A Dynamic Capital Accumulation Model in Markets with Network Externality

We propose a differential game model in markets with network externalities where two firms compete in capital accumulation by investing. We obtain the following findings: (i) when the marginal costs are equal across firms, the capacities and investment efforts at the steady states increase with network intensity and compatibility parameters for both firms; (ii) when the marginal costs differ across firms, the capacity and investment effort for firm with low (resp. high) marginal cost at the steady states may decrease with compatibility (resp. network intensity) parameter when substitutability is big enough.