The following is an interpretation of the rivalry between
the United States and the Soviet Union for geopolitical influence during the
1970s and 1980s.9 Each side has the choice of two strategies: Aggressive and
Restrained. The Soviet Union wants to achieve world domination, so being
Aggressive is its dominant strategy. The United States wants to pre‑ vent
the Soviet Union from achieving world domination; it will match Soviet
aggressiveness with aggressiveness, and restraint with restraint. Specifically,
the payoff table is:
For each player, 4 is best and 1 is worst.
(a) Consider this game when the two countries move
simultaneously. Find the Nash equilibrium.
(b) Next consider three different and alternative ways in
which the game could be played with sequential moves:
(i) The United States moves first, and the Soviet Union
(ii) The Soviet Union moves first, and the United States
(iii) The Soviet Union moves first, and the United States
moves second, but the Soviet Union has a further move in which it can change
its first move. For each case, draw the game tree and find the subgame-perfect
(c) What are the key strategic matters (commitment,
credibility, and so on) for the two countries?