Consider a first-price sealed-bid auction of a single object with two bidders j = 1, 2. Bidder 1' s valuation is v1 = 2, and bidder 2' s valuation is v2 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts (e.g. $1). In the event of a tie, the object is awarded by a flip of a fair coin. (a) Write down this auction as a 2 × 2 matrix game. Hint: note that each bidder can choose a bid from {0, 1, 2, 3, 4, 5, .. }. Your matrix will be incomplete since you cannot write a matrix with infinite rows and columns (b) Eliminate the strictly dominated strategies. Write down the resulting matrix game. (c) An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of this game? Āre the Nash equilibria efficient? %D

Consider a first-price sealed-bid auction of a single object with two bidders j = 1, 2. Bidder 1' s valuation is v1 = 2, and bidder 2' s valuation is v2 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts (e.g. $1). In the event of a tie, the object is awarded by a flip of a fair coin. (a) Write down this auction as a 2 × 2 matrix game. Hint: note that each bidder can choose a bid from {0, 1, 2, 3, 4, 5, .. }. Your matrix will be incomplete since you cannot write a matrix with infinite rows and columns (b) Eliminate the strictly dominated strategies. Write down the resulting matrix game. (c) An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of this game? Āre the Nash equilibria efficient? %D

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.10P

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