Private Value Auction

1
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?

2

• 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

3

• 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

4

• 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

5
(No Transcript)
6

• Revenue equivalence
• Between strategically equivalent First price
  Dutch and English Second price
• Between FP/D E/SP (only if risk neutral)
• Why b1z2 is equivalent to b1z1/2? 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

7
(No Transcript)