## 3 Online Auction-Based Resource Allocation Method
### Auction Mechanism  
Generally, there are three important components in an auction model, the buyer, the seller, and the auctioneer. In this paper, the ground users are considered the buyers and the satellites are the sellers. The ground users need to purchase resources from the satellites for the MEC services and the satellites can gain profit by providing MEC services. A satellite with large communication coverage can also be considered as the auctioneer. The multi-round auction-based satisfaction maximization mechanism is divided into three main phases. Firstly, the ground users provide computation requirements to the auctioneer, and provide bids based on the broadcast information of the auctioneer. Then, the auctioneer performs resource checking, utility calculation, and task assignment based on the bid information. Finally, when the matching between users and satellites is finished, the auctioneer determines the final pricing based on the matching results. In the first phase of the auction, the users provide requirements to the auctioneer. In the second phase of the auction, the auctioneer uses a bidding strategy to measure which satellites better fit the users' criteria, and determines whether the users can be served by the satellites based on a matching strategy. After determining the matching, the final pricing strategy for each user is determined based on the bids. In this paper, we consider that the bids submitted by the users at different satellites can be different. Since the tasks are also different for each user, the final revenue for the user would be different. In order to allocate the satellites' resources more effectively, the user's initial profit is considered for matching the supply and demand between the satellites and the users. The user's initial cost-benefit represents the difference between the user's bid price and the satellite's declared price, which is given by,  
\[\delta_{ij}=bid(i,j)-Ask(j),i\in M,j\in N, \tag{10}\]where \(bid(i,j)\) denotes the bid of user \(i\) to satellite \(j\), and \(Ask(j)\) denotes the lowest service price of satellite \(j\). Every user wants to save on cost and obtain the most benefit with the least cost. Therefore, the satellites with a higher initial cost-benefit should have a higher chance of winning the bids. The auctioneer will give priority to the satellites with lower task costs for users. In other words, the auctioneer selects the satellites from the user's perspective and decides which satellite is better for the users. Thus, in order to maximize service satisfaction, we need to design a matching strategy, i.e., to solve the service matching between the satellites and the users. In this paper, the matching of users can be described as a winner determination problem, i.e., determining whether a satellite is available to serve a user. At the beginning of the auction, all sellers submit their bids to the auctioneer based on the buyers' information. The auctioneer determines the set of user matching candidates, i.e., which buyers and sellers match each other, based on calculating the user's resource requirement bidding ratio. During each round of matching, each satellite is matched with only one buyer. When multiple buyers select the same seller, the seller can make a reverse selection. To ensure the satisfaction of satellites, service satisfaction is used for seller-to-buyer selection. In other words, in the case of multiple users selecting the same satellite, the satellites pre-calculate the satisfaction brought by each user of the service based on the bid price and select the user with the greatest satisfaction for matching. As seen from the above equation, the seller prefers to choose the user with a higher overall price-performance ratio for the service. Thus, the seller selects a buyer from the candidate set to match with based on the overall price-performance value. The remaining users in the candidate set are considered failed matches and the next round of the auction is conducted.