Optimal decisions for selling on an online group buying platform in a competitive fuzzy game environment

Online group buying platforms (OGBPs) as a new form of e-commerce, offer a new channel for vendors to provide discounts on assorted services through promotion, and attract new customers with the opportunity to experience their services. This paper is conducted based on genuine issues observed in OGBPs where a vendor decides to advertise its service by offering a discount coupon on an OGBP. Accordingly, we propose a fuzzy, dual-channel supply chain, with one OGBP and one vendor who sells her/his service through both offline and online channels. Considering the cognitive uncertainty of parameters in a supply chain, all parameters of the problem are specified as fuzzy variables based on experts' opinions. This paper develops a demand function of online customers depending on online and offline prices, sales period on the OGBP and vendor's credibility. The vendor's credibility is also affected by service level and advertisements. Furthermore, in the competitive OGB market, two game structures, i.e., a centralized model and a decentralized model called as OGBP-leader Stackelberg, are considered under different refunding and revenue sharing scenarios of unredeemed coupons. By comparing these scenarios, the purpose of this paper is to examine the optimal approach for OGBP's pricing strategy and vendor's decisions. Expected value models are developed to evaluate how members decide commission price, online price, service quality, and sales period of a service in each scenario. According to the results, the vendor or OGBP that provide a full refund to the customers maximizes the expected profits compared to No-refund policy; sharing the entire revenue from the coupons sales with the vendor increases the commission price. This increases the online price and reduces the quality, sales period and expected profits; the vendor's generosity, meaning providing a refund to customers and earning revenue from redeemed coupons, is in favor of both the vendor and OGBP; and we investigate the impact of quality and credibility factors under a fuzzy environment on optimal profits.