Adv. Math. Econ. 8, 449-465 (2006)

The Bertrand equilibrium in a price competition game

Makoto Yano

Faculty of Economics, Keio University

Received: September 16, 2005 Revised: September 28, 2005

JEL classification: 043, L13

Mathematical Subject Classification (2000): 91B24

Abstract. In my recent study, I have developed a Bertrand-Edgeworth game in which the price and the allocation identical to those in a long-run competitive equilibrium can be supported as a Nash equilibrium even if the number of sellers is small. Because that study focuses on markets with free entry, it has not directly examined the Bertrand-Edgeworth debate, concerning a market without free entry. Focusing on such a market, the present study demonstrates that the standard Bertrand equilibrium can be supported as a Nash equilibrium in Yano’s game.