Đầu tiên, các cơ chế phức tạp của một cuộc đấu giá VCG có thể khó hiểu cho các nhà thầu. Nó không phải là trực quan và nhà thầu cũng có thể không thực hiện theo các chiến lược thích hợp. Thứ hai, nó là rất khó để thực hiện. Điều này là bởi vì với từng nhà thầu phải nộp một số lượng rất lớn các hồ sơ dự thầu, | 322 AUCTIONS First the complex mechanism of a VCG auction can be hard for bidders to understand. It is not intuitive and bidders may well not follow the proper strategy. Secondly it is very hard to implement. This is because each bidder must submit an extremely large number of bids and the auctioneer must solve a NP-complete optimization problem to determine the optimal partition. No fast polynomial-time solution algorithm is available for NP-complete problems so the winner determination problem can be unrealistically difficult to solve. There are several ways that bidding can be restricted so that the optimal partitioning problem becomes a tractable optimization problem . one solvable in polynomial time . Unfortunately these restrictions are rather strong and are not applicable in many cases of practical interest. One possibility is to move the responsibility for solving the winner determination problem from the seller to the bidders. Following a round of bidding the bidders are challenged to find allocations that maximize the social welfare. Double Auctions Another interesting type of multi-unit auction is the double auction. In this auction there are multiple bidders and sellers. The bidders and sellers are treated symmetrically and participate by bidding prices called offers and asks at which they are prepared to buy and sell. These bids are matched in the market and market-clearing prices are generated by some rule. The double auction is one of the most common trading mechanisms and is used extensively in the stock and commodity exchanges. In an asynchronous double auction also called a Continuous Double Auction CDA the offers to buy and sell may be submitted or retracted at any time. A public order book lists at each time t the currently highest buy offer b t and currently lowest sell offer s t . As soon as b t s t a sale takes place and the values of b t and s t are updated. Today s stock exchanges usually work with CDAs and they have also been .
