Free and second‐best entry in oligopolies with network effects

Abstract

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (businessstealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.

A note on the social efficiency of free entry in Cournot oligopoly in a pure network goods market

“…See also footnote 10. 33 The inverse demand function satisfies the assumptions of Gama and Samano (2021). Furthermore, assuming…”

“…Recently, theoretical papers have been published on the social efficiency of free entry in Cournot oligopoly with network effects, including for example, Gama (2019), Toshimitsu (2020), and Gama and Samano (2021). To review these studies that are very closely related to ours, we investigate two issues, which we will explain in detail in the following section.…”

“…He demonstrates that if the degree of network effects is sufficiently large, the number of firms under vertically related market structures, and technology licensing (see Basak & Mukherjee, 2016;Ghosh & Morita, 2007a, 2007b free entry is socially insufficient, based on the second-best criteria. Furthermore, based on Amir and Lazzati (2011), Gama and Samano (2021) show that there is a socially inefficient entry under sufficiently strong network effects.…”

Externalities, entry bias, and optimal subsidy policy for cleaner environment

“…Amir et al (2014) extend this analysis to allow for limited increasing returns to scale in production and argue that under Cournot competition free-entry equilibrium number of firms is excessive even compared with the first-best solution-a result that emerges in a special case of the present analysis. Finally, Gama and Samano (2021) introduce positive network (consumption) externalities in the Cournot model of free entry of Mankiw and Whinston (1986) finding that insufficient entry is possible under network effects as the latter creates a social gain of entry through the network size expansion. 4 Contribution of this paper in this stream of literature is twofold.…”

“…The broad result of this stream of literature conforms to the general intuitive argument of Tinbergen that the number of policy instruments must be no less than the number of policy targets, except in special cases (Arrow, 1958;Tinbergen, 1952). For example, Katsoulacos and Xepapadeas (1995) argue that social welfare may be enhanced by imposing a license fee on entry in addition 4 The result of insufficient entry, which is caused by business-enhancing competition in the standard models with no network effects, is obtained by Gama and Samano (2021) under business-stealing competition, provided that network effects are strong enough. 5 Perry (1984), Suzumura and Kiyono (1987), Nachbar et al (1998), and Amir and Lambson (2003), to name a few, also demonstrate the inefficiency of free-entry equilibrium in alternative scenarios.…”