More Escalation

This chapter contains proofs of two very pretty theorems dealing with auctions. The first is the result due to Barry O’Neill that prescribes optimal play (for rational bidders) in the dollar auction from Chapter 1. We prove this theorem in Sections 6.2 and 6.3. The second result we present is William Vickrey s celebrated theorem from the theory of auctions. This theorem, proved in Section 6.4, shows that honesty is the best policy in what is called a “second-price sealed-bid auction” or a “Vickrey auction.” In Section 6.4, we explain the sense in which a Vickrey auction is a “generalized Prisoners Dilemma.” Finally in the conclusion, we compare the degree to which the two theorems are truly normative. (Briefly, the former requires the knowledge that one s opponent is rational; the latter does not.)