The dynamics of economic games based on product differentiation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:268

Article

Askar, S. S.^1,2  Alshamrani, Ahmad¹ 

[1] King Saud Univ, Dept Stat & Operat Res, Coll Sci, Riyadh 11451, Saudi Arabia

[2] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt

关键词: Discrete dynamical system;    Triopoly games;    Puu triopoly games;    Nash equilibria;    Stability;    Bifurcations;   

DOI  :  10.1016/j.cam.2014.02.032

来源: Elsevier

【 摘 要 】

The time evolution of dynamic triopoly games is modeled by a discrete dynamical system obtained by the iteration of a three-dimensional map. We present in this paper four games: a rational Cournot triopoly, a rational Bertrand triopoly, a Puu triopoly with quantity competition, and a cooperative Cournot triopoly game. For each game, the Nash equilibrium of the game is computed and complete analytical and numerical studies of the stability conditions for the fixed points, which are the Nash equilibria, are given. The analysis of bifurcations which cause qualitative changes in the behavior of games and cause loss of stability of Nash equilibrium is investigated through numerical explorations. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free