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


  • This paper was previously circulated in a larger version with the title “Free entry equilibria: General approach and macroeconomic applications”. We thank an anonymous referee for very useful suggestions, as well as Stefano Bosi and Bertrand Wigniolle for their discussions of our paper. We gratefully acknowledge financial support by the Agence Nationale de la Recherche.


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.