Excess Intertia and Cross-Model Validation

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Relating Two Models of Network Externalities

As with any two models that describe similar phenomena, it would be interesting and useful to cross-validate the Farrell and Saloner model against the Katz and Shapiro model of network externalities. Ideally, we would like to demonstrate that the two models are equivalent; that is, that they encompass the same results.

Unfortunately, this is difficult for the models we have chosen. In the Farrell and Saloner model, excess inertia results when firms have incomplete information. By contrast, the players in the Katz and Shapiro model have full information, and their decisions are fully predictable. It turns out to be quite difficult to incorporate uncertainty into the Katz and Shapiro model.

One thing that we can do easily, however, is use the Katz and Shapiro model to demonstrate the payoffs used in the Farrell and Saloner model. Recall that Farrell and Saloner exogenously set these payoffs according to some distribution. Using the Katz and Shapiro model, we can show that the payoffs should indeed have the structure that Farrell and Saloner assume.

Our approach begins by translating the Farrell and Saloner game into our established framework. In this view, when two firms adhere to a standard, they are part of the same compatibility network. To model an inferior standard, we assume the firms have a low network externality function (i.e. v(x)). When they adhere to different standards, they are not connected in a network, and the one with the superior standard has a stronger network externality function. Finally, when both firms adhere to the superior standard, they are once again part of the same network, with a strong network externality function. On the next slide, we try all these configurations in succession and compare the firm outputs.

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