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Designing competitive loyalty programs: a stochastic game-theoretic model to guide the choice of reward structure

Author

Listed:
  • Amir Gandomi

    (Hofstra University)

  • Amirhossein Bazargan

    (Ryerson University)

  • Saeed Zolfaghari

    (Ryerson University)

Abstract

We develop a game-theoretic model to guide the choice of the reward structure in customer loyalty programs. We model a duopoly market in which one firm adopts a loyalty program. Firms independently and simultaneously set the prices and rewards. Heterogeneous customers buy homogeneous products in a multi-period setting. Customers are segmented into three groups based on their level of strategic behavior, which is expressed in terms of their degree of forward-lookingness. We use two exogenous parameters to represent the size of each segment. A third parameter captures the point pressure effect, which refers to the increase in customer spending as they approach a reward threshold. In each period, customers choose the firm that maximizes their utility, which is a function of offered prices, rewards, and the distance to the next reward. We use the logit model to model the customer choice behavior. Customers’ accumulated purchases evolve as a Markov chain. We derive the limiting distribution of accumulated purchases, which is subsequently used to formulate the firm’s expected revenue functions. We develop two algorithms to find the Nash equilibrium for both the linear and nonlinear rewards in term of the three parameters. Using a thorough numerical analysis, we show that the choice of the structure becomes more critical as the size of the strategic segment increases. The nonlinear scheme is superior when the size of the highly-strategic segment is very small. The linear rewards is superior in markets where the size of the highly-strategic segment and the sensitivity to distance are simultaneously not small.

Suggested Citation

  • Amir Gandomi & Amirhossein Bazargan & Saeed Zolfaghari, 2019. "Designing competitive loyalty programs: a stochastic game-theoretic model to guide the choice of reward structure," Annals of Operations Research, Springer, vol. 280(1), pages 267-298, September.
    • Handle: RePEc:spr:annopr:v:280:y:2019:i:1:d:10.1007_s10479-019-03179-1
    DOI: 10.1007/s10479-019-03179-1
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    References listed on IDEAS

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    1. Yuheng Cao & Aaron L Nsakanda & Moustapha Diaby, 2015. "Planning the supply of rewards with cooperative promotion considerations in coalition loyalty programmes management," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(7), pages 1140-1154, July.
    2. Gandomi, Amir & Zolfaghari, Saeed, 2018. "To tier or not to tier: An analysis of multitier loyalty programs׳ optimality conditions," Omega, Elsevier, vol. 74(C), pages 20-36.
    3. von Weizsacker, C Christian, 1984. "The Costs of Substitution," Econometrica, Econometric Society, vol. 52(5), pages 1085-1116, September.
    4. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    5. Van den Poel, Dirk & Lariviere, Bart, 2004. "Customer attrition analysis for financial services using proportional hazard models," European Journal of Operational Research, Elsevier, vol. 157(1), pages 196-217, August.
    6. Byung-Do Kim & Mengze Shi & Kannan Srinivasan, 2001. "Reward Programs and Tacit Collusion," Marketing Science, INFORMS, vol. 20(2), pages 99-120, June.
    7. T. Boulogne & E. Altman & O. Pourtallier, 2002. "On the Convergence to Nash Equilibrium in Problems of Distributed Computing," Annals of Operations Research, Springer, vol. 109(1), pages 279-291, January.
    8. Mara Lederman, 2007. "Do enhancements to loyalty programs affect demand? The impact of international frequent flyer partnerships on domestic airline demand," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1134-1158, December.
    9. Ran Kivetz, 2005. "Promotion Reactance: The Role of Effort-Reward Congruity," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 31(4), pages 725-736, March.
    10. Xavier Drèze & Joseph C. Nunes, 2009. "Feeling Superior: The Impact of Loyalty Program Structure on Consumers' Perceptions of Status," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 35(6), pages 890-905, April.
    11. Joseph C. Nunes & Xavier Drze, 2006. "The Endowed Progress Effect: How Artificial Advancement Increases Effort," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 32(4), pages 504-512, March.
    12. Dasu, Sriram & Tong, Chunyang, 2010. "Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 662-671, August.
    13. Ran Kivetz, 2003. "The Effects of Effort and Intrinsic Motivation on Risky Choice," Marketing Science, INFORMS, vol. 22(4), pages 477-502, December.
    14. Ran Kivetz & Oleg Urminsky & Yuhuang Zheng, 2006. "The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention," Natural Field Experiments 00658, The Field Experiments Website.
    15. Steven M. Shugan, 2005. "Brand Loyalty Programs: Are They Shams?," Marketing Science, INFORMS, vol. 24(2), pages 185-193.
    16. Vladimir Marianov & H. A. Eiselt, 2016. "On agglomeration in competitive location models," Annals of Operations Research, Springer, vol. 246(1), pages 31-55, November.
    17. Siddharth S. Singh & Dipak C. Jain & Trichy V. Krishnan, 2008. "Research Note--Customer Loyalty Programs: Are They Profitable?," Management Science, INFORMS, vol. 54(6), pages 1205-1211, June.
    18. Bazargan, Amirhossein & Karray, Salma & Zolfaghari, Saeed, 2017. "Modeling reward expiry for loyalty programs in a competitive market," International Journal of Production Economics, Elsevier, vol. 193(C), pages 352-364.
    19. Gandomi, A. & Zolfaghari, S., 2013. "Profitability of loyalty reward programs: An analytical investigation," Omega, Elsevier, vol. 41(4), pages 797-807.
    20. Yue Dai & Xiuli Chao & Shu-Cherng Fang & Henry Nuttle, 2005. "Game Theoretic Analysis of a Distribution System with Customer Market Search," Annals of Operations Research, Springer, vol. 135(1), pages 223-228, March.
    21. Kang, Jun & Alejandro, Thomas Brashear & Groza, Mark D., 2015. "Customer–company identification and the effectiveness of loyalty programs," Journal of Business Research, Elsevier, vol. 68(2), pages 464-471.
    22. Praveen K. Kopalle & Yacheng Sun & Scott A. Neslin & Baohong Sun & Vanitha Swaminathan, 2012. "The Joint Sales Impact of Frequency Reward and Customer Tier Components of Loyalty Programs," Marketing Science, INFORMS, vol. 31(2), pages 216-235, March.
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