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Design of an Optimal Frequency Reward Program in the Face of Competition

  • Arpit Goel
  • Nolan Skochdopole
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)

Abstract

We optimize the design of a frequency reward program against traditional pricing in a competitive duopoly, where customers measure their utilities in rational economic terms. We assume two kinds of customers: myopic and strategic [19]. Every customer has a prior loyalty bias [6] toward the reward program merchant, a parameter drawn from a known distribution, indicating an additional probability of choosing the reward program merchant over the traditional pricing merchant. Under this model, we characterize the customer behavior: the loyalty bias increases the switching costs [11] of strategic customers until a tipping point, after which they strictly prefer and adopt the reward program merchant. Subsequently, we optimize the reward parameters to maximize the revenue objective of the reward program merchant. We show that under mild assumptions, the optimal parameters for the reward program design to maximize the revenue objective correspond exactly to minimizing the tipping point of customers and are independent of the customer population parameters. Moreover, we characterize the conditions for the reward program to be better when the loyalty bias distribution is uniform - a minimum fraction of population needs to be strategic, and the loyalty bias needs to be in an optimal range. If the bias is high, the reward program creates loss in revenues, as customers effectively gain rewards for “free”, whereas a low value of bias leads to loss in market share to the competing merchant. In short, if a merchant can estimate the customer population parameters, our framework and results provide theoretical guarantees on the pros and cons of running a reward program against traditional pricing.

References

  1. 1.
    Anderson, A., Huttenlocher, D., Kleinberg, J., Leskovec, J.: Steering user behavior with badges. In: Proceedings of the 22nd International Conference on World Wide Web, WWW 2013, pp. 95–106. ACM, New York (2013). http://doi.acm.org/10.1145/2488388.2488398
  2. 2.
    Berry, J.: The 2013 colloquy loyalty census. COLLOQUY industry report (2013). http://www.colloquy.com/files/2013-COLLOQUY-Census-Talk-White-Paper.pdf
  3. 3.
    Brooks, S.: CVS to target: 21 best loyalty rewards programs (2015). http://www.reviewjournal.com/business/money/cvs-target-21-best-loyalty-rewards-programs
  4. 4.
    Cinlar, E.: Markov renewal theory. Adv. Appl. Probab. 1(2), 123–187 (1969). http://www.jstor.org/stable/1426216 MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dreze, X., Nunes, J.C.: Using combined-currency prices to lower consumers perceived cost. J. Mark. Res. 41(1), 59–72 (2004)CrossRefGoogle Scholar
  6. 6.
    Fader, P.S., Schmittlein, D.C.: Excess behavioral loyalty for high-share brands: deviations from the dirichlet model for repeat purchasing. J. Mark. Res. 478–493 (1993)Google Scholar
  7. 7.
    Gao, L., Huang, Y., Simonson, I.: The influence of initial possession level on consumers’ adoption of a collection goal: a tipping point effect. J. Mark. 78(6), 143–156 (2014)CrossRefGoogle Scholar
  8. 8.
    Hartmann, W.R., Viard, V.B.: Do frequency reward programs create switching costs? A dynamic structural analysis of demand in a reward program. Quant. Mark. Econ. 6(2), 109–137 (2008)CrossRefGoogle Scholar
  9. 9.
    Hull, C.L.: The goal-gradient hypothesis and maze learning. Psychol. Rev. 39(1), 25 (1932)CrossRefGoogle Scholar
  10. 10.
    Kivetz, R., Urminsky, O., Zheng, Y.: The goal-gradient hypothesis resurrected: purchase acceleration, illusionary goal progress, and customer retention. J. Mark. Res. 43(1), 39–58 (2006)CrossRefGoogle Scholar
  11. 11.
    Klemperer, P.: Competition when consumers have switching costs: an overview with applications to industrial organization, macroeconomics, and international trade. Rev. Econ. Stud. 62(4), 515–539 (1995)CrossRefMATHGoogle Scholar
  12. 12.
    Kopalle, P.K., Neslin, S.: The economic viability of frequency reward programs in a strategic competitive environment. In: Tuck School of Business at Dartmouth Working Paper No. 01–02 (2001). Available at SSRN: https://ssrn.com/abstract=265431 or http://dx.doi.org/10.2139/ssrn.265431
  13. 13.
    Lewis, M.: The influence of loyalty programs and short-term promotions on customer retention. J. Mark. Res. 41(3), 281–292 (2004)CrossRefGoogle Scholar
  14. 14.
    Liu, Y.: The long-term impact of loyalty programs on consumer purchase behavior and loyalty. J. Mark. 71(4), 19–35 (2007)CrossRefGoogle Scholar
  15. 15.
    Ryu, G., Feick, L.: A penny for your thoughts: referral reward programs and referral likelihood. J. Mark. 71(1), 84–94 (2007)CrossRefGoogle Scholar
  16. 16.
    Sharp, B., Sharp, A.: Loyalty programs and their impact on repeat-purchase loyalty patterns. Int. J. Res. Mark. 14(5), 473–486 (1997)CrossRefGoogle Scholar
  17. 17.
    Stourm, V., Bradlow, E.T., Fader, P.S.: Stockpiling points in linear loyalty programs. J. Mark. Res. 52(2), 253–267 (2015)CrossRefGoogle Scholar
  18. 18.
    Villas-Boas, J.M.: A short survey on switching costs and dynamic competition. Int. J. Res. Mark. 32(2), 219–222 (2015)CrossRefGoogle Scholar
  19. 19.
    Yilmaz, O., Pekgun, P., Ferguson, M.: Would you like to upgrade to a premium room? Evaluating the benefit of offering standby upgrades. Manuf. Serv. Oper. Manag. 19(1), 1–18 (2017)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Management Science and EngineeringStanford UniversityStanfordUSA
  2. 2.Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA

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