Coordinating omnichannel pricing under BOPS: The role of money-back guarantees in channel pricing decisions

Abstract

This paper develops a three-stage Stackelberg dynamic game model to investigate pricing coordination in a decentralised Buy-Online-Pick-up-in-Store (BOPS) retail system under money-back guarantee (MBG) policies. The model incorporates two behavioural parameters, product matching rate and offline inconvenience cost, and derives closed-form equilibrium pricing solutions under both MBG and non-MBG scenarios. Comparative statics and numerical simulations are conducted to examine how these behavioural factors and a platform-provided per-order subsidy influence online retail price, offline retail price, and wholesale price. The results show that a higher product matching rate generally strengthens pricing power across channels, while the pricing effect of MBG depends on the interaction between product-fit uncertainty and offline inconvenience cost. MBG can stabilise the online retailer’s pricing response under different offline inconvenience conditions, but it may also create asymmetric pricing incentives between online and offline channels. These findings contribute to the literature on dynamic games and omnichannel retail operations by linking refund policy design with strategic pricing coordination in BOPS systems.