A Pure Strategy Nash Equilibrium Bertrand Game with Strictly Positive Profits

Articles

A Pure Strategy Nash Equilibrium Bertrand Game with Strictly Positive Profits [EBM 2016]
DOI: 10.4236/jss.2016.43009 PP.54 - 56
Author(s)
Yongjian Pu, Lei Zhu
ABSTRACT
This paper explores the existence of pure strategy Nash equilibrium of a Bertrand game with strictly positive profits. We show that when fixed cost is small enough, there always exists pure strategy Nash equilibrium with strictly positive profits if firms have quadratic cost functions and linear demand curve.
KEYWORDS
Bertrand Game, Nash Equilibrium, Pure Strategy, Strictly Positive Profits
References
[1]
Baye, M.R. and Morgan, J. (1999) A Folk Theorem for One-Shot Bertrand Games. Economics Letters, 65, 59-65.
http://dx.doi.org/10.1016/S0165-1765(99)00118-4
[2]
Kaplan, T.R. and Wettstein, D. (2000) The Possibility of Mixed-Strategy Equilibria with Constant-Returns-to-Scale Technology under Bertrand Competition. Spanish Economic Review, 2, 65-71.
http://dx.doi.org/10.1007/s101080050018
[3]
Dastidar, K.G. (1995) On the Existence of Pure Strategy Bertrand Equilibrium. Economic Theory, 5, 19-32.
http://dx.doi.org/10.1007/BF01213642
[4]
Bagh, A. (2010) Pure Strategy Equilibria in Bertrand Games with Discontinuous Demand and Asymmetric Tie-break- ing Rules. Economics Letters, 108, 277-279.
http://dx.doi.org/10.1016/j.econlet.2010.05.016