9.5, Ex p.284
a. Consider the final subgame associated with the letter having been sent. The
strategic form is shown in FIG SOL9.5.1. Defect is a dominant strategy for both
Borodin and Melekhin, so there is a unique Nash eqm of (defect, defect).
Next, consider the final subgame associated with the letter not having been sent.
The strategic form is shown in FIG SOL9.5.2. It has two Nash eqa: (defect, defect)
and (renege, renege).
Now turn to the subgame that is the game itself. If the Nash eqm is (defect, defect) at
both final subgames, the captain prefers not to send the letter as it results in a
payoff of 8while sending the letter means a lower payoff of 7. This gives one
SPNE: (do not send letter, defect / defect, defect / defect).
Now suppose the Nash eqm at the subgame in which the letter is not sent is (renege,
renege). If the letter is sent captain the again earns a payoff of 7, and if the letter is
not sent his payoff is 4, as both officers renege. A second SPNE is then (send letter,
defect / renege, defect / renege).
b. The payoffs are such that if the letter is sent, then it is a dominant strategy for each
of the two officers to defect. However, if the letter is not sent, then there are two
Nash eqa for that subgame: one in which both officers defect and one in which both
renege. If the letter is not sentretaining the opportunity to return to the Soviet
Union w/o their plan to defect having been discovered then an officer wants to
renege unless everyone else is planning to defect. By sending the letter, the captain
ensures that the officers will continue to defect; while if the letter is not sent, then
induced eqm play could mean that they renege and the plan to defect fails.