# American Institute of Mathematical Sciences

• Previous Article
The approximation algorithm based on seeding method for functional $k$-means problem
• JIMO Home
• This Issue
• Next Article
Two-echelon trade credit with default risk in an EOQ model for deteriorating items under dynamic demand
doi: 10.3934/jimo.2021071

## 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

Received  July 2020 Revised  February 2021 Published  April 2021

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

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.

Citation: Caichun Chai, Tiaojun Xiao, Zhangwei Feng. Evolution of revenue preference for competing firms with nonlinear inverse demand. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021071
##### References:

show all references

##### References:
The overall flowchart for the proposed methodology
Phase portrait when $c(17+\sqrt{193})/6<a<c(4+\sqrt{13})$
Phase portrait when $a\leq c(17+\sqrt{193})/6$
Phase portrait when $a\geq c(4+\sqrt{13})$
Firms' payoffs change with the degree of revenue preference
The dynamics of firms' revenue preference
The material payoff matrix
 $R$ $P$ $R$ $2a^2(a-5c),$ $(a-3c)(2a-c)(a+2c),$ $2a^2(a-5c)$ $(a-3c)^2(2a-c)$ $P$ $(a-3c)^2(2a-c),$ $2(a-c)^3,$ $(a-3c)(2a-c)(a+2c)$ $2(a-c)^3$
 $R$ $P$ $R$ $2a^2(a-5c),$ $(a-3c)(2a-c)(a+2c),$ $2a^2(a-5c)$ $(a-3c)^2(2a-c)$ $P$ $(a-3c)^2(2a-c),$ $2(a-c)^3,$ $(a-3c)(2a-c)(a+2c)$ $2(a-c)^3$
 [1] Xiaoyi Zhou, Tong Ye, Tony T. Lee. Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021038 [2] René Aïd, Roxana Dumitrescu, Peter Tankov. The entry and exit game in the electricity markets: A mean-field game approach. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021012 [3] David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002 [4] Jiahui Chen, Rundong Zhao, Yiying Tong, Guo-Wei Wei. Evolutionary de Rham-Hodge method. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3785-3821. doi: 10.3934/dcdsb.2020257 [5] Enkhbat Rentsen, N. Tungalag, J. Enkhbayar, O. Battogtokh, L. Enkhtuvshin. Application of survival theory in Mining industry. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 443-448. doi: 10.3934/naco.2020036 [6] Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 [7] Lara Abi Rizk, Jean-Baptiste Burie, Arnaud Ducrot. Asymptotic speed of spread for a nonlocal evolutionary-epidemic system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021064 [8] Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 [9] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 [10] Fioralba Cakoni, Shixu Meng, Jingni Xiao. A note on transmission eigenvalues in electromagnetic scattering theory. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021025 [11] Akio Matsumoto, Ferenc Szidarovszky. Stability switching and its directions in cournot duopoly game with three delays. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021069 [12] Mrinal K. Ghosh, Somnath Pradhan. A nonzero-sum risk-sensitive stochastic differential game in the orthant. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021025 [13] Hideaki Takagi. Extension of Littlewood's rule to the multi-period static revenue management model with standby customers. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2181-2202. doi: 10.3934/jimo.2020064 [14] Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021042 [15] Wei Wang, Yang Shen, Linyi Qian, Zhixin Yang. Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021072 [16] W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 [17] Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021020 [18] Chloé Jimenez. A zero sum differential game with correlated informations on the initial position. A case with a continuum of initial positions. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021009 [19] John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004 [20] Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $C^{1}$ domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3415-3445. doi: 10.3934/dcds.2021002

2019 Impact Factor: 1.366

## Tools

Article outline

Figures and Tables