Recall the example from Exercise S3 in which two division
managers’ choices of High or Low effort levels determine their salary payments.
In part (b) of that exercise, the cost of exerting High effort is assumed to be
$60,000 a year. Suppose now that the two managers play the game in part (b) of
Exercise S3 repeatedly for many years. Such repetition allows scope for an
unusual type of cooperation in which one is designated to choose High effort
while the other chooses Low. This cooperative agreement requires that the
High-effort manager make a side payment to the Low-effort manager so that their
payoffs are identical.
(a) What size of side payment guarantees that the final
payoffs of the two managers are identical? How much does each manager earn in a
year in which the cooperative agreement is in place?
(b) Cooperation in this repeated game entails each
manager’s choosing her assigned effort level and the High-effort manager making
the designated side payment. Defection entails refusing to make the side
payment. Under what values of the rate of return can this agreement sustain
cooperation in the managers’ repeated game?