we are able to find something that is, to the best of our knowledge, entirely novel, namely solution paths where the solution path intersects itself. That is, the solution path of the second stage crosses the solution path of the first stage in the state space. That is remarkable as it is not possible in a conventional optimal control model, see e.g. Hartl (1987), Grass et al. (2008). It becomes possible here because whether the firm has or has not already used up its single opportunity to switch strategies acts in a sense as an additional state variable. So being in the exact same point in the state space as conventionally defined, does not imply being in the exact same situation with respect to this broader conception of the state space.

The rest of this paper is organized as follows. The optimal control model is presented in Section 2. Section 3 contains the mathematical analysis, while Section 4 presents the results. Finally, Section 5 concludes.