Consider the payoff matrix listed below: IS |1, -1 3, 0 |0, 3 |1, 2 |0, 0 3, 1 5, 3 |2,1 2, 1 Which of the following is true? a. Player 1 has a dominant strategy, but not player 2 b. Neither player has a dominant strategy c. Player 2 has a dominant strategy but not player 1 d. Both players have a dominant strategy

3. The following is an interpretation of the rivalry between the United States (USA) and the Soviet Ünion (USSR) during the cold war. Each side has the choice of two strategies: Aggressive and Restrained. The payoff table is given as follows: USSR Restrained Aggressiveness Restrained 4,3 1,4 USA Aggressiveness 3,1 2,2 a) Consider this game when the two countries move simultaneously. Find all pure strategy Nash equilibria. b) Next consider three alternative ways in which the game could be played with sequential moves: (i) The USA moves first and the USSR moves second. (i) the USSR moves first and the USA moves second. (i) The USSR moves first, and the USA moves second, but the USSR has a further move after the USA moves. For each case, draw the game tree and find the subgame-perfect Nash equilibrium. c) What are the key strategic issues (commitment, credibility and so on) for the two countries. (Note: Be concise. Your answer should not exceed 300 words].

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Strategy A Player 1 B Player 2 C D E F 19, 4 9, 15 7, 18 11, 13 8, 10 17, 7 12, 15 4, 9 a. What is player 1's optimal strategy? Strategy B Player 1 does not have an optimal strategy. Strategy A b. Determine player 1's equilibrium payoff. 8 *

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