1. Game Theory Assignment For all of these games, P1 chooses between the columns, and P2 chooses between the rows.

2. Find all the dominant strategies For each game, find as many dominant strategies (for both players) as you can. P1: 10, P2: 10P1: -10, P2: -10 P1: 10, P2: 10 Action 1Action 2 Action 1 Action 2 6, 09, 2 -3, 2-5, 9 Action 1Action 2 P1: 10, P2: -10P1: -10, P2: 10 P1: 10, P2: -10P1: -10, P2: 10 1, 3-1, 9 8, -15, 4 Action 1 Action 2 Action 1 Action 2 Action 1 Action 2 Action 1Action 2 Action 1Action 2

3. Zero-sum, constant-sum, or general-sum? For each game, determine whether it is zero- sum, constant-sum, or general-sum. 2, -2-11, 11 -4, 49, -9 Action 1Action 2 Action 1 Action 2 6, 09, 2 -3, 9-5, 16 Action 1Action 2 2, 46, 0 1, 53, 3 Action 1 Action 2 Action 1 Action 2 Action 1Action 2

4. Pareto optima? For each game, find all outcomes that are pareto optimal. 2, -2-11, 11 -4, 49, -9 Action 1Action 2 Action 1 Action 2 1, 10, 1 1, 00, 0 Action 1Action 2 0, 11, 2 1, 32, 2 Action 1 Action 2 Action 1 Action 2 Action 1Action 2 1, 3-1, 9 8, -15, 4 Action 1 Action 2 Action 1Action 2

5. Pure Strategy Nash equilibria? For each game, find all pure-strategy Nash equilibria. (Note that a strategy is still a “best response” if the other option is tied in terms of payoff for the player.) 2, -2-11, 11 -4, 49, -9 Action 1Action 2 Action 1 Action 2 1, 10, 1 1, 00, 0 Action 1Action 2 0, 11, 2 1, 32, 2 Action 1 Action 2 Action 1 Action 2 Action 1Action 2 1, 3-1, 9 8, -15, 4 Action 1 Action 2 Action 1Action 2

6. Mixed Strategy Nash equilibria? Find a mixed strategy Nash equilibrium that is not also a pure strategy Nash equilibrium. 5, -5-1, 1 -5, 59, -9 Action 1Action 2 Action 1 Action 2