# Microsoft Word - Document2 1. Question 3. Your job is to analyze the signaling game shown in the next page. Specifically, you find one separating equilibrium, one pooling equilibrium, and one...

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Microsoft Word - Document2 1. Question 3. Your job is to analyze the signaling game shown in the next page. Specifically, you find one separating equilibrium, one pooling equilibrium, and one semi-separating equilibrium, by controlling parameters ?and ?. The values of other parameters (?,?,??,??)are to be individually given by the instructor. (So, each student has different parameters.) 1) Find values of ?and ?such that you find a separating equilibrium. Construct the separating equilibrium, and write down the equilibrium (including both strategies and beliefs). [Hint: Fix ?and try several different values of negative ?. Try two extremes: ?is negative but very close to zero, and ?is an extremely huge negative value. Don’t discard the unsuccessful attempts: you can recycle it for the questions on pooling and semi-separating equilibria.] 2) Find values of ?and ?such that you find a pooling equilibrium. Construct the pooling equilibrium, and write down the equilibrium (including both strategies and beliefs). [Hint: If you did not find an “unsuccessful” case in 1), now is the time to fail. Find a value of ? that does not work for a separating equilibrium. Then move the value of ?, with fixed ?. Try extremes (but too extreme values like ?=99.9999will make your calculations difficult, so I recommend to use reasonably large/small values). You will find a pooling or semi-separating equilibrium.] 3) Find values of ?and ?such that you find a semi-separating equilibrium. Construct the semi- separating equilibrium, and write down the equilibrium (including both strategies and beliefs). [Hint: See the hint for 2). Once again, if your ?is too extreme, the calculation will be harder. Just try reasonable values.] ?should be a negative value. P should be a value between 0 and 100. Both variables can be integers, for any of the above questions.
Jan 07, 2022
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