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Determining optimal marketing and pricing policies by considering customer lifetime network value in oligopoly markets

 Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran

* Corresponding author: Sahar Vatankhah

Received  November 2020 Revised  April 2021 Early access June 2021

Nowadays, the customer network effects are becoming a central issue for the companies, while the previous studies have been only limited to customer lifetime value and its related models. Therefore, this paper aims to presents a model for calculating customer lifetime value, and simultaneously the network effects are considered. For this purpose, an oligopoly market is considered in which companies compete with each other. The companies individually have a number of buyers and sellers. Interestingly, their policy is based on offering services to their buyers free, and receiving the membership fees from the sellers instead. Customers influence each other, and their word-of-mouth marketing leads to a change in the number of companies' customers. This interaction is also observed among the sellers. In the absence of buyers, the presence of sellers is meaningless. In other words, there is a remarkable proportion between the number of buyers and sellers, which directly affects the companies' profitability. Each company seeks to determine the optimal marketing and pricing policies, considering the effects of the network. By applying differential game theory, the companies are able to receive the market share, advertising, and pricing strategy. The Genetic Algorithm is employed to solve the model. Finally, a numerical example and model validation are provided to demonstrate the proposed model capabilities.

Citation: Sahar Vatankhah, Reza Samizadeh. Determining optimal marketing and pricing policies by considering customer lifetime network value in oligopoly markets. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021112
References:
 [1] P. D. Berger and N. I. Nasr, Customer lifetime value: Marketing models and applications, Journal of Interactive Marketing, 12 (1998), 17-30.  doi: 10.1002/(SICI)1520-6653(199824)12:1<17::AID-DIR3>3.0.CO;2-K. [2] R. Blattberg, G. Getz and J. Thomas, Customer Equity: Building and Managing Relationships as Valuable Assets, Harvard Business Review Press, 1 (2001), 200-201. [3] M. Däs, J. Klier, M. Klier, G. Lindner and L. Thiel, Customer lifetime network value: customer valuation in the context of network effects, Electronic Markets, 27 (2017), 307-328. [4] S. Dewnarain, H. Ramkissoon and F. Mavondo, Social customer relationship management: An integrated conceptual framework, Journal of Hospitality Marketing & Management, 28 (2019), 172-188.  doi: 10.1080/19368623.2018.1516588. [5] B. Donkers, P. C. Verhoef and M. G. de Jong, Modeling CLV: A test of competing models in the insurance industry, Quantitative Marketing and Economics, 5 (2007), 163-190.  doi: 10.1007/s11129-006-9016-y. [6] P. S. Fader, B. G. S. Hardie and K. L. Lee, "Counting your customers" the easy way: An alternative to the Pareto/NBD model, Marketing Science, 24 (2005), 275-284.  doi: 10.1287/mksc.1040.0098. [7] M. Grossmann, C. Brock, T. Reimer and M. Hubert, The Relevance of Positive Word-of-Mouth Effects on the Customer Lifetime Value-A Replication and Extension in the Context of Start-ups, SMR-Journal of Service Management Research, 3 (2019), 148-160.  doi: 10.15358/2511-8676-2019-3-148. [8] S. Gupta, D. Hanssens, B. Hardie, W. Kahn, V. Kumar, N. Lin, N. Ravishanker and S. Sriram, Modeling customer lifetime value, Journal of Service Research, 9 (2006), 139-155.  doi: 10.1177/1094670506293810. [9] S. Gupta, C. F. Mela and J. M. Vidal-Sanz, The value of a "free" customer, Harvard Business School, 7 (2009), 7-35. [10] S. Gupta and V. Zeithaml, Customer metrics and their impact on financial performance, Marketing Science, 25 (2006), 718-739.  doi: 10.1287/mksc.1060.0221. [11] M. Haenlein, A. M. Kaplan and A. J. Beeser, A model to determine customer lifetime value in a retail banking context, European Management Journal, 25 (2007), 221-234.  doi: 10.1016/j.emj.2007.01.004. [12] O. Hinċal, A. B. Altan-Sakarya and A. M. Ger, Optimization of multireservoir systems by genetic algorithm, Water Resources Management, 25 (2011), 1465-1487. [13] J. E. Hogan, K. N. Lemon and B. Libai, What is the true value of a lost customer?, Journal of Service Research, 5 (2003), 196-208.  doi: 10.1177/1094670502238915. [14] P. Horák, Customer Lifetime Value in B2B Markets: Theory and Practice in the Czech Republic, Int. J. Bus. Manag., 12 (2017), 47-55. [15] D. Horsky and L. S. Simon, Advertising and the diffusion of new products, Marketing Science, 2 (1983), 1-17.  doi: 10.1287/mksc.2.1.1. [16] H. Hwang, T. Jung and E. Suh, An LTV model and customer segmentation based on customer value: A case study on the wireless telecommunication industry, Expert Systems with Applications, 26 (2004), 181-188.  doi: 10.1016/S0957-4174(03)00133-7. [17] P. Jasek, L. Vrana, L. Sperkova, Z. Smutny and M. Kobulsky, Modeling and application of customer lifetime value in online retail, In Informatics, Multidisciplinary Digital Publishing Institute, 5 (2018), 2. [18] P. Jasek, L. Vrana, L. Sperkova, Z. Smutny and M. Kobulsky, Comparative analysis of selected probabilistic customer lifetime value models in online shopping, Journal of Business Economics and Management, 20 (2019), 398-423.  doi: 10.3846/jbem.2019.9597. [19] I. G. Juanamasta, N. M. N. Wati, E. Hendrawati, W. Wahyuni, M. Pramudianti, N. S. Wisnujati and M. Umanailo, The role of customer service through customer relationship management (Crm) to increase customer loyalty and good image, International Journal of Scientific and Technology Research, 8 (2019), 2004-2007. [20] M. S. Kahreh, M. Tive, A. Babania and M. Hesan, Analyzing the applications of customer lifetime value (CLV) based on benefit segmentation for the banking sector, Procedia-Social and Behavioral Sciences, 109 (2014), 590-594.  doi: 10.1016/j.sbspro.2013.12.511. [21] S.-Y. Kim, T.-S. Jung, E.-H. Suh and H.-S. Hwang, Customer segmentation and strategy development based on customer lifetime value: A case study, Expert Systems with Applications, 31 (2006), 101-107.  doi: 10.1016/j.eswa.2005.09.004. [22] J. Klier, M. Klier, F. Probst and L. Thiel, Customer Lifetime Network Value, In Proceedings of the 35th International Conference on Information System (ICIS), 1 (2014), 1-21. [23] P. Kotler, Marketing during periods of shortage, Journal of Marketing, 38 (1974), 20-29. [24] S. Mirjalili, in evolutionary algorithms and neural networks, Springer, (2019), 43–55. doi: 10.1007/978-3-319-93025-1. [25] S. Monalisa, P. Nadya and R. Novita, Analysis for customer lifetime value categorization with RFM model, Procedia Computer Science, 161 (2019), 834-840.  doi: 10.1016/j.procs.2019.11.190. [26] M. J. Mosadegh and M. Behboudi, Using social network paradigm for developing a conceptual framework in CRM, Australian Journal of Business and Management Research, 1 (2011), 63. [27] A. Prasad, S. P. Sethi and P. A. Naik, Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.  doi: 10.1016/j.automatica.2012.08.031. [28] W. J. Reinartz and V. Kumar, On the profitability of long-life customers in a noncontractual setting: An empirical investigation and implications for marketing, Journal of Marketing, 64 (2000), 17-35.  doi: 10.1509/jmkg.64.4.17.18077. [29] R. T. Rust, K. N. Lemon and V. A. Zeithaml, Driving customer equity: Linking customer lifetime value to strategic marketing decisions, Marketing Science Institute Cambridge, MA, 1 (2001), 108. [30] F. Safari, N. Safari and G. A. Montazer, Customer lifetime value determination based on RFM model, Marketing Intelligence & Planning, 2016. doi: 10.1108/MIP-03-2015-0060. [31] B. Sohrabi and A. Khanlari, Customer lifetime value (CLV) measurement based on RFM model, Iranian Accounting & Auditing Review, 14 (2007), 7-20. [32] P. Talón-Ballestero, L. González-Serrano, C. Soguero-Ruiz, S. Muñoz-Romero and J. L. Rojo-Álvarez, Using big data from customer relationship management information systems to determine the client profile in the hotel sector, Tourism Management, 68 (2018), 187-197. [33] X. Wang, T. Liu and J. Miao, A deep probabilistic model for customer lifetime value prediction, arXiv preprint, 2019. arXiv: 1912.07753. [34] C. Woarawichai, T. Kullpattaranirun and V. Rungreunganun, Applying genetic algorithms for inventory lot-sizing problem with supplier selection under storage capacity, International Journal of Computer Science Issues, 9 (2012), 18-23. [35] I.-C. Yeh, K.-J. Yang and T.-M. Ting, Knowledge discovery on RFM model using Bernoulli sequence, Expert Systems with Applications, 36 (2009), 5866-5871.  doi: 10.1016/j.eswa.2008.07.018.

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References:
 [1] P. D. Berger and N. I. Nasr, Customer lifetime value: Marketing models and applications, Journal of Interactive Marketing, 12 (1998), 17-30.  doi: 10.1002/(SICI)1520-6653(199824)12:1<17::AID-DIR3>3.0.CO;2-K. [2] R. Blattberg, G. Getz and J. Thomas, Customer Equity: Building and Managing Relationships as Valuable Assets, Harvard Business Review Press, 1 (2001), 200-201. [3] M. Däs, J. Klier, M. Klier, G. Lindner and L. Thiel, Customer lifetime network value: customer valuation in the context of network effects, Electronic Markets, 27 (2017), 307-328. [4] S. Dewnarain, H. Ramkissoon and F. Mavondo, Social customer relationship management: An integrated conceptual framework, Journal of Hospitality Marketing & Management, 28 (2019), 172-188.  doi: 10.1080/19368623.2018.1516588. [5] B. Donkers, P. C. Verhoef and M. G. de Jong, Modeling CLV: A test of competing models in the insurance industry, Quantitative Marketing and Economics, 5 (2007), 163-190.  doi: 10.1007/s11129-006-9016-y. [6] P. S. Fader, B. G. S. Hardie and K. L. Lee, "Counting your customers" the easy way: An alternative to the Pareto/NBD model, Marketing Science, 24 (2005), 275-284.  doi: 10.1287/mksc.1040.0098. [7] M. Grossmann, C. Brock, T. Reimer and M. Hubert, The Relevance of Positive Word-of-Mouth Effects on the Customer Lifetime Value-A Replication and Extension in the Context of Start-ups, SMR-Journal of Service Management Research, 3 (2019), 148-160.  doi: 10.15358/2511-8676-2019-3-148. [8] S. Gupta, D. Hanssens, B. Hardie, W. Kahn, V. Kumar, N. Lin, N. Ravishanker and S. Sriram, Modeling customer lifetime value, Journal of Service Research, 9 (2006), 139-155.  doi: 10.1177/1094670506293810. [9] S. Gupta, C. F. Mela and J. M. Vidal-Sanz, The value of a "free" customer, Harvard Business School, 7 (2009), 7-35. [10] S. Gupta and V. Zeithaml, Customer metrics and their impact on financial performance, Marketing Science, 25 (2006), 718-739.  doi: 10.1287/mksc.1060.0221. [11] M. Haenlein, A. M. Kaplan and A. J. Beeser, A model to determine customer lifetime value in a retail banking context, European Management Journal, 25 (2007), 221-234.  doi: 10.1016/j.emj.2007.01.004. [12] O. Hinċal, A. B. Altan-Sakarya and A. M. Ger, Optimization of multireservoir systems by genetic algorithm, Water Resources Management, 25 (2011), 1465-1487. [13] J. E. Hogan, K. N. Lemon and B. Libai, What is the true value of a lost customer?, Journal of Service Research, 5 (2003), 196-208.  doi: 10.1177/1094670502238915. [14] P. Horák, Customer Lifetime Value in B2B Markets: Theory and Practice in the Czech Republic, Int. J. Bus. Manag., 12 (2017), 47-55. [15] D. Horsky and L. S. Simon, Advertising and the diffusion of new products, Marketing Science, 2 (1983), 1-17.  doi: 10.1287/mksc.2.1.1. [16] H. Hwang, T. Jung and E. Suh, An LTV model and customer segmentation based on customer value: A case study on the wireless telecommunication industry, Expert Systems with Applications, 26 (2004), 181-188.  doi: 10.1016/S0957-4174(03)00133-7. [17] P. Jasek, L. Vrana, L. Sperkova, Z. Smutny and M. Kobulsky, Modeling and application of customer lifetime value in online retail, In Informatics, Multidisciplinary Digital Publishing Institute, 5 (2018), 2. [18] P. Jasek, L. Vrana, L. Sperkova, Z. Smutny and M. Kobulsky, Comparative analysis of selected probabilistic customer lifetime value models in online shopping, Journal of Business Economics and Management, 20 (2019), 398-423.  doi: 10.3846/jbem.2019.9597. [19] I. G. Juanamasta, N. M. N. Wati, E. Hendrawati, W. Wahyuni, M. Pramudianti, N. S. Wisnujati and M. Umanailo, The role of customer service through customer relationship management (Crm) to increase customer loyalty and good image, International Journal of Scientific and Technology Research, 8 (2019), 2004-2007. [20] M. S. Kahreh, M. Tive, A. Babania and M. Hesan, Analyzing the applications of customer lifetime value (CLV) based on benefit segmentation for the banking sector, Procedia-Social and Behavioral Sciences, 109 (2014), 590-594.  doi: 10.1016/j.sbspro.2013.12.511. [21] S.-Y. Kim, T.-S. Jung, E.-H. Suh and H.-S. Hwang, Customer segmentation and strategy development based on customer lifetime value: A case study, Expert Systems with Applications, 31 (2006), 101-107.  doi: 10.1016/j.eswa.2005.09.004. [22] J. Klier, M. Klier, F. Probst and L. Thiel, Customer Lifetime Network Value, In Proceedings of the 35th International Conference on Information System (ICIS), 1 (2014), 1-21. [23] P. Kotler, Marketing during periods of shortage, Journal of Marketing, 38 (1974), 20-29. [24] S. Mirjalili, in evolutionary algorithms and neural networks, Springer, (2019), 43–55. doi: 10.1007/978-3-319-93025-1. [25] S. Monalisa, P. Nadya and R. Novita, Analysis for customer lifetime value categorization with RFM model, Procedia Computer Science, 161 (2019), 834-840.  doi: 10.1016/j.procs.2019.11.190. [26] M. J. Mosadegh and M. Behboudi, Using social network paradigm for developing a conceptual framework in CRM, Australian Journal of Business and Management Research, 1 (2011), 63. [27] A. Prasad, S. P. Sethi and P. A. Naik, Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.  doi: 10.1016/j.automatica.2012.08.031. [28] W. J. Reinartz and V. Kumar, On the profitability of long-life customers in a noncontractual setting: An empirical investigation and implications for marketing, Journal of Marketing, 64 (2000), 17-35.  doi: 10.1509/jmkg.64.4.17.18077. [29] R. T. Rust, K. N. Lemon and V. A. Zeithaml, Driving customer equity: Linking customer lifetime value to strategic marketing decisions, Marketing Science Institute Cambridge, MA, 1 (2001), 108. [30] F. Safari, N. Safari and G. A. Montazer, Customer lifetime value determination based on RFM model, Marketing Intelligence & Planning, 2016. doi: 10.1108/MIP-03-2015-0060. [31] B. Sohrabi and A. Khanlari, Customer lifetime value (CLV) measurement based on RFM model, Iranian Accounting & Auditing Review, 14 (2007), 7-20. [32] P. Talón-Ballestero, L. González-Serrano, C. Soguero-Ruiz, S. Muñoz-Romero and J. L. Rojo-Álvarez, Using big data from customer relationship management information systems to determine the client profile in the hotel sector, Tourism Management, 68 (2018), 187-197. [33] X. Wang, T. Liu and J. Miao, A deep probabilistic model for customer lifetime value prediction, arXiv preprint, 2019. arXiv: 1912.07753. [34] C. Woarawichai, T. Kullpattaranirun and V. Rungreunganun, Applying genetic algorithms for inventory lot-sizing problem with supplier selection under storage capacity, International Journal of Computer Science Issues, 9 (2012), 18-23. [35] I.-C. Yeh, K.-J. Yang and T.-M. Ting, Knowledge discovery on RFM model using Bernoulli sequence, Expert Systems with Applications, 36 (2009), 5866-5871.  doi: 10.1016/j.eswa.2008.07.018.
The model of this study
The Genetic Algorithm procedure [33]
Number of buyers and the number of sellers of company 1 in 30 months
Number of buyers and the number of sellers of company 1 in 30 months
Number of buyers and the number of sellers of company 3 in 30 months
Number of buyers and the number of sellers of company 3 in 30 months
Number of buyers and the number of sellers of company 3 in 30 months
literature review
 Authors Considered elements / defined model The main similarities The main differences Berger and Nasr (1998) [2] ● Two steps should be taken to calculate CLV: 1. Projecting the net cash flows that the company is likely to take from customers. 2. The present value computation of that stream of cash flows. CLV is investigated 1. Network effects are not Considered. 2. The net cash flows are examined. 3. mathematical models are considered. 4. Differences between monopoly market and oligopoly market regarding CLV and network effects are not clarified. Rust et al.(2000) [27] ● A method to determine CLV that incorporates customer-specific brand switching metrics. ● The Markov model is employed in this study to model the customer's probability of switching from one brand to another by a transition matrix. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Blattberg et al.(2001) [1] ● Customer lifetime value is the sum of three components, which are: return on the acquisition, return on retention, and return on cross-selling 1. CLV is investigated. 2. a method is proposed to raise the companies' profitability. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Hogan et al. (2003)[13] ● They showed that after losing a customer, a company will not only lose the cash flow it can earn from that customer in the future but will also lose the cash flow that can be gained from other customers due to less customer attraction as a result of reduced social impact. 1. Network effects are Considered. 2. The target is increasing the companies profitability. 1. The Genetic Algorithm is not used to solve the model. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Hwang et al. (2004) [16] ● Three factors are considered. According to the studies conducted regarding CLV, these factors have been neglected. The factors are past profit contribution, Potential benefit, and defection probabilities of the customer. ● Besides, a framework is presented to analyze customer values and segment them according to their values. 1. CLV calculation is considered. 2. The target is increasing the companies' profitability. 1. Network effects are not Considered. 2. This paper considers customer retention as the most critical issue. 3. Differences between the monopoly market and oligopoly market regarding CLV and Fader et al. (2005) [6] ● Customers are grouped based on three factors of RFM. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Gupta et al.(2006)[10] ● A joint model of buyer and seller growth is developed to calculate the customers' value. ● Three sources, including marketing actions (price and advertising), direct network effects (such as buyer to buyer effects), and indirect network effects (such as buyer to seller effects), constitute this growth. ● The company's concern is related to optimal pricing determination and advertising according to the customer growth limitations. The growth model is used to solve this problem simultaneously. 1. Network effects are Considered. 2. CLV calculation is considered. 3. The target is to increase the companies' profitability. 1. The Genetic Algorithm is not used to solve the model. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. 3. Oligopoly market is not considered. Kim et al. (2006) [20] ● A framework is provided to analyze the customer's value and segment them according to their value. ● After the segmentation, strategies related to each segment are proposed. ● Customer defection and cross-selling opportunities are considered in this article. The customer value is analyzed. 1. Network effects are not Considered. 2. The customers are segmented according to their value. 3. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Haenlein et al.(2007) [11] ● A model is proposed for customer lifetime value calculation. ● This calculation is conducted according to the Markov chain model and classification, and regression tree. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Yeh et al. (2009)[34] ● Considering the time parameter based on the first purchase and churn probability and developing the RFM model. They expanded a model to consider their desired parameters. 1. Network effects are not Considered. 2. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Prasad et al. (2012) [25] ● The churn effects are considered. ● The companies' market share is related to market churn, the advertising decisions they made, and their competitors' advertising decisions. ● Differential game theory is applied to extract a feedback Nash equilibrium according to the symmetric and asymmetric competition. 1. The presented model regarding advertising in an oligopoly is considered dynamically. 2. The target is increasing the companies' profitability. 1. Churn effect in dynamic oligopoly markets is considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. 3. Counteracting the churn effect is considered. Klier et al.(2014) [35] ● A model for customer valuation is developed. ● This model is based on customer lifetime network value. 1. Network effects are Considered. 2. A real-world dataset of a company is employed to show the application customer lifetime network value. The difference between the monopoly market and the oligopoly market regarding CLV and network effects is not clarified. Das et al. (2017)[3] ● Customer lifetime network value is divided into two parts: 1. The present value of individual cash flows and 2. The present value of network contribution 1. Network effects are Considered. 2. A real-world dataset of a company is employed to show the application customer lifetime network value. The difference between the monopoly market and the oligopoly market regarding CLV and network effects is not clarified. Grossmann et al.(2019) [7] ● This paper seeks to show how much the word-of-mouth effects are significant and play a prominent role in estimating CLV in start-up businesses. 1. Network effects are Considered. 2. CLV calculation is considered. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified.
 Authors Considered elements / defined model The main similarities The main differences Berger and Nasr (1998) [2] ● Two steps should be taken to calculate CLV: 1. Projecting the net cash flows that the company is likely to take from customers. 2. The present value computation of that stream of cash flows. CLV is investigated 1. Network effects are not Considered. 2. The net cash flows are examined. 3. mathematical models are considered. 4. Differences between monopoly market and oligopoly market regarding CLV and network effects are not clarified. Rust et al.(2000) [27] ● A method to determine CLV that incorporates customer-specific brand switching metrics. ● The Markov model is employed in this study to model the customer's probability of switching from one brand to another by a transition matrix. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Blattberg et al.(2001) [1] ● Customer lifetime value is the sum of three components, which are: return on the acquisition, return on retention, and return on cross-selling 1. CLV is investigated. 2. a method is proposed to raise the companies' profitability. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Hogan et al. (2003)[13] ● They showed that after losing a customer, a company will not only lose the cash flow it can earn from that customer in the future but will also lose the cash flow that can be gained from other customers due to less customer attraction as a result of reduced social impact. 1. Network effects are Considered. 2. The target is increasing the companies profitability. 1. The Genetic Algorithm is not used to solve the model. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Hwang et al. (2004) [16] ● Three factors are considered. According to the studies conducted regarding CLV, these factors have been neglected. The factors are past profit contribution, Potential benefit, and defection probabilities of the customer. ● Besides, a framework is presented to analyze customer values and segment them according to their values. 1. CLV calculation is considered. 2. The target is increasing the companies' profitability. 1. Network effects are not Considered. 2. This paper considers customer retention as the most critical issue. 3. Differences between the monopoly market and oligopoly market regarding CLV and Fader et al. (2005) [6] ● Customers are grouped based on three factors of RFM. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. Gupta et al.(2006)[10] ● A joint model of buyer and seller growth is developed to calculate the customers' value. ● Three sources, including marketing actions (price and advertising), direct network effects (such as buyer to buyer effects), and indirect network effects (such as buyer to seller effects), constitute this growth. ● The company's concern is related to optimal pricing determination and advertising according to the customer growth limitations. The growth model is used to solve this problem simultaneously. 1. Network effects are Considered. 2. CLV calculation is considered. 3. The target is to increase the companies' profitability. 1. The Genetic Algorithm is not used to solve the model. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. 3. Oligopoly market is not considered. Kim et al. (2006) [20] ● A framework is provided to analyze the customer's value and segment them according to their value. ● After the segmentation, strategies related to each segment are proposed. ● Customer defection and cross-selling opportunities are considered in this article. The customer value is analyzed. 1. Network effects are not Considered. 2. The customers are segmented according to their value. 3. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Haenlein et al.(2007) [11] ● A model is proposed for customer lifetime value calculation. ● This calculation is conducted according to the Markov chain model and classification, and regression tree. CLV calculation is considered. 1. Network effects are not Considered. 2. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Yeh et al. (2009)[34] ● Considering the time parameter based on the first purchase and churn probability and developing the RFM model. They expanded a model to consider their desired parameters. 1. Network effects are not Considered. 2. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified. Prasad et al. (2012) [25] ● The churn effects are considered. ● The companies' market share is related to market churn, the advertising decisions they made, and their competitors' advertising decisions. ● Differential game theory is applied to extract a feedback Nash equilibrium according to the symmetric and asymmetric competition. 1. The presented model regarding advertising in an oligopoly is considered dynamically. 2. The target is increasing the companies' profitability. 1. Churn effect in dynamic oligopoly markets is considered. 2. Differences between the monopoly market and oligopoly market regarding CLV and network effects are not clarified. 3. Counteracting the churn effect is considered. Klier et al.(2014) [35] ● A model for customer valuation is developed. ● This model is based on customer lifetime network value. 1. Network effects are Considered. 2. A real-world dataset of a company is employed to show the application customer lifetime network value. The difference between the monopoly market and the oligopoly market regarding CLV and network effects is not clarified. Das et al. (2017)[3] ● Customer lifetime network value is divided into two parts: 1. The present value of individual cash flows and 2. The present value of network contribution 1. Network effects are Considered. 2. A real-world dataset of a company is employed to show the application customer lifetime network value. The difference between the monopoly market and the oligopoly market regarding CLV and network effects is not clarified. Grossmann et al.(2019) [7] ● This paper seeks to show how much the word-of-mouth effects are significant and play a prominent role in estimating CLV in start-up businesses. 1. Network effects are Considered. 2. CLV calculation is considered. Differences between the monopoly market and the oligopoly market regarding CLV and network effects are not clarified.
The input parameters value
 $M^{B}=1000000M^{S}=300000$ $B_1=0.5$ $c_1=0.5$ $b_2=0.5$ $c_2=0.5$ $N_0^{B_1}=N_0^{B_2}=N_0^{B_3}=20$ $N_0^{S_1}=N_0^{S_2}=N_0^{S_3}=20$ $r_1=r_2=r_3=0.6$ alfaP=0.1 alfaA=0.1 $c_1=c_2=c_3=0.6$ alfapi=1 alfaAi=1
 $M^{B}=1000000M^{S}=300000$ $B_1=0.5$ $c_1=0.5$ $b_2=0.5$ $c_2=0.5$ $N_0^{B_1}=N_0^{B_2}=N_0^{B_3}=20$ $N_0^{S_1}=N_0^{S_2}=N_0^{S_3}=20$ $r_1=r_2=r_3=0.6$ alfaP=0.1 alfaA=0.1 $c_1=c_2=c_3=0.6$ alfapi=1 alfaAi=1
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