[2021] Economics 482 Game Theory and Economics - Midterm Exam - Q1 Nash equilibrium
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1. Below is a 2-player simultaneous-move game in matrix form, in which each player has three actions:
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1. (a) For each of the six actions in the game (x1, y1 and z1 for player 1; x2, y2 and z2 for player 2), state whether or not that action is strictly dominated (by a pure strategy or a mixed strategy), along with an explanation that makes clear how you know. (3 points)
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2. (b) Does either player have a strictly or weakly dominant action in this game? Say how you know. (2 points)
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3. (c) Find the set of rationalizable actions for each player. Although you do not have to provide a definition of a rationalizable action, your answer must demonstrate that you know why an ac- tion is or is not rationalizable, i.e., you must show that you used the criteria of rationalizability to reach your answer. An answer with no explanation is worth no credit. (13 points)
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4. (d) Find all Nash equilibria of the game in pure strategies. (4 points)
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5. (e) Find one Nash equilibrium of the game in which neither player uses a pure strategy, i.e., both
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use mixed strategies that are not pure strategies. (11 points)
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