Economics, Finance and Quantitative Analysis
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.
Digital Object Identifier (DOI)
Mathews, Timothy and Schwartz, Jesse A., "A Note on k-price Auctions with Complete Information When Mixed Strategies are Allowed" (2017). Faculty Publications. 4228.