ECON3057/4438/8038 Industrial Organisation
Assessment 1
产业组织经济代写 (a) Identify all values of x for which A strictly dominates B and C for Player 1, and find all pure and mixed strategy Nash equilibria given
1. 产业组织经济代写
Consider the following strategic game, where x and y are real numbers:
(a) Identify all values of x for which A strictly dominates B and C for Player 1, and find all pure and mixed strategy Nash equilibria given those values.
(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, find all pure and mixed strategy Nash equilibria.
(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 player’s expected payoffs corresponding to each of his pure strategies.
(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.
(e) Focus on the MSNE you found in part (d). Suppose that there is an increase of x while y remains the same. Which players’ equilibrium strategies change? Does this surprise you? Provide some explanation.
2. 产业组织经济代写
Consider the following description of a two player (Player 1 and Player 2) extensive form game.
(a) Identify the feasible strategies for each player and construct the normal form representation of this game. Just use one copy of the strategies that are equivalent to each other.
(b) Use the normal form representation you identified in part (a) and find all pure strategy Nash equilibria.
(c) Are there any mixed strategy Nash equilibria where both players play all their pure strategies with strictly positive probabilities? Explain.
(d) If we were to start the game at Player 1’s second information set, the game is a simultaneous move game with Player 1 choosing {U; D} and Player 2 choosing {L; C; R}. Consider this smaller game only (starting from Player 1’s second 1information set), find the subgame perfect Nash equilibria in pure and mixed strategies.
(e) Find the subgame perfect Nash equilibria to the whole game (the original game starting with Player 1’s first information set). Focus on pure strategies.
(f) Compare your answers in parts (d) and part (e). Focus on pure strategies. Brieáy comment on how the outcome changes and give some intuition.
3. 产业组织经济代写
Answer the following questions on the SSNIP test.
(a) Describe the SSNIP (Small but Significant Non-transitory Increase in Prices) test. What is the test for? What is the main idea behind the test? What is the standard procedure?
(b) What is the danger of using the current market prices for the SSNIP test? While the current market prices may not be appropriate for the test, would we end up with a too wide or too narrow market definition?
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