Two faculty members in the Economics department both want to recruit a top graduate student to...

  

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Two faculty members in the Economics department both want to recruit a top graduate student to their department. Either faculty member can ensure the student will accept the offer by getting on the phone and shamelessly promoting the graduate program. However, there is some cost to making this call. Assume the payoffs can be represented as follows: Call 1-01, 1-02 1,1-02 Call Dont Call Dont Call 1-01, 1 0,0 where 01 and 82 represent the costs for player 1 and 2 respectively. Assume the faculty members choose their actions simultaneously and the faculty have private information about their costs of making the call. That is, faculty mem- ber i knows 8i, and believes that Oj is a random draw from a uniform distribution on [c,c]. Faculty member is belief about Oj is commonly known. (a) Find the normal form representation of this game of incomplete information. (b) Now imagine that 01 and 82 are independent random draws from a uniform distribution on [0,2]. Find a symmetric BNE in cutoff strategies.1 (c) The equilibrium outcome found in (b) is inefficient in several ways. (i) Explain why there is under-investment. (ii) Explain why there is "misscoordination between faculties. Two faculty members in the Economics department both want to recruit a top graduate student to their department. Either faculty member can ensure the student will accept the offer by getting on the phone and shamelessly promoting the graduate program. However, there is some cost to making this call. Assume the payoffs can be represented as follows: Call 1-01, 1-02 1,1-02 Call Dont Call Dont Call 1-01, 1 0,0 where 01 and 82 represent the costs for player 1 and 2 respectively. Assume the faculty members choose their actions simultaneously and the faculty have private information about their costs of making the call. That is, faculty mem- ber i knows 8i, and believes that Oj is a random draw from a uniform distribution on [c,c]. Faculty member is belief about Oj is commonly known. (a) Find the normal form representation of this game of incomplete information. (b) Now imagine that 01 and 82 are independent random draws from a uniform distribution on [0,2]. Find a symmetric BNE in cutoff strategies.1 (c) The equilibrium outcome found in (b) is inefficient in several ways. (i) Explain why there is under-investment. (ii) Explain why there is "misscoordination between faculties.

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a The normal form representation of the game of incomplete information is given below Player 1 Ca... View the full answer