Almost common value auctions and discontinuous equilibria

In almost common value auctions, even a small private payoff advantage is usually supposed to have an explosive effect on the outcomes in a second-price sealed-bid common value auction. According to (Bikhchandani in J. Econ. Theory 46:97–119, 1988) and (Klemperer in Eur. Econ. Rev. 42:757–769, 1998) the large set of equilibria obtained for common value auction games drastically shrinks, so that the advantaged player always wins the auction, at a price that sharply decreases the seller’s payoff. Yet this result has not been observed experimentally. In this paper, we show that Bikhchandani’s equilibria are not the only equilibria of the game. By introducing discontinuities in the bids, we establish a new family of perfect equilibria with interesting properties, among them: (i) the advantaged bidder does no longer win the auction regardless of her private information, (ii) she may pay a much higher price than in Bikhchandani’s equilibria, (iii) there is no ex-post regret, (iv) the intersection with level-k reasoning is not empty. We also show that a private advantage limits the number of possible discontinuities: one can introduce any number of discontinuities in the common value auction, but this is not possible in presence of a private advantage.