Private Value Auction. Common value : The same value for everyone, but different bidders have different information about the underlying value Private Value : Bidders i = 1, 2, … know the value of the item to themselves with certainty ( z i ).
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Private Value Auction Common value: The same value for everyone, but different bidders have different information about the underlying value Private Value: Bidders i= 1, 2, … know the value of the item to themselves with certainty (zi). Independent Private Value (IPV) when bidders valuations are drawn independently of each other. Bidders do not know their rivals’ valuations, but they know the distribution from which they are drawn (complete information). “Poker”?
Question: How much to bid? What does theory say about it? • Simple case: Distribution is uniform, subjects are risk neutral (max E(U)= max E(V), bid function bi(zi) is monotonic. Only 2 bidders
EV = prob (win)× (zi – bi) + Prob (lose)× 0 = k bi (zi – bi) • 0 = k (zi – bi) + k bi (-1) • bi = zi/2 • If N persons prob(win) = (kbi)n-1 • bi = ((N-1)/N) zi • As N infinity, bi = zi • If risk averse: E(u) = (v)1/2 • If risk seeker: E(u) = v2
Notice that there is no reference (as usual) to institutions: i.e. To the rules that govern the exchange of messages and binding contracts. • We will notice the institutions and mention 4 standard examples
Revenue equivalence • Between strategically equivalent First price = Dutch and English = Second price • Between FP/D = E/SP (only if risk neutral) • Why b1=z2 is equivalent to b1=z1/2? Davis, Holt p. 282 • Experimental procedures • N subjects bidding for a single unit of a fictitious commodity • P periods • Subjects’ valuations are determined randomly prior to each period and are private information • Each period, Highest bidder makes a profit = values of the item minus price • Different information treatments