A note on k-price auctions with complete information when mixed strategies are allowed

摘要

Restricting attention to players who use pure strategies, Tauman (2002) proves that in a k-price auction (k >= 3) for every Nash equilibrium in which no player uses a weakly dominated strategy: (i) the bidder with the highest value wins the auction and (ii) pays a price higher than the second-highest value among the players, thereby generating more revenue for the seller than would occur in a first- or second price auction. We show that these results do not necessarily hold when mixed strategies are allowed. In particular, we construct an equilibrium for k >= 4 in which the second-highest valued player wins the auction and makes an expected payment strictly less than her value. This equilibrium-which exists for any generic draw of player valuations-involves only one player using a nondegenerate mixed strategy, for which the amount of mixing can be made arbitrarily small.(C) 2017 Elsevier B.V. All rights reserved.