A theory of premium auctions

In premium auctions, sellers stimulate competition by rewarding a number of
highest bidders. Previous theoretical investigations considered special cases where
premium auctions could be expected to perform well. This paper provides a theory
of the English premium auction for the canonical case in which risk averse or risk
seeking bidders with symmetric private values compete. We show that for a given
number of bidders the expected revenue in the premium auction increases in the
bidders' degree of risk tolerance. A surprising result is that the premium auction is
more attractive to risk averse bidders. A "zero-expected-utility-for-premium effect"
is key to the results.
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Keywords: premium auction, English auction, risk averse, risk seeking, pre-
mium effects