Two-Player Location Game in a Closed-Loop Market with Quantity Competition

Author:

Chen Xiaofeng12ORCID,Song Qiankun2,Zhao Zhenjiang3

Affiliation:

1. School of Economics and Management, Chongqing Jiaotong University, Chongqing 400074, China

2. Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China

3. Department of Mathematics, Huzhou University, Huzhou 313000, China

Abstract

This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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