## 5 Category I: Energy Transaction
### Buyer-Seller Matching
#### 5.2.2 Auction Mechanism  
Many works focus on the design of auction mechanisms. When blockchain technology has not been adopted, [PERSON] et al. [85] proposed an efficient double auction mechanism to maximize the participants' utilities and the social welfare in a distributed system structure, which is completed by the controller in an iterative way, avoiding the need of private information. It is also widely used in distributed grid transactions [67; 86; 87]. After the blockchain is widely adopted, this auction mechanism's main claim is to match the parties at auction, not the goods to be traded [88; 89]. The charging and discharging parties send bidding vectors to the auctioneer respectively, and auctioneer carries out multiple iterative auctions on the price matrix of both parties. The buyer and seller solve their optimal price and the best matching object from multiple iterations. The same mechanism is used in the system and an adaptive aggressive strategy is adopted to adjust the quotation according to the market changes. To prevent unexpected situations, the interests of users can also be guaranteed through multi-signed digital certificates [5]. Furthermore, there are other auction mechanisms that build on top of this. The Double Auction in [90] adopts the average mechanism, in which the reserve price is calculated on an average basis and the seller with a lower reserve price will be allocated to the buyer with a higher bid in a greedy way. The method in [91] considers the double auction as the second stage of the auction mechanism. The first stage is the call auction stage, in which buyers and sellers conduct one-time matching transactions and provide guiding prices of various types of energy for each period. In addition to this classic double auction mechanism, there are many classic strategies and methods used in the design of auction mechanisms, such as the game theory method. On account of the contradiction and interactivity of energy transaction, the game theory method will be an effective tool to improve the system. The application of game theory in blockchain-based energy trading has been comprehensively studied in [61]. In [92], the non-cooperative game theory--Nash equilibrium--is used to adjust the matching process to achieve the optimal matching. Each player assumes to know the equilibrium strategy of the other player, and users in the system cannot increase their revenue by only modifying their own orders. In another major study, contract theory is also used in the auction mechanism. Contract theory is a typical branch of economics, which studies the economic behaviors and results of different contractors in a specific trading environment. In the scenario of EV charging [93], a dynamic optimal contract assignment and energy allocation algorithm is designed. Based on the contract theory, the optimal contracts are designed to satisfy consumers' distinct energy consumption preferences and maximize the operator's utility. For the problem of edge resource allocation on mobile devices, it can also be realized by auction mechanism. For example, the method in [94] considers the configuration externality and authenticity, which can maximize the personal welfare. A similar auction method is proposed in [58], and a multi-layer neural network structure for the optimal auction analysis is constructed. This model also verifies the effectiveness of using deep learning for deriving the optimal auction mobile blockchain with high revenue. Additionally, some researchers have studied the auction mechanism in the energy trading market. For example, a battery state model for electric vehicles is proposed in [95], which is responsible for clarifying the factors that buyers and sellers need to consider when determining the transaction price and volume during the auction process. The auctioneer determines the optimal allocation by controlling the bidding increment.