Dominance-solvable common-value large auctions

We consider second-price common-value auctions with an increasing number of bidders. We define a strategy of bidder i to be (ex-post, weakly) asymptotically dominated if there is another strategy for i that does, in the limit, as well against any sequence of strategies of iʼs opponents, and with positive probability does strictly better against at least one sequence. Our main result provides a sufficient condition on the information structure for the process of iteratively deleting asymptotically dominated strategies to terminate after just two iterations, with only one strategy left for each player. This strategy is fully characterized. We also show that, under standard assumptions, a similar condition to that of Wilson (1977) implies our sufficient condition and therefore implies asymptotic dominance solvability.