Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form game shown below. Management and a labor union are bargaining over how much of a $50 surplus to give to the union. The $50 is divisible up to one cent. The players have one shot to reach an agreement. Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer. Both players get zero if the total amounts asked for exceed $50. Which of the following is true?
A) There are multiple Nash equilibria.
B) ($25, $25) is a Nash equilibrium.
C) A Nash equilibrium is also a perfect equilibrium.
D) There are multiple Nash equilibria, and ($25, $25) is a Nash equilibrium.

Question

Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form game shown below.  Management and a labor union are bargaining over how much of a $50 surplus to give to the union. The $50 is divisible up to one cent. The players have one shot to reach an agreement. Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer. Both players get zero if the total amounts asked for exceed $50. Which of the following is true?
A) There are multiple Nash equilibria. 
B) ($25, $25) is a Nash equilibrium. 
C) A Nash equilibrium is also a perfect equilibrium. 
D) There are multiple Nash equilibria, and ($25, $25) is a Nash equilibrium.

Quizplus · Accepted Answer

There are multiple Nash equilibria in this game. If management asks for $0 or a very small amount, the union will likely accept since they will receive most of the surplus. If management asks for close to $25, the union may accept or reject depending on their preference. If management asks for more than $25, the union will likely reject since they will receive a smaller share of the surplus. Therefore, ($25, $25) is one of the Nash equilibria, along with other possible equilibria. A Nash equilibrium is not necessarily a perfect equilibrium, as there may be multiple equilibria that satisfy the conditions of Nash equilibrium but not necessarily perfect equilibrium.

Suppose That You Are a Manager