Question

Consider a firm and a union bargaining over how to split the firm’s revenue (which we assume is $100). The firm first makes an offer of an amount it will give the union (which goes to the workers as wages). Assume the firm has to choose the amount in multiples of 50. After the firm has made its offer, the union chooses whether to accept or reject. If it accepts, the revenue is divided accordingly; assume payoffs of each player are equal to the amount of revenue received. If the union rejects, there is a strike and both firm and union get a payoff of 0.

a. Write a game tree for this game, with actions labelled and payoffs written in.

b. List the strategies available to the union. List the strategies available to the firm.

c. Find a solution to the game using backward induction. Explain why this solution is a subgame perfect equilibrium.

d. Recall that every subgame perfect equilibrium is also a Nash equilibrium. Are there any Nash equilibria of this game that are not subgame perfect equilibria?

e. Explain how the union could make itself better off by removing some of its possible actions in the game.

Answer 1

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