By Vijay Krishna
It is a first-class booklet at the subject, yet we want a "Dummies" model. Auctions have gotten part of daily life -- been on EBay in recent years? performed the inventory marketplace? I want Dr. Krishna had a model of this fabric with out the rigorous math that i'll in an undergrad path.
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Extra resources for Auction Theory
In a second-price auction, such a bidder faces some uncertainty about the price he or she will pay since that is determined by the second-highest bid. Suppose that the other bidders are following their equilibrium (and weakly dominant) strategy of bidding their values so that the second-highest bid is Y1 . Let ρ (x, z) be the risk premium associated with the “price gamble”–it is the certain amount the bidder would forgo in order to remove the associated uncertainty. 7) and CARA implies that we can write ρ (z) ≡ ρ (x, z) since the risk premium depends only on the gamble being faced–which is entirely determined by z–and not on the “wealth level” x.
5. Optimal Reserve Price however, by the possibility that while the highest value Y1 exceeds r, the second-highest value, Y2 , is smaller than r (in all other cases, the reserve price has no eﬀect). Now the application of the reserve price means that the object will be sold for r rather than Y2 . The probability of the first event is F (r)2 and the loss is at most r. So for small r, the expected loss is at most rF (r)2 . The probability of the second event is 2F (r) (1 − F (r)), and for small r, the gain is of order r, so the expected gain is of order 2rF (r) (1 − F (r)).
14) L I (x0 ) = (X, W ) : B I (X, W ) < B I (x0 , 1) and define m I , F I , and G I in a fashion completely analogous to the corresponding objects for a second-price auction. 3 is the second-highest of N draws from the distribution F I . 14), respectively, imply that L I (x) ⊂ L II (x). 1. 10) implies that for all x, F I (x) ≤ F II (x) and a strict inequality holds for all x ∈ (0, 1) . We have thus argued that F I stochastically dominates F II . 3 Suppose that bidders are subject to financial constraints.
Auction Theory by Vijay Krishna