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.

D. There are multiple Nash equilibria, and ($25, $25) is a Nash equilibrium.

Explanation:

Interestingly, this a real scenario application of the Nash equilibrium concept.

Using this concept the best case scenario is that since Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer, it means they both have an equal amount interest on the $50 surplus such that if one party deviate from his chosen strategy both players would get zero if the total amounts asked for exceed $50.

Thus, any amount greater than $25, $25 each would lead to zero benefits between the parties.