Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare | Zendy

Sameh Askar | Zendy; A. A. Elsadany | Zendy

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Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare

Author(s) -

Sameh Askar,

A. A. Elsadany

Publication year - 2021

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2021/6697341

Subject(s) - cournot competition , duopoly , mathematical economics , nonlinear system , chaotic , maximization , invariant (physics) , social welfare , fixed point , profit maximization , mathematics , economics , profit (economics) , computer science , mathematical optimization , microeconomics , mathematical analysis , physics , artificial intelligence , mathematical physics , quantum mechanics , political science , law

In this paper, we study the competition between two firms whose outputs are quantities. The first firm considers maximization of its profit while the second firm considers maximization of its social welfare. Adopting a gradient-based mechanism, we introduce a nonlinear discrete dynamic map which is used to describe the dynamics of this game. For this map, the fixed points are calculated and their stability conditions are analyzed. This includes investigating some attracting set and chaotic behaviors for the complex dynamics of the map. We have also investigated the types of the preimages that characterize the phase plane of the map and conclude that the game’s map is noninvertible of type Z 4 − Z 2 .

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