Technical Appendix

Main Menu           Previous Topic                                                           Next Topic

Equilibrium Reaction Correspondence Curve

The authors of "Network Externalities, Competition and Compatibility" derive the following: For any Fulfilled Expectations Cournot Equilibrium (FECE), if the output of firm i is equal to x, then the combined output of all the firms outside of that firm's network can be described by the firm's equilibrium reaction correspondence equation:


where A is a constant associated with the number of consumers that are willing to enter the market, m is the number of firms in firm i's network, and v(y) is the externality function. v(y) can be any function, as long as it satisfies the following conditions: v'>0, v"<0, and lim[v'(y)] = 0 as y->infinity. For the base-case in the tutorial, we chose the simplest possible function that satisfies these conditions:


Furthermore, in the base-case, A and β  take on the following values:

A = 15, β = 5  [3]

                   Previous Slide                                                           Next Slide