Pricing and modularity decisions under competition

Feng Tao; Hao Shao; KinKeung Lai

doi:10.3934/jimo.2018152

Article Contents

2020, Volume 16, Issue 1: 289-307. Doi: 10.3934/jimo.2018152

This issue Previous Article Mechanism design in a supply chain with ambiguity in private information Next Article On the M-eigenvalue estimation of fourth-order partially symmetric tensors

Pricing and modularity decisions under competition

a.
Department of Management Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China
b.
Shanghai University of International Business and Economics, Gubei Road, 200336, Shanghai, China
c.
Shanghai Wage Intelligent Technology Co., Ltd
d.
College of Economics, Shenzhen University, Shenzhen, China
e.
International Business School, Shaanxi Normal University, Xian, China

* Corresponding author: Hao Shao
* Corresponding author: Hao Shao

Received: September 30, 2017

Revised: April 30, 2018

Early access: September 2018

Published: October 2019

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Abstract

This paper considers price and modularity of competition between two firms with deterministic demand, in which demand is dependent on both the prices and the modularity levels determined by two firms. Bertrand competition and Stackelberg competition are formulated to derive the equilibrium solutions analytically. Because of the complexity, an intensive numerical study is conducted to investigate the impact of the sensitive parameters on equilibrium prices and modularity levels, as well as optimal profits of the two firms. An important and interesting finding is that optimal profits of the two firms under both types of competition are decreasing with the modularity cost when the price and modularity sensitivities are low, where both firms are worse-off due to decrease of the modularity levels; but they are increasing when the price and modularity sensitivities are high, where both firms are better-off at the expense of modular design. Our research reveals that Stackelberg game improves the modularity levels in most of the cases, though both firms perform better in Bertrand competition in these cases when jointly deciding the prices and modularity levels in the two firms.

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Mathematics Subject Classification: Primary: 90B50, 90B30; Secondary: 49K20.

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Figure 1. Effect of own price sensitivity

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Figure 2. Effect of competitor's price sensitivity

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Figure 3. Effect of own modularity sensitivity

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Figure 4. Effect of competitor's modularity sensitivity

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Figure 5. Effect of competitor's modularity sensitivity

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Figure 6. Effect of competitor's modularity sensitivity

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Figure 7. Effect of competitor's modularity sensitivity

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Figure 8. Effect of competitor's modularity sensitivity

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