26 Private Value Auctions: A First Look
derived in Proposition 2.2). Now suppose that after the auction is over,
both the losing and winning bids are publicly announced. In addition,
there is the possibility of postauction resale: The winner of the auction
may, if he so wishes, offer the object to the other bidder at a fixed “take-it-
or-leave-it” price of p. If the other bidder agrees, then the object changes
hands, and the losing bidder pays the winning bidder p. Otherwise, the
object stays with the winning bidder, and no money changes hands. The
possibility of postauction resale in this manner is commonly known to
both bidders prior to participating in the auction. Show that β remains an
equilibrium even if resale is allowed. In particular, show