Monotonicity and Rationalizability in a Large First Price Auction
证明，在第一价格拍卖中，随着竞拍者数量增加，单调且理性的出价策略会使获胜出价收敛到竞争均衡价格，且无需对称假设，仅用可理性化策略即可得到类似信息聚合结果。
This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases ( Wilson, 1977 ). Instead of analysing the symmetric Nash equilibrium, we examine rationalizable strategies ( Bernheim (1984) , Pearce (1984) ) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the "truthful" valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to that of Wilson (1977) , while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed. Copyright 2005, Wiley-Blackwell.