经济Assessment 1代做 ECON3057/4438Industrial Organisation

ECON3057/4438/8038 Industrial Organisation
Assessment 1

经济Assessment 1代做 Identify all values of x for which A is strictly dominated (by a mixed or pure strategy) for player 1. Identify all values

1. [30 points] Consider the following strategic game, where x and y are real numbers:  经济Assessment 1代做

(a) Identify all values of x for which A strictly dominates B and C for Player 1, and Önd all pure and mixed strategy Nash equilibria given those values. (4 points)

(b) Identify all values of x for which A is strictly dominated (by a mixed or pure strategy) for player 1. Identify all values of y for which A is strictly dominated (by a mixed or pure strategy) for player 2. Given these values of x and y, Önd all pure and mixed strategy Nash equilibria. (7 points)

(c) Let pA, pB and pC denote the probabilities of player 1 choosing actions A, B and C, respectively. Similarly, let qA, qB and qC denote a strategy for player 2. Use this notation to write down each playerís expected payo§s corresponding to each of his pure strategies. (6 points)

(d) Find all values of x and y for which there exists a MSNE where each player plays each of his actions with strictly positive probability. Carefully explain why the conditions you found are necessary, and derive the corresponding equilibrium strategies as functions of x and y. (7 points)

(e) Focus on the MSNE you found in part (d). Suppose that there is an increase of x while y remains the same. Which playersíequilibrium strategies change? Does this surprise you? Provide some explanation. (6 points)

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