Revenue and Efficiency in Uniform-price Private Value Auctions

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Revenue and Efficiency in Uniform-price Private
Value Auctions
Michal Bresky

• Michal.Bresky_at_cerge-ei.cz

(Summer 2007)
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Properties of Private-value Uniform-price
Auctions with the Reservation Price
Literature Dasgupta and Maskin (1986) RES, Reny
(1996) Econometrica, Simon and Zame (1990)
Econometrica, Matthew and Swinkels (1999)
Econometrica, Amman and Leininger (1996) GEB,
Krishna and Morgan (1997) JET, Engelbrecht-Wiggan
s and Kahn (1998a,b) GEB, Engelbrecht-Wiggans and
Chakraborty (2005) ET, Ausubel and Cramton
(2002,2004) ET, Back and Zender (1993) RFS,
Noussair (1995) ET.

• Seller's goals
• Revenue - to raise high revenue.
• Efficiency - to distribute units to those who
  value them the most.
• Fair competition - to prevent collusion among
  bidders and attract large number of bidders
  before auction.
• Market structure - to prevent monopoly in using
  the sold units after auction.

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Properties of Private-value Uniform-price
Auctions with the Reservation Price

• Results
• The equilibrium strategy is strictly increasing.
• The reservation price increases the bidder
  strategy.
• The proper reservation price improves the
  efficiency of final allocation ex ante.

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THE GAME
identical units of goods for sale.
bidders in an auction.
.
Independence is required between a pair of values
of two different bidders.
.
Uniform-price auction - the auction price for
winning the unit is the 1st rejected bid,
The ex post payoff when losing the unit is 0.
A tie occurs when kth and k-1st highest bids
are equal (random tie-breaking).
Ex post payoff is
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Shape of equilibrium strategies
In equilibrium the first unit bid strategy is
In equilibrium the subsequent unit bid strategy
is
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No Ties in Equilibrium with Positive Probability
Tie
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No Bidding at Positive Reservation Price with
the Number of Bids Restriction
Note In my game l2. Then the inequality is
2.ngtkgt2
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The Effect of Reservation Price on Continuous
Equilibrium Strategy
This condition is necessary because subsequent
bid increases both the probability of winning
subsequent unit and the price the bidder pays for
the initial unit if subsequent bid is the first
rejected bid.
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The Effect of Reservation Price on Continuous
Equilibrium Strategy
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The Effect of Reservation Price on Efficiency
SLoss
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The Effect of Reservation Price on Efficiency
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Thank you for your attantion.