Browsing by Author "Zolfaghari, Saeed"

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‘Buy n times, get one free’ loyalty cards: Are they profitable for competing firms? A game theoretic analysis
(2017-08-10) Bazargan, Amirhossein; Karray, Salma; Zolfaghari, Saeed
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.
Modeling reward expiry for loyalty programs in a competitive market
(2017-08-10) Bazargan, Amirhossein; Karray, Salma; Zolfaghari, Saeed
This paper investigates reward expiry for loyalty programs. It provides insights into the profitability of setting reward expiry for competing firms and identifies conditions under which such a policy would be beneficial. We develop and solve a game-theoretic model that reflects consumer behavior in choosing products and redeeming rewards. Applying a new iterative algorithm, we get the Nash equilibrium outputs for three scenarios (games): (1) neither firm sets an expiry date, (2) both firms set an expiry date, and (3) only one firm sets an expiry date. Comparison of the firms' profits across scenarios shows that the firms' prices and profits are affected by the loyalty program of the competing firm and by consumers' valuation of rewards and of time to rewards. In particular, a firm offering rewards that do not expire should increase its price if the competing firm changes its reward policy from no expiry to expiry, even when the expiry period is quite long. Finally, when customers highly value rewards and time, reward expiry is a dominant strategy for both firms. This means that firms would benefit from setting expiry on their loyalty rewards only if their customers highly value both rewards and time. Alternatively, both firms' rewards should not expire if consumers have low valuations of both rewards and time.