Detrimental Network Effects and Pokemon Game Versions
We’ve talked a lot about goods in this class that possess network effects where the payoff increases for each user as the count of users increases. In some cases, though, it makes sense to consider network effects where the payoff decreases as the number of users increases.
They’ve done it again — in a few days, the Pokemon Company is releasing two versions of the same game (where the only difference in the actual software is the value of one flag) for a cool $59.99 each — or currently $119.99 (yes, one cent more than 2 * 59.99) if you buy a bundle of both. For players, the main difference to consider between these versions is the presence of different Pokemon within each. These Pokemon can be traded between players with either version, so back in the day when trading Pokemon happened face-to-face, having access to both versions within a group of friends was beneficial for all involved as it gave everyone access to each set of exclusives. This can be represented as a game: imagining a simple case where two people X and Y need to choose which version to get, and the payoffs are defined as 1 for each player if they choose different versions and 0 if they choose the same version, we get the following payoff matrix:
| X ↓ , Y→ | Version A | Version B |
| Version A | 0, 0 | 1, 1 |
| Version B | 1, 1 | 0, 0 |
The two Nash Equilibria here exist when people choose different versions, reflecting the common sense conclusion that it’s best to have variety in a communal setting. To more accurately reflect the temperamental nature of kids’ preferences, we can define xa, xb to be the intrinsic payoff of choosing Versions A and B respectively to X (and correspondingly ya, yb for Y) which makes things more complicated — for example, if Y strongly prefers version A to the point that ya > 1.5 and yb < 0.5, (A, B) is no longer a Nash Equilibrium as Y would have a higher payoff choosing version A. This reflects that, in practice, it can be hard to coordinate a situation that seems on the face of it to be socially optimal, especially in second grade.
| X ↓ , Y→ | Version A | Version B |
| Version A | xa, ya | 1 + xa, 1 + yb |
| Version B | 1 + xa, 1 + ya | xb, yb |
Moving away from the schoolyard, newer Pokemon games feature more complex online trading boards and markets, where another effect of the version split is highlighted: if you possess a copy of the less-adopted version, you have access to exclusive Pokemon that are more valuable to trade with users of the other version — in this case, the majority of users. This gives the user of the less-adopted version more leverage in the trading market, making it beneficial to choose the less popular version. So, here, there’s a detrimental network effect attached to the choice of one version over another. To get a sense of what this means, we can assume a potential player x has a reservation price r(x) = 1-x for version A (representing the player’s intrinsic preference for the exclusive Pokemon in version A over B), and the network effect f(x) = 1-x is used (representing the decreasing value as more players adopt the game) to calculate the true reservation price r(x)f(x):
Here, the green line is r(x)f(x), and the red line is r(x)f(1-x) for reference to a somewhat-corresponding positive network effect. The price p = 0.2 is being displayed here as a blue line, representing the cost a user pays to adopt version A over B — potentially, the degree to which the price of A is higher than B. The purple line represents r(x), showing how the detrimental network effect deviates from a situation without its presence. Something interesting to note here is that unlike the positive network effects we studied in class, r(x)f(x) only has one equilibrium at this value of p in the range (0, 1). Furthermore, we can see that the presence of the network effect decreases the number of users willing to purchase the good with a certain value for r(x), displaying how the presence of this effect offsets the intrinsic value users place on a good.
Of course, in the real world, this effect doesn’t decrease sales at all. Many users will opt to go with the slightly-overpriced double pack and maximize their ability to trade, which is why this business model is still employed with these games after all these years.