Equilibrium and revenue in a family of common‐value first‐price auctions with differential information

We study a discrete common‐value auction environment with two asymmetrically informed bidders. Equilibrium of the first‐price auction is in mixed strategies, which we characterize using a doubly recursive solution method. The distribution of bids for the ex post strong player stochastically dominates that for the ex post weak player. This result complements Maskin and Riley’s (2000) similar result for asymmetric private‐value auctions. Finally, comparison with the dominance‐solvable equilibrium in a second‐price auction shows the Milgrom–Weber (1982a) finding that the second‐price auction yields at least as much revenue as the first‐price auction fails with asymmetry: in some cases the first‐price auction provides greater expected revenue, in some cases less.