# Consider a game between a union and the company that employs the union membership. The union can…

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:

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(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

(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.