Q4 - A Large Game At least once per game theory class, students are commonly asked to solve a long MSNE problem. Spend the time now so you are confident and prepared for future questions. (a) Start by eliminating all strictly dominated strategies in the above game. (b) If you are left with a 32 game in (a), graph the expected payoffs for player 1 , assuming that P2 is mixing between their two remaining strategies. Eliminate any strategy/strategies that are non-rationalizable, in the mixed-strategy sense. If you were left with a 2x2 game in part (a), proceed to part (c). Hint: This may sound like it would be easier to return to (a) and try to the reduce the game further, if you have not already done so. In my opinion, it is easier to just do (b) as described above. (c) Derive the conditions for each player which tell us when they are indifferent between their remaining strategiess. (d) Using your results from part (c), derive the best-response correspondences for each player. (e) Graph the best-response correspondences for each player. (f) Record all NE that you have found. How many NE are there? (g) Suppose you are working for a data science firm and are asked to give an analysis of your prediction(s) for the outcome of the game. Using the 2x2 game you were left with by the end of (b), give a brief explanation of what your prediction(s) mean and provide a comment as to whether you think some might be better predictions than others. Q4 - A Large Game At least once per game theory class, students are commonly asked to solve a long MSNE problem. Spend the time now so you are confident and prepared for future questions. (a) Start by eliminating all strictly dominated strategies in the above game. (b) If you are left with a 32 game in (a), graph the expected payoffs for player 1 , assuming that P2 is mixing between their two remaining strategies. Eliminate any strategy/strategies that are non-rationalizable, in the mixed-strategy sense. If you were left with a 2x2 game in part (a), proceed to part (c). Hint: This may sound like it would be easier to return to (a) and try to the reduce the game further, if you have not already done so. In my opinion, it is easier to just do (b) as described above. (c) Derive the conditions for each player which tell us when they are indifferent between their remaining strategiess. (d) Using your results from part (c), derive the best-response correspondences for each player. (e) Graph the best-response correspondences for each player. (f) Record all NE that you have found. How many NE are there? (g) Suppose you are working for a data science firm and are asked to give an analysis of your prediction(s) for the outcome of the game. Using the 2x2 game you were left with by the end of (b), give a brief explanation of what your prediction(s) mean and provide a comment as to whether you think some might be better predictions than others