## 3 Online Auction-Based Resource Allocation Method
### Dynamic Pricing and Allocation Algorithm  
In the final stage of the auction, the auctioneer needs to determine the final price to be paid by the user. After a bidder has been awarded a bid, they need to pay the pricing according to the relevant payment rules. The determination of the payment rules has a crucial impact on the auction mechanism. At the same time, the payment rules also affect the revenue of satellites. Reasonable payment rules can ensure the incentive compatibility of the auction mechanism and promote the buyer to be able to make reasonable bids. In this paper, the Vickrey auction [36] method is used for the final payment pricing of the buyer, also known as the second-price sealed-bid auction. The highest bidder wins, but only pays the second-highest bidder's price. This auction mechanism can motivate bidders to report their true bids. Therefore, we use the Vickrey auction mechanism by calculating the second-highest bid as the final price.  
To maximize the service satisfaction of satellites, we propose an online multi-round auction resource allocation (OMARA) algorithm, as shown in Algorithm 1. In Algorithm 1, the user first bids for the service provider that satisfies the service price and resource requirements. When more than one service provider exists to meet the user's needs, the user selects the service provider with the highest cost-benefit to bid. Secondly, after the user has completed the bidding process, the service provider begins to establish a service relationship with the user. When more than one user selects the same service provider at the same time, the service provider enters a reverse selection, i.e., the right to choose changes. The service provider calculates the service satisfaction level and selects the user with the highest level of satisfaction for the service. In other words, the resource allocation mechanism based on online multi-round auctions selects at most one user per iteration of the process. Finally, when a new service cycle begins, users who have not yet completed their services continue to bid and the service provider selects the most suitable user as the winner. Such an online mechanism guarantees the stability and reliability of the mechanism while safeguarding the interests of the users.  
```
Input:\(N\), \(M\), Bid, \(Ask,D_{N},O_{N},F_{N},V_{N}\), \(T_{m}^{N},H_{M},L_{M},C_{M}\) Output: Optimal matching matrix \(A^{*}=\{a_{ij}\},i\in M,j\in N\); optimal final price \(p_{ij},i\in M,j\in N\); for\(i=1\) to \(M\) \(s_{1}=s_{2}=s_{3}=s_{4}=\varnothing\) for\(t=1\) to \(N\) if Bid\((i,j)\geq\) Ask\((j)\)then if\(D_{i}\leq H_{j}\)then\(s_{1}\gets j\); endif if\(F_{i}\leq C_{i}^{max}\)then\(s_{2}\gets j\); endif if\(L_{j}>0\)then\(s_{3}\gets j\); endif if\(T_{i}\leq T_{m}^{i}\)then\(s_{4}\gets j\); endif endfor \(s_{0}=s_{1}\cap s_{2}\cap s_{3}\cap s_{4}\); if\(size(s_{0})>1\)  Calculate \(\delta_{ij}\) by (10);  the buyer chooses seller \(m\) with biggest to server; \(a(i,m)=1\); elif\(size(s_{0})==1\) \(a(i,s_{0})=1\); endif endfor endfor for\(j=1\) to \(M\) if\(\sum_{i=1}^{M}a_{ij}>1\)then  calculate \(s_{ij}\) by (8);  The seller chooses the buyer with biggest \(s_{ij}\) to server; endif endfor
```  
**Algorithm 1**Online Multi-round Auction-based Resource Allocation Algorithm