Today the fog computing has become an essential technology to reconcile the differences between cloud computing and edge devices by providing processing resources closer to the original data source. For meeting the quality of service (QoS) requirements of users, we need to study the decentralized nature of fog computing along with all the challenges it poses upon efficient resource allocation. This paper explores the application of a double auction mechanism in game theory between two fog nodes acting as sellers (providers) and users as buyers (requesters). Both present their respective bids and ask to the auctioneer, determining a market-clearing price that maximizes social welfare, affirming resources are allocated to users who value them the most. Through simulations, we compare and analyze the proposed mechanism with traditional allocation methods, why it involves higher computational complexity due to the bidding process, potential solutions, and model in fog computing environments.