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Revenue and Efficiency in Uniform-price Private Value Auctions. Michal Bres ky. Michal.Bresky@ cerge -ei. cz. (Summer 2007). Properties of Private-value Uniform-price Auctions with the Reservation Price. Literature:
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Revenue and Efficiency in Uniform-price Private Value Auctions Michal Bresky Michal.Bresky@cerge-ei.cz (Summer 2007)
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-Wiggans 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.
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.
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:
Shape of equilibrium strategies In equilibrium the first unit bid strategy is: In equilibrium the subsequent unit bid strategy is:
No Bidding at Positive Reservation Price with the Number of Bids Restriction Note: In my game l=2. Then the inequality is 2.n>k>2
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.