Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism

S S Askar,Adel Ouannas

doi:10.1155/2020/6620570

S S Askar, Adel Ouannas

Open Access

https://doi.org/10.1155/2020/6620570

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Abstract

We study a Bertrand duopoly game in which firms adopt a gradient-based mechanism to update their prices. In this competition, one of the firms knows somehow the price adopted by the other firm next time step. Such asymmetric information of the market price possessed by one firm gives interesting results about its stability in the market. Under such information, we use the bounded rationality mechanism to build the model describing the game at hand. We calculate the equilibrium points of the game and study their stabilities. Using different sets of parameter values, we show that the interior equilibrium point can be destabilized through flip and Neimark–Sacker bifurcations. We compare the region of stability of the proposed model with a classical Bertrand model without asymmetric information. The results show that the proposed game’s map is noninvertible with type Z 0 − Z 2 or Z 1 − Z 3 , while the classical model is of type Z 0 − Z 2 only. This explains the quite complicated basins of attraction given for the proposed map.

Highlights

Introduction eBertrand competition was introduced as a model describing an economic game by the famous scientist Joseph Louis François Bertrand [1]
We consider a Bertrand game whose players adopt a gradient-based mechanism in order to update their prices according to the following discrete dynamical map: p1,t+1
We will compare between maps (6) and (7) in order to see the influences of asymmetric information on the complex dynamic characteristics of the game’s equilibrium points

Summary

Introduction

Introduction eBertrand competition was introduced as a model describing an economic game by the famous scientist Joseph Louis François Bertrand [1]. Ere are few studies of Bertrand games about the complex dynamic characteristics of their equilibrium points. We consider a Bertrand game whose players adopt a gradient-based mechanism in order to update their prices according to the following discrete dynamical map: p1,t+1

Results

Conclusion