3.2.4 Oligopoly Under Incompatibility
One of the most interesting issues in the economics of networks is the interaction of oligopolists producing incompatible goods. A full analysis of such a market, in conjunction with the analysis of compatible oligopolists, will allow us to determine the incentives of individual firms to choose technologies that are compatible or incompatible with others.
Given any set of firms S = {1, ..., N}, we can identify a subset of S that adheres to the same technical "standard" as a coalition. Then the partition of S into subsets defines a coalition structure CS = {C1, ..., Ck}. Compatibility by all firms means that there is a single coalition that includes all firms. Total incompatibility, where every firm adheres to its own unique standard, means that k = N.
A number of criteria can be used to define the equilibrium coalition structure. A purely non-cooperative concept without side payments requires that, after a firm joins a coalition, it is better off at the resulting market equilibrium, just from revenues from its own sales.17 At a non-cooperative equilibrium with side payments, firms divide the profits of a coalition arbitrarily to induce firms to join a coalition. Yet firms do not cooperate in output decisions. Katz and Shapiro (1985) show that the level of industry output is greater under compatibility than at any equilibrium with some incompatible firm(s). This is not sufficient to characterize the incentives of firms to opt for compatibility.
Intuitively, a firm benefits from a move to compatibility if (i) the marginal externality is strong; (ii) it joins a large coalition; and (iii) it does not thereby increase competition to a significant degree by its action. On the other hand, the coalition benefits from a firm joining its "standard" if (i) the marginal externality is strong; (ii) the firm that joins the coalition is large; (iii) competition does not increase significantly as a result of the firm joining the coalition. Clearly, in both cases, the second and the third criteria may create incentives that are in conflict; this will help define the equilibrium coalition structure.18
Katz and Shapiro (1985) show that if the costs of achieving compatibility are lower for all firms than the increase in profits because of compatibility, then the industry move toward compatibility is socially beneficial. However, it may be true that the (fixed) cost of achieving compatibility is larger than the increase in profits for some firms, while these costs are lower than the increase in total surplus from compatibility. Then profit maximizing firms will not achieve industry-wide compatibility while this regime is socially optimal. Further, if a change leads to less than industry-wide compatibility, the private incentives to standardize may be excessive or inadequate. This is because of the output changes that a change of regime has on all firms. Similarly, the incentive of a firm to produce a one-way adapter, that allows it to achieve compatibility without affecting the compatibility of other firms, may be deficient or excessive because the firm ignores the change it creates on other firms' profits and on consumers surplus.