Bertrand-Edgeworth Equilibrium in Oligopoly

Hirata, Daisuke (2008): Bertrand-Edgeworth Equilibrium in Oligopoly.

Abstract

This paper investigates simultaneous move capacity constrained price competition game among three firms. I find that equilibria in an asymmetric oligopoly are substantially different from those in the duopoly and symmetric oligopoly. I characterize mixed strategy equilibria and show there exist possibilities of i) the existence of a continuum of equilibria ii) the smallest firm earning the largest profit per capacity and iii) non-identical supports of equilibrium mixed strategies, all of which never arise either in the duopoly or symmetric oligopoly. In particular, the second finding sheds light on a completely new pricing incentive in Bertrand competitions.

• Item Type: MPRA Paper
• Language: English
• Keywords: Price Competition, Oligopoly, Capacity Constraint, Homogeneous Goods
• Subjects: L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games