Discriminating Bidders Can Improve Efficiency in Auction

Abstract

Auction is widely used in allocation and procurement of resources due to its desirable properties: efficiency and revenue maximization. It is well- known, however, that auction may fail to achieve efficiency when allocative externalities exist. Such a result may happen in the auction of the resources that are very scarce, for example, radio spectrum. This is because allocation of the resources has effects on competition of the firms in the aftermarket, and thus a firm that utilizes the resources less efficiently may make a higher bid to lessen competition. This paper shows first that efficient allocation may not be achieved by auction even when the number of bidders is 2, while it is shown in the literature that auction may result in inefficient allocation when the number of bidders is greater than or equal to 3. There exist 2 firms, who make a bid to win the scarce resources that increase the value or decrease the production cost of their own product. After the auction ends, the firms engage in Bertrand competition on the Hotelling line. Inefficient allocation may happen even under the second-price auction rule, and it happens only when the firms are different in the initial value or the initial cost of their products as well as in the value of the auctioned resources. The firm who has been the leader loses a large portion of the market if it fails to win the auction, and thus makes a high bid even when the other firm can use the resources more efficiently. Allocative efficiency Pareto improves when the smaller firm’s bid counts more than the leader’s bid. This paper suggests a modified rule that the smaller firm wins the auction when its bid multiplied by some constant is greater than the leader’s bid. The multiplier can be calculated from the market shares. It is equal to 1 when the two firms are the same, and is increasing in the leader’s market share. Allocation is efficient in a strictly larger set of parameters under the modified rule than under the standard second-price auction rule.

Keywords

• 주파수경매(Spectrum Auction)
• 배분적 외부성(Allocative Externalities)
• 배분적 효율성(Allocative Efficiency)
• 호텔링 모형(Hotelling Model)