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# Practice questions - p is such that the worker accepts This...

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Econ 171 Fall 2008 Practice Questions & Solutions - Part III: Perfect Bayesian Equilibrium Perfect Bayesian equilibrium practice questions with solutions below: 28.2, 28.3, 29.1, 29.3, 29.4 28.2 (a) No. (b) Yes. The strategy profile is ( AA prime ,Y ), with belief q 3 / 5. (c) See the figure below. X Y AA prime 4 , 3 4 , 3 AB prime 5 , 2 2 , 5 BA prime 5 , 3 2 , 1 BB prime 6 , 2 0 , 3 28.3 (a) Yes. It is ( RL prime ,U ), with q = 1. (b) Yes. It is ( LL prime ,D ), with q 1 / 3. 29.1 Education would not be a useful signal in this setting because high types and low types have the same incentive to become educated. Therefore the high types cannot distinguish themselves from the low types by getting an education. 29.3 (a) There is no separating equilibrium because the low type always wants to imitate the high type. (b) Yes, there is such an equilibrium, provide that
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Unformatted text preview: p is such that the worker accepts. This requires 2 p-(1-p ) ≥ 0, which simpliFes to p ≥ 1 / 3. The equilibrium is given by ( O H O L ,A ), with belief q = p . (c) Yes, there is such an equilibrium, regardless of p . It is given by ( N H N L ,R ), with belief q ≤ 1 / 3. 29.4 Clearly, the PBE strategy proFle is a BNE. In fact there is no other BNE, because the presence of the C type in this game (and the rationality of this type) implies that Player 2’s information set is reached with positive probability. This relation does not hold in general, of course, because of the possibility of unreached information sets. 1...
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