1. The following is an interpretation of the rivalry between the United States and the Soviet Union for geopolitical influence in the 1970s and 1980s. Each side has the choice of two strategies: Aggressive and Restrained. The following payoff matrix prevails: Soviet Union Restrained Aggressive Restrained (4, 3) (1,4) Aggressive (3,1) (2, 2) For each player, 4 is best and 1 is worst. a. Does either country have a dominant strategy? b. Suppose the countries move simultaneously. Find the Nash equilibrium. c. Next consider three different and alternative ways in which the game could be played with sequential moves: i. The U.S. moves first and the Soviet Union moves second ii. The Soviet Union moves first and the U.S. moves second iii. The Soviet Union moves first, the U.S. moves second, but the Soviet Union has a further move where they can change their first move. For each case, draw the game tree and find the sub-game perfect equilibrium. d. What are the key strategic issues (e.g. commitment, credibility etc.) for the two countries?
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