A game-theoretic analysis of retailers’ loyalty rewards for store and national brands

Retailer-controlled loyalty programs (LPs) are increasingly common, yet their strategic interaction with private-label store brands (SBs) and national brands (NBs) in a competitive supply chain remains underexplored. We propose a two-stage Stackelberg–Nash model in which a single NB manufacturer sets a wholesale price, anticipating duopolistic retailers who simultaneously choose retail prices and brand-specific reward rates. Consumer demand follows a multinomial logit process that incorporates behavioral features, namely reward sensitivity, slippage (unredeemed rewards), and brand preference. Our results show that SBs command consistently higher reward rates and margins, with NB rewards bounded by margin erosion under double marginalization. Under high slippage or reward sensitivity, retailers may concentrate rewards on SBs, which can erode NB manufacturer profits. However, when NB rewards are offered, manufacturer and retailer incentives often align via enhanced demand and wholesale pass-through. These findings reveal the critical role of retail–brand competition in shaping LP design: retailers must balance demand steering and cost control across brands, while manufacturers must anticipate how reward strategies can shift vertical power.