Consider a first-price auction to sell an object in which there are 3 bidders. Recall that in a first-price auction, the bidder who makes the highest bid wins. And the price he pays for the object is equal to his bid. Here, we also assume that if there is a tie, the bidder with the biggest index wins. For instance, if (b1.b2.b3)-(5,6,6), bidders 2 and 3 make the highest bids. The bidder who wins the object is bidder 3 because 3>2. We will also assume that the bids have to be integers. So, a bid can be 0,1.2.3. but it cannot be 3.67 or 5.2. Let the three bidders valuations of the object be vi-$10, v2-$15, v3-s20 Let the bids made by the three bidders be: (b1,b2.b3) (a) is the case when (b1,b2.b3)-(0,15,15) a Nash equilibrium? Explain why it is or it is not a Nash equilibrium. (b) is the case when (b1.b2.b3)-(0,14.15) a Nash equilibrium? Explain why it is or it is not a Nash equilibrium.

Consider a first-price auction to sell an object in which there are 3 bidders. Recall that in a first-price auction, the bidder who makes the highest bid wins. And the price he pays for the object is equal to his bid. Here, we also assume that if there is a tie, the bidder with the biggest index wins. For instance, if (b1.b2.b3)-(5,6,6), bidders 2 and 3 make the highest bids. The bidder who wins the object is bidder 3 because 3>2. We will also assume that the bids have to be integers. So, a bid can be 0,1.2.3. but it cannot be 3.67 or 5.2. Let the three bidders valuations of the object be vi-$10, v2-$15, v3-s20 Let the bids made by the three bidders be: (b1,b2.b3) (a) is the case when (b1,b2.b3)-(0,15,15) a Nash equilibrium? Explain why it is or it is not a Nash equilibrium. (b) is the case when (b1.b2.b3)-(0,14.15) a Nash equilibrium? Explain why it is or it is not a Nash equilibrium.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 9MC

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