考虑竞拍者市场势力的可分物品拍卖机制设计

Designing auctions for divisible goods with bidders' market power

将竞拍者的市场势力和拍卖博弈的多重均衡问题纳入一个统一的分析框架研究考虑竞拍者市场势力的可分物品拍卖机制设计和选择问题.通过在竞拍者面临的剩余供给中引入不确定性来刻画竞拍者的市场势力,对可分物品拍卖博弈潜在的多重均衡进行精炼,得到统一价格、歧视性价格和Vickrey 3种拍卖机制下竞拍者唯一和对称的线性均衡报价函数,并分别从卖方的期望收益、成交价格的波动性和激励潜在竞拍者进入等3个方面对拍卖机制进行比较.结果表明,在卖方的期望收益方面,歧视性价格机制最高,Vickrey机制次之,统一价格机制最低;在成交价格的波动性方面,歧视性价格机制最低,Vickrey机制次之,统一价格机制最高;在激励潜在竞拍者进入方面,统一价格机制下竞拍者进入最多,Vickrey机制次之,歧视性价格机制最少.最后,进一步考察了市场规模、卖方的风险态度以及进入对拍卖机制设计的影响,以期为拍卖组织者针对不同的目标进行拍卖机制设计和选择提供理论借鉴.

Both bidders＇ potential market power and multiple equilibrium in auction games are important problems in designing auctions for divisible goods. This paper puts the two problems above into one uniform framework to investigate the auction design in divisible goods market. We capture the market power of the large bidder by introducing uncertainty in the residual supply of the buyers when bidding, refine the potential continuum multiple equilibrium, and then obtain the unique and symmetrical linear equilibrium bidding func- tions based on the uniform price, discriminatory price and Vickrey auction formats, respectively. We rank these three formats in terms of the criteria employed in the practical design of the markets for divisible goods, such as expected revenue, stabilizing prices, and encouraging bidder participation. The main conclusions are ： First, the expected revenue under the discriminatory price auction is more than that under the Vickrey auc- tion, which is more than that under the uniform price auction, but all three auctions would not obtain total market surplus; Second, the discriminatory price auction gives rise to the lowest stop-out price volatility, the equilibrium price based on the Vickrey auction has a higher volatility, and the price volatility under the uni- form price auction is the highest among the three formats; Third, the uniform price auction would encourage more entries than other auctions, the Vickrey auction encourages less, and participation under the discrimina- tory price auction is the least, but all three formats would encourage more entries than Pareto efficient market size. Our model accommodates both small and large markets, as well as different risk preferences of the sell- ers. The results have important implications for the auctioneers designing the auction format according to different objectives.