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Recent Advances in Game Theory and Applications pp 111–130Cite as

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An Infinite Horizon Differential Game of Optimal CLV-Based Strategies with Non-atomic Firms

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Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

Abstract

We study the structure of optimal customer acquisition and customer retention strategies as a differential game over an infinite horizon in an industry with a large number of non-atomic firms. The optimal retention effort is constant over time and the optimal acquisition effort is proportional to the size of potential customer base. Greater customer profitability leads to higher per- capita acquisition and retention efforts, larger size of firms, and lower churn rate. A greater discount rate leads to lower per-capita acquisition and retention efforts, smaller firm size, and a greater churn rate. Tougher competition lowers the firms’ acquisition and retention expenditures and it does not affect per-capita values. Both the churn rate and the share of acquisition expenditures in the total marketing budget decrease as firms grow over time. We revisit the concepts of the customer lifetime value (CLV) and the value of the firm in the dynamic equilibrium of an industry with a large number of players and demonstrate the equivalence between maximization of the value of the firm and maximization of a firm’s individual CLV.

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Acknowledgements

We are grateful to the organizers and participants of 2015 European Meeting on Game Theory (SING11-GTM 2015) in St. Petersburg for their comments. We also thank organizers participants and referees of 2014 AMS conference at Indianapolis, USA, as well as seminar participants at the HSE, SWUFE, and EUSP for comments and suggestions on early drafts. Especially we thank Chakravarthi Narasimhan and Philip Dybvig for their encouragement and comments. Finally, we thank editors and anonymous referee for their careful consideration of our paper and valuable comments and suggestions that have helped us improve it.

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Authors and Affiliations

  1. Department of Economics, School of Business Administration, University of Miami, Jenkins Building, 5250 University Drive, Coral Gables, FL, 33146-6550, USA

    Gerasimos Lianos

  2. National Research University Higher School of Economics, 20 Myasnizkaya str., Moscow, 101000, Russia

    Igor Sloev

Authors
  1. Gerasimos Lianos
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  2. Igor Sloev
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Correspondence to Igor Sloev .

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Editors and Affiliations

  1. Department of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, Russia

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Karelia Research Center of Russian Academy of Sciences, Petrozavodsk, Russia

    Vladimir V. Mazalov

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© 2016 Springer International Publishing Switzerland

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Lianos, G., Sloev, I. (2016). An Infinite Horizon Differential Game of Optimal CLV-Based Strategies with Non-atomic Firms. In: Petrosyan, L., Mazalov, V. (eds) Recent Advances in Game Theory and Applications. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43838-2_6

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