Coexistence of large firms and less efficient small firms under price competition with free entry

This study constructs a game of technology selection and Bertrand-like price competition in a market with free entry. It demonstrates the existence of a Nash equilibrium in which a small number of firms adopting a large-scale technology coexist with, and charge a lower price than, a large number of firms adopting a small-scale technology. In this equilibrium, both available technologies and resources are allocated efficiently. This result provides a new economic rationale for antitrust law in general and, in particular, the US Sherman Act, wchich regards free entry and price competition as of foremost importance for maintaining market quality.     

Free entry equilibria with positive profits: A unified approach to quantity and price competition games

Free entry equilibria are usually characterized by the zero profit condition. We plead instead for a strict application of the Nash equilibrium concept to a symmetric simultaneous game played by actual and potential entrants, producing under decreasing average cost. Equilibrium is then typically indeterminate, with a number of active firms varying between an upper bound imposed by profitability and a lower bound required by sustainability. We use a canonical model with strategies represented by prices, although covering standard regimes of quantity and price competition, to show that in equilibrium the critical (profit maximizing) price must lie between the break-even and the limit prices.