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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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