Consider a game between a union and the company that employs the union membership. The union can threaten to strike (or not) to get the company to meet its wage and benefits demands. When faced with a threatened strike, the company can choose to concede to the demands of the union or to defy its threat of a strike. The union, however, does not know the company’s profit position when it decides whether to make its threat; it does not know whether the company is sufficiently profitable to meet its demands—and the company’s assertions in this matter cannot be believed. Nature determines whether the company is profitable; the probability that the firm is unprofitable is p. The payoff structure is as follows:
(i) When the union makes no threat, the union gets a payoff of 0 (regardless of the profitability of the company). The company gets a payoff of 100 if it is profitable but a payoff of 10 if it is unprofitable. A passive union leaves more profit for the company if there is any profit to be made.
(ii) When the union threatens to strike and the company concedes, the union gets 50 (regardless of the profitability of the company) and the company gets 50 if it is profitable but 240 if it is not.
(iii) When the union threatens to strike and the company defies the union’s threat, the union must strike and gets 2100 (regardless of the profitability of the company). The company gets 2100 if it is profitable and 210 if it is not. Defiance is very costly for a profitable company but not so costly for an unprofitable one.
(a) What happens when the union uses the pure threat to strike unless the company concedes to the union’s demands?
(b) Suppose that the union sets up a situation in which there is some risk, with probability q , 1, that it will strike after the company defies its threat. This risk may arise from the union leadership’s imperfect ability to keep the membership in line. Draw a game tree similar to Figure 14.4. for this game.
(c) What happens when the union uses brinkmanship, threatening to strike with some probability q unless the company accedes to its demands?
(d) Derive the effectiveness and acceptability conditions for this game, and determine the values for p and q for which the union can use a pure threat, brinkmanship, or no threat at all.
