Evolution of revenue preference for competing firms with nonlinear inverse demand

Caichun Chai; Tiaojun Xiao; Zhangwei Feng

doi:10.3934/jimo.2021071

Article Contents

2022, Volume 18, Issue 4: 2351-2367. Doi: 10.3934/jimo.2021071

This issue Previous Article Design of probabilistic $ l_2-l_\infty $ filter for uncertain Markov jump systems with partial information of the transition probabilities Next Article Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering

Evolution of revenue preference for competing firms with nonlinear inverse demand

1.
School of Management Science and Engineering, Nanjing University of Finance and Economics, Nanjing 210023 China
2.
Center for Behavioral Decision and Control, School of Management and Engineering, Nanjing University, Nanjing 210093, China
3.
School of Business, Ningbo University, Ningbo 315211, China

^* Corresponding author: Caichun Chai
^* Corresponding author: Caichun Chai

Received: July 2020

Revised: February 2021

Early access: April 2021

Published: July 2022

This study is funded by the National Natural Science Foundation of China (71871112, 71601098), and Natural Science Foundation of the Jiangsu Province (BK20190791)

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Abstract

This paper studies evolutionarily stable preferences of competing firms across independent markets. Two models are considered according to whether firms' preferences are discrete or continuous. When preferences are discrete, firms have two marketing strategies: profit maximization and revenue maximization. We find that, whether pure and mixed strategies are evolutionarily stable depends on the spectrum of pricing capability. When the pricing capability is moderate, the mixed strategy is an evolutionarily stable strategy. Revenue maximization is evolutionarily stable under relatively high pricing capability, whereas, in case of low pricing capability, firms opt to maximize their profits. Further, the stability of revenue preference is also examined under continuous preferences. We derive the conditions, under which a unique evolutionarily stable revenue preference appears as well as it is continuously stable. Our main results still hold when we extend our model to a general framework.

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Mathematics Subject Classification: Primary: 91A22; Secondary: 93D20.

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Figure 1. The overall flowchart for the proposed methodology

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Figure 2. Phase portrait when $ c(17+\sqrt{193})/6<a<c(4+\sqrt{13}) $

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Figure 3. Phase portrait when $ a\leq c(17+\sqrt{193})/6 $

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Figure 4. Phase portrait when $ a\geq c(4+\sqrt{13}) $

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Figure 5. Firms' payoffs change with the degree of revenue preference

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Figure 6. The dynamics of firms' revenue preference

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Table 1. The material payoff matrix

$R$ $P$

$R$ $2a^2(a-5c), $ $(a-3c)(2a-c)(a+2c), $

$2a^2(a-5c)$ $(a-3c)^2(2a-c)$

$P$ $(a-3c)^2(2a-c), $ $2(a-c)^3, $

$(a-3c)(2a-c)(a+2c)$ $2(a-c)^3$

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