Question

Management and a labor union are bargaining over how much of a $100 surplus to give to the union. The $100 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 $100. Which of the following is NOT a Nash equilibrium? a. Management requests $50 and the labor union accepts $50. b. Management requests $70 and the labor union accepts $20. c. Management requests $100 and the labor union accepts $0. d. Neither management requesting $100 and the labor union accepting $0 nor management requesting $70 and the labor union accepting $20 are Nash equilibria.

Answer 1

(d)
b is not nash equilibrium because when mgmt requests $70, labour union has the option of accepting $30, as it would not want to leave the rest of the award unspent.
Similarly, c  is not n.e. because the union does not get anything by accepting $0, when mgmt requests $100. It can ask for a higher amount and ensure that mgmt does not get anything. Hence, the mgmt would have to ensure that some amount is shared with the union.

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