Two individuals are bargaining over the distribution of $100 in which payoffs must be in increments of $5. Each player must submit a one-time bid. If the sum of the bids is less than or equal to $100, each player gets the amount of the bid and the game ends. If the sum of the bids is greater than $100, the game ends and the players get nothing. Does this game have a Nash equilibrium? What is the most likely equilibrium strategy profile for this game?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Two individuals are bargaining over the distribution of $100 in which payoffs must be in increments of $5. Each player must submit a one-time bid. If the sum of the bids is less than or equal to $100, each player gets the amount of the bid and the game ends. If the sum of the bids is greater than $100, the game ends and the players get nothing.

Does this game have a Nash equilibrium?

What is the most likely equilibrium strategy profile for this game?

 

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