‘Buy n times, get one free’ loyalty cards: Are they profitable for competing firms? A game theoretic analysis

Amirhossein Bazargan, Salma Karray and Saeed Zolfaghari

European Journal of Operational Research, 2018, vol. 265, issue 2, 621-630

Abstract: This paper evaluates whether firms offering loyalty programs (LPs) should choose a restricted redemption policy by imposing a specific number of purchases before customers can redeem their points. Such restriction is commonly offered in form of ‘buy n times, get one free’ loyalty cards. We develop a multinomial logit model where consumer's utility depends on the value of the product and of the rewards. Using an iterative algorithm, we numerically solve a Nash game for two firms offering loyalty programs. Optimal strategies and profits are obtained for three different scenarios (games): (1) both firms do not restrict redemption; (2) both firms restrict redemption; and (3) only one firm restricts redemption while the other firm does not. Our main findings indicate that each firm's optimal strategies are significantly affected by whether the competitor decides to restrict or not to restrict redemption. In particular, a firm that restricts reward redemption should offer a higher price if its competitor also restricts redemption. Further, the dominant strategy of the game depends on customers’ valuations of time and rewards. For example, when customers highly value time but do not highly value rewards, the dominant strategy for both firms is not to restrict redemption. Alternatively, firms can face a Prisoner dilemma situation leading to unrestricted redemption policy for intermediate levels of customer valuation of both time and rewards.

Keywords: OR in marketing; Iterative algorithm; Multinomial logit models; Loyalty programs; Game theory (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221717306756
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:265:y:2018:i:2:p:621-630

DOI: 10.1016/j.ejor.2017.07.048

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().