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Section  Mathematics 
Title  Altruistic (Berge) equilibrium in the model of Bertrand duopoly 
Author(s)  Bel'skikh Yu.A.^{a}, Zhukovskii V.I.^{b}, Samsonov S.P.^{b} 
Affiliations  Moscow State University of Technologies and Management^{a}, Lomonosov Moscow State University^{b} 
Abstract  In 1883 the French mathematician J. Bertrand (18221900) 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 noncooperative 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 noncooperative 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 measurenull) 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  noncooperative game, Nash equilibrium, Berge equilibrium, model of Bertrand duopoly 
UDC  519.833 
MSC  91A10, 91B26 
DOI  10.20537/vm160103 
Received  25 November 2015 
Language  Russian 
Citation  Bel'skikh Yu.A., Zhukovskii V.I., Samsonov S.P. Altruistic (Berge) equilibrium in the model of Bertrand duopoly, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 2745. 
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