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The Game Theory behind Lock Screen Ads

Recently, Google has announced a new policy for its Play Store: “Unless the exclusive purpose of the app is that of a lock screen, apps may not introduce ads or features that monetize the locked display of a device” (source: http://www.androidpolice.com/2017/11/30/google-finally-bans-apps-include-shady-lock-screen-ads/). While this change seems very straight-forward and trivial, that Google is just trying to help users here, it can also be argued that this policy change also benefits app creators. To see how, let’s analyze the situation using a bit of game theory.

Let us start with the standard setup for the evolutionarily stable strategies in Chapter 7 of “Networks, Crowds, and Markets: Reasoning About a Highly Connected World” by David Easley and Jon Kleinberg: we have a large set of apps that routinely compete randomly with each other in a two player symmetric game. The game has two strategies, namely LSA (lock screen ads) or NLSA (no lock screen ads). This may seem like an odd setup for the original situation, but let’s try to justify it: first, it seems like each app should be playing a “one-player” game, since they are just adding a separate form of revenue which seems independent of what the other apps are doing; however, if other apps are also displaying ads on the lock screen, then this diminishes the benefit of having ads on the lock screen, and our two-player formalization can capture this. Another assumption of this model is that apps are, in some sense, disposable or non-unique. We know that this is not the case in the real Play Store, as large very popular apps, such as Chrome or Messenger, are known by everyone and have a huge perception issue if they started showing ads on the lock screen. However, many smaller apps are more disposable and do not have to deal with large perception issues, and thus our construction can model this segment of the ecosystem rather well. Third, we also assume that the apps that a user installs and uses are somewhat independent (so each app ends up competing with all other apps in the ecosystem randomly), but this tends not to be true in reality. However, models that account for this (as well as the different kinds of apps) are well beyond the scope of this post. Finally, evolutionary models assume that the players are not making their own choices, but that natural selection is. In this case, we can say that apps in the ecosystem actually follow this somewhat closely, as the app turnover is very high, and there are lots of “mutations” (app developers trying novel techniques to try to increase revenue) since the players do not know the actual payoffs. With these assumptions, we can see that we can actually draw some (limited) insight about a portion of the app ecosystem.

Now for selecting our game, let us propose the following based on the additional revenue apps would receive from lock screen adds: an app receives a payoff of 5 if NLSA is played against NLSA, a payoff of 4 of if NLSA is played against LSA (since the competing app steals some of the user’s attention), a payoff of 8 if LSA is played agains NLSA, and a payoff of 6 if LSA is played against LSA. Using this game, we see that there is only one evolutionarily stable strategy, and that is playing LSA. In fact, it is actually better for all the apps, since it increases the overall revenue. However, it seems like these payoffs are not capturing certain properties that we would expect to arise in the original situation: for example, if all the apps have lock screen ads, this diminishes the value of the Play Store to users, and they will likely, then, download fewer apps or uninstall apps to not have to deal with the ads. This affects both the cases where the app uses lock screen ads. Let us change these payoffs to account for these cases: an app receives a payoff of 6 if LSA is played agains NLSA (since they get some benefit, but might just be uninstalled), and a payoff of 4 if LSA is played against LSA (they are competing for attention, and also might be uninstalled, or never installed if the market has so many LSA). Now, we still only have one evolutionarily stable strategy, again being LSA; so over time, the apps will still tend to have lock screen ads. However, now all the apps would benefit most if they all did not use LSA, as the overuse of lock screen ads drives down the benefit of all the users. This just like a tragedy of the commons, where the evolutionary nature of strategies of the apps will cause the app ecosystem to have many apps with lock screen ads, which is bad for users and for app developers.

Now there are several ways to avoid this failure: the first way is for the users to be so strict against apps with lock screen adds that playing LSA against NLSA (forcing the payoff below 5), which would then cause NLSA to be the evolutionarily stable strategy. The other option is to prevent the LSA strategy from being played altogether. In fact, this is what Google’s new policy change does: by prohibiting these lock screen ads, Google has now averted this tragedy of the commons, and has improved the Play Store not only for users, but potentially also for app developers too.

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