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A note on k-price auctions with complete information when mixed strategies are allowed
- Mathews, Timothy, Schwartz, Jesse A.
- Economics letters 2017 v.153 pp. 6-8
- auctions, income, prices
- 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.