An object is sold in a first-price auction – thus, the highest bidder wins the object and price is equal to the highest bid. There are two bidders, an "Odd" bidder (player 1) and an "Even" bidder (player 2). The odd bidder must bid an odd integer between 1 and 9, while the Even bidder must bid an even integer between 2 and 10. (So the strategy sets are {1,3, ...,9} and {2, 4, .., 10}.) The value of the object to the Odd bidder is 8, and value of the object to the Even bidder is 7. The payoff to the winner is the value of the object minus the price, and the payoff to the loser is 0. (a) Write the game in its strategic form. (b) Find all Nash equilibria.

An object is sold in a first-price auction – thus, the highest bidder wins the object and price is equal to the highest bid. There are two bidders, an "Odd" bidder (player 1) and an "Even" bidder (player 2). The odd bidder must bid an odd integer between 1 and 9, while the Even bidder must bid an even integer between 2 and 10. (So the strategy sets are {1,3, ...,9} and {2, 4, .., 10}.) The value of the object to the Odd bidder is 8, and value of the object to the Even bidder is 7. The payoff to the winner is the value of the object minus the price, and the payoff to the loser is 0. (a) Write the game in its strategic form. (b) Find all Nash equilibria.

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 4MC

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Consider a second-price auction (i.e. the highest bid wins, but the winner only pays the second-highest bid), where one bidder is willing to pay much more for the object than anyone else. These are the individual valuations (each bidder only knows their own) Bidder 1 Bidder 2 Bidder 3 Bidder 4 Bidder 5 Bidder 6 Bidder 7 What is the difference between the amount Bidder 2 bids and the amount Bidder 2 pays in equilibrium? 50 O $1,315 $5,600 $3,045 $2,015,400 $5,600 $5,900 $1,500 $3,110 $1,315 O $2,015,400
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