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. $\begin{array}{c}
\text { Worker }\
\text { Manager}
\begin{array}{|l|l|l|}
\hline & \text { Work } & \text { Shirk } \
\hline & & \
\text { Monitor } & -1,1 & 1,-1 \
\hline \text { Don't } \
\text { Monitor }& 1,-1 & -1,1\
\hline
\end{array}\end{array}$ 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. $\begin{array}{c}
\text { Worker }\
\text { Manager}
\begin{array}{|l|l|l|} 
\hline & \text { Work } & \text { Shirk } \
\hline & & \
\text { Monitor } & -1,1 & 1,-1 \
\hline \text { Don't } \
\text { Monitor }& 1,-1 &  -1,1\
\hline
\end{array}\end{array}$ 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

The game described has multiple Nash equilibria because different splits of the $50 surplus can be agreed upon as long as both parties are rational and aim to maximize their utility without exceeding the total surplus. The ($25, $25) split is a Nash equilibrium because neither party has an incentive to deviate from this agreement as any deviation would not improve their payoff, assuming rational behavior and the desire to avoid a disagreement that results in a $0 payoff for both. Additionally, in the context of bargaining, any division of the $50 that both parties agree upon and that does not exceed the total amount can be considered a Nash equilibrium, making multiple equilibria possible.

Suppose That You Are a Manager Management and a Labor Union Are Bargaining Over How Much