Abstract: This article studies the design of multidimensional auctions,when firms bid on both price and non-price(quality).We have built a new scoring rule on the basis of Che Model's by adding a parameter,and studied the equilibrium of the first-score auction and secondscore auction ulnder different quality preference.The results show that the first-score auction and second-score auction are equivalent no matter how the new parameter changes.Under the new scoring rule,the buyer can easily build the quality threshold and choose the firm according to his own quality preference.If the coordination mechanism exists after some firm wins,win-win will come true and it will maximize the social welfare.

Key words: multidimensional, optimal mechanism, first-score auction, second-score auction