Geodesic
One Guaranteed Equilibrium in Bertrand Duopoly under Uncertainty
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 48-54 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper considers Bertrand duopoly on a market of a differentiated product taking into account possible import. The price which is assigned for importers is nonstochastic uncertainty. The model of the duopoly is formalized as a non-cooperative two-person game under uncertainty. When the players choose their strategies, they tend to increase the price but they are guided by the value of uncertainty. The decision of the game is given as a strongly guaranteed equilibrium. It is based on the concept of an analog of a vector maximin. In the first stage (the analog of the interior minimum in the maximin) a continuous function is constructed for each player. This function is connected with the worst uncertainty. In the second stage (the analog of the exterior maximum in the maximin) Nash equilibrium is seen in «Guarantees game». «Guarantees game» is obtained after substitution uncertainties found earlier in the payoff functions. The strongly guaranteed equilibrium is built in an explicit form. The sufficient conditions for the existence of such decision are defined.
Keywords: guaranteed equilibrium; non-cooperative game; game under uncertainty; Bertrand duopoly. 
@article{VYURU_2013_6_4_a4,
     author = {A. A. Mansurova and I. S. Stabulit and S. A. Shunaylova},
     title = {One {Guaranteed} {Equilibrium} in {Bertrand} {Duopoly} under {Uncertainty}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {48--54},
     year = {2013},
     volume = {6},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a4/}
}
TY  - JOUR
AU  - A. A. Mansurova
AU  - I. S. Stabulit
AU  - S. A. Shunaylova
TI  - One Guaranteed Equilibrium in Bertrand Duopoly under Uncertainty
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2013
SP  - 48
EP  - 54
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a4/
LA  - ru
ID  - VYURU_2013_6_4_a4
ER  - 
%0 Journal Article
%A A. A. Mansurova
%A I. S. Stabulit
%A S. A. Shunaylova
%T One Guaranteed Equilibrium in Bertrand Duopoly under Uncertainty
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2013
%P 48-54
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a4/
%G ru
%F VYURU_2013_6_4_a4
A. A. Mansurova; I. S. Stabulit; S. A. Shunaylova. One Guaranteed Equilibrium in Bertrand Duopoly under Uncertainty. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 48-54. http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a4/

[1] J. Bertrand, “Book review of theorie mathematique de la richesse sociale and of recherches sur les principles mathematiques de la theorie des richesses”, J. de Savants, 67 (1883), 499–508

[2] X. Vives, “On the Efficiency of Bertrand and Cournot Equilibria with Product Differentiation”, J. of Economic Theory, 36 (1985), 166–175 | DOI | MR | Zbl

[3] J. Zhang, J. Ma, “Research on the Price Game Model for Four Oligarchs with Different Decision Rules and Its Chaos Control”, Nonlinear Dynamics, 70:1 (2012), 323–334 | DOI | MR

[4] G. Symeonidis, “Price and Non-Price Competition with Endogenous Market Structure”, J. of Economics and Management Strategy, 9 (2000), 53–83 | DOI

[5] Zhukovskiy V. I., Kudryavtsev K. N., Smirnova L. V., Guaranteed Solutions of Conflicts and Their Applications, URSS, M., 2013

[6] Zhukovskiy V. I., Kudryavtsev K. N., “Equilibring Conflicts under Uncertainty. Analogue of a Maximin”, Matematicheskaya Teoriya Igr i Ee Prilozheniya, 5:2 (2013), 3–45 | MR