Different factors affect customers' decisions on the selection of a service. Two of the essential factors are the price and the level of service provided by a seller to customers. The seller's credibility is also among the influential factors in selecting and buying a service that is reinforced by advertisements (offline advertisement or sales through an online group buying platform) and the provided service level. Accordingly, this study develops a fuzzy mathematical model to simultaneously determine price, service level, and advertisement level in a dual channel supply chain during two current and future courses according to the cooperative game between the seller and the platform. All parameters of the problem are determined as fuzzy variables. The seller can sell her/his service through individual sales strategy (offline) or mixed strategy, selling her/his service through the platform (online) and offline channels. The aim is to determine the optimal strategy for the seller when deciding to join the group buying platform, which is compared with the individual strategy. By considering the structures of group buying platforms, different refunding policies and revenue sharing policies are developed under six scenarios for the centralized model . The optimal solutions of the problem are then defined using the game theory approach and fuzzy sets theory for each scenario. Ultimately, a numerical example is provided to indicate the effectiveness of theoretical results of models and developing management insights. Besides, performed sensitivity analyses in this article also provide the effect of the change in essential parameters on seller decisions.
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