Auction Theory, by Vijay Krishna

By Vijay Krishna

Vijay Krishna’s 2e of Auction Theory improves upon his 2002 bestseller with a brand new bankruptcy on package deal and place auctions in addition to end-of-chapter questions and bankruptcy notes. entire proofs and new fabric approximately collusion supplement Krishna’s skill to bare the elemental proof of every thought in a mode that's transparent, concise, and simple to persist with. With the addition of a ideas handbook and different instructing aids, the 2e keeps to function the entrance to correct conception for many scholars doing empirical paintings on auctions.

  • Focuses on key public sale varieties and serves because the doorway to correct conception for these doing empirical paintings on auctions
  • New bankruptcy on combinatorial auctions and new analyses of theory-informed applications 
  • New chapter-ending workouts and problems of various difficulties support and toughen key points

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Example text

If β (Y2 ) < x < β (Y1 ) < b, this is better than bidding x, since it results in a profit, whereas bidding x would not. If, however, x < β (Y2 ) < β (Y1 ) < b, then bidding b results in a loss. When b − x ≡ ε is small, the gain in the first case is of order ε2 , whereas the loss in the second case is of order ε3 . Thus, it is optimal to bid higher than one’s value in a third-price auction. Comparing equilibrium bids in first-, second-, and third-price auctions in case of symmetric private values, we have seen that β I (x) < β II (x) = x < β III (x) (assuming, of course, that the distribution of values is log-concave).

For a model of interest group lobbying as an all-pay auction, albeit in a complete information setting, see Baye, Kovenock, and de Vries (1993). 2 Some Applications of the Revenue Equivalence Principle 35 the over-bidding phenomenon . The explicit derivation of equilibrium strategies is due to Wolfstetter (2001). Auctions with an uncertain number of bidders have been considered by McAfee and McMillan (1987b), Matthews (1987), and Harstad, Kagel, and Levin (1990). The first two papers are particularly interested in how risk-averse bidders—considered in the next chapter—are affected by uncertainty regarding the number of competitors they face.

Suppose bidder i wins by bidding above his budget. If the second-highest bid is below his budget, then he would have also won by bidding wi . If the second-highest bid is above his budget, he has to renege, does not get the object, and pays the fine, resulting in a negative surplus. Second, if xi ≤ wi , then the budget constraint does not bind and the same argument as in the unconstrained situation implies that it is a weakly dominant 1 The independence holds only across bidders. The possibility that for each bidder the values and budgets are correlated is admitted.

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