博弈论考试代写 Econ 3057, 4438, 8038代写 Industrial Organisation代写

Econ 3057, 4438, 8038: Industrial Organisation

Mid term

博弈论考试代写 1.[40 marks] Consider the following description of a two player (Player 1 and Player 2) extensive form game. (a) Identify the feasible strategies

1.[40 marks] 博弈论考试代写

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. (6 points)

(b) Use the normal form representation you identified in part (a) and find all pure strategy Nash equilibria. (4 points)

(c) Are there any mixed strategy Nash equilibria where both players play all their pure strategies with strictly positive probabilities? Explain. (4 points)

(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 information set), find the subgame perfect Nash equilibria in pure and mixed strategies. (12 points)

(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. (8 points)

(f) Compare your answers in parts (d) and part (e). Focus on pure strategies. Briefly comment on how the outcome changes and give some intuition. (6 points)

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