This article is cited in 3 papers

MATHEMATICS

Altruistic (Berge) equilibrium in the model of Bertrand duopoly

Yu. A. Bel'skikh^a, V. I. Zhukovskii^b, S. P. Samsonov<sup>b

a</sup> Moscow State University of Technologies and Management named after K. G. Rasumovskii, ul. Shulaikinoi, 2, Orekhovo-Zuevo, 142601, Russia
^b Department of Optimal Control, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia

Abstract: In 1883 the French mathematician J. Bertrand (1822–1900) constructed the model of price competition on oligopoly market in which firms compete between themselves changing the price of goods.
The mathematical model of Bertrand duopoly is represented by a non-cooperative game of two persons in normal form. Two equilibriums are formalized for it: Berge equilibrium (BE) and Nash equilibrium (NE).
It is assumed that
a) maximal price and cost price of both players coincide (it's naturally for the market of one product);
b) the coalition of two players is prohibited (this is non-cooperative character of the game);
c) the price is higher than the cost price for otherwise the sellers (players) would hardly appear on the market.
In the present article for almost all values of parameters of the model (except the measure-null) the constructive method of the choice of concrete equilibrium (BE or NE) depending on the maximal price of the product established in the market is suggested.

Keywords: non-cooperative game, Nash equilibrium, Berge equilibrium, model of Bertrand duopoly.

UDC: 519.833

MSC: 91A10, 91B26

Received: 25.11.2015

DOI: 10.20537/vm160103

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