Two players, Player 1 and Player 2, are playing a repeated prisoner's dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Player 2 A B Player 1 A 10,10 1,150 B 150, 1 2,2 Select one:

Consider the following sequential-move game: This game involves three players, each making sequential decisions. The game proceeds as follows: • Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). • Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and `b`. The payoffs are determined by the sequence of choices made by all three players. Each payoff is represented by the triplet (x,y,z), where x, y, and z denote the payoffs for Player 1, Player 2, and Player 3, respectively. For example, if Player 1 chooses 'Left', Player 2 chooses 'I', and Player 3 chooses `a` the resulting payoff would be (3,1,2). This indicates that Player 1 receives a payoff of $3, Player 2 receives a payoff of $1, and Player 3 receives a payoff of $2 for this particular sequence of actions. Left Player 2 Player 1 Right Player 2 Player 3 Player 3…

Consider the following game where two players have to decide if they want to buy a movie ticket or a baseball ticket. They have the highest payoffs when they both buy tickets to the same activity, but must decide simultaneously what to buy without knowing what the other person will do.  a. Does either player have a dominant strategy? b. How many equilibria does this game have? c. Is this an example of a prisoner’s dilemma? Explain. d. What will be the outcome if your friend buys their ticket first and you can observe their choice?

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].