FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Strong Nash equilibrium for oligopoly with quantity and price settings |
Nastych M.A. |
2019, issue 2, P. 223–234 |
Abstract |
| This paper investigates the existence of strong Nash equilibrium in Cournot and Bertrand oligopoly models with smooth general functions of demand and costs. Strong Nash equilibrium can be considered as the sufficient conditions for firms not to have incentives to collude or to merge. Unlike the concept of Nash equilibrium, the concept of strong Nash equilibrium takes into account the possibility of joint deviations of the players. It gives an intuition of its applicability to the analysis of profitability of coalitions formations. Given the existence of Nash equilibrium in the model, I derive the necessary and sufficient condition for this equilibrium to be SNE in quantity setting model. Thus, Nash equilibrium in the quantity setting oligopoly is strong iff it is a saddle point of demand function or, equivalently, it is a competitive equilibrium. I obtain non-existence result for SNE in price settings oligopoly. The peculiarity of derived conditions leads to the proposition that firms do have incentives to collude or to merge in the most cases. It explains the growth of a number of international M&A deals with the well--known statistics of wide-spread failures among them. |
Keywords: non-cooperative game, strong Nash equilibrium, Cournot, Bertrand, quantity setting, price setting |
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References |
| [1] J.P. Neary, “Cross–border mergers as instruments of comparative advantage”, The Review of Economic Studies, 74:4, (2007), 1229–1257. doi 10.1111/j.1467-937X.2007.00466.x. [2] B. Shitovitz, “Oligopoly in markets with a continuum of traders”, Econometrica: Journal of the Econometric Society, 41:3, (1973), 467–501. doi 10.2307/1913371. [3] A.A. Cournot, Recherches sur les principes mathematiques de la theorie des richesses par Augustin Cournot, L. Hachette, 1838. [4] J. Farrell, C. Shapiro, “Horizontal mergers: an equilibrium analysis”, The American Eco-nomic Review, 80:1, (1990), 107–126. [5] M.K. Perry, R.H. Porter, “Oligopoly and the incentive for horizontal merger”, The American Economic Review, 75:1, (1985), 219–227. [6] S.W. Salant, S. Switzer, R.J. Reynolds, “Losses from horizontal merger: the e?ects of an exogenous change in industry structure on Cournot–Nash equilibrium”, The Quarterly Journal of Economics, 98:2, (1983), 185–199. [7] R. J. Aumann, “Acceptable points in general cooperative n-person games”, Contributions to the Theory of Games, v. IV, Annals of mathematics studies 40, Princeton University Press, 1959, 287–324. [8] B.D. Bernheim, M.D. Whinston, “Coalition–proof Nash equilibria II. Applications”, Journal of Economic Theory, 42:1, (1987), 13–29. doi 10.1016/0022-0531(87)90100-1. [9] K.G. Dastidar, “On the existence of pure strategy Bertrand equilibrium”, Economic Theory, 5:1, (1995), 19–32. doi 10.1007/BF01213642. [10] P.R. Chowdhury, “Strong Bertrand Equilibria”, Keio economic studies, 41:1, (2004), 59–64. [11] R. Nessah, G. Tian, “On the existence of strong Nash equilibria”, Journal of Mathematical Analysis and Applications, 414:2, (2014), 871–885. doi 10.1016/j.jmaa.2014.01.030. [12] D.T. Armentano, Y. Brozen, Antitrust and Monopoly. Anatomy of a Policy Failure, Independent Institute, 1990, 312 pp. [13] S. Loertscher, L.M. Marx, “Merger Review for Markets with Buyer Power”, Journal of Political Economy, 0(ja), (2018), 1–53. |