This chapter contains a proof of a very pretty theorem due to Barry O’Neill that prescribes optimal play (for rational bidders) in the dollar auction from Chapter 6. We prove this theorem in Sections 12.2 and 12.3. In Section 12.4, we explain the sense in which a Vickrey auction is a “generalized Prisoner’s Dilemma.”
KeywordsStrong Version Special Number Mathematical Induction High Bidder Game Tree
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