Abstract
We make further attempts to investigate equilibrium stability of a nonlinear Cournot duopoly game. Our studies in this paper focus on the cooperation that may be obtained among duopolistic firms. Discrete time scales under the assumption of unknown inverse demand function and linear cost are used to build our models in the proposed games. We introduce and study here an adjustment dynamic strategy beside the so-called tit-for-tat strategy. For each model, the stability analysis of the fixed point is analyzed. Numerical simulations are carried out to show the complex behavior of the proposed models and to point out the impact of the models’ parameters on the cooperation.
Highlights
There are often several duopolistic firms in economic market where competition among them is controlled by the amount of commodities they produce, the demand scheme they adopt, and the profit each firm wants to maximize
The dynamic case in which the equilibrium point (Nash equilibrium) is sought and its complex dynamic characteristics are of main interest has been studied in literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
We argue that there is a cooperation between firms in repeated Cournot duopoly games with a generalized price function
Summary
There are often several duopolistic firms in economic market where competition among them is controlled by the amount of commodities they produce, the demand scheme they adopt, and the profit each firm wants to maximize. We argue that there is a cooperation between firms in repeated Cournot duopoly games with a generalized price function. Since firm rationality contradicts with Pareto optimality (in cooperation case), Nash equilibrium in duopoly game is not Pareto optimal. In the well-known short game of prisoner’s dilemma, the Nash equilibrium point is Pareto optimal as cooperation is obtainable. We introduce a duopoly game based on a generalized nonlinear inverse demand function. The complex dynamic characteristics of this map are studied and the stability of the Nash equilibrium is investigated. The structure of the paper is as follows: In Section 2 a description of a Cournot duopoly game based on a generalized inverse demand function is presented. We end the paper with some conclusions to show the significance of our results
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