MIT 14 123 - Problem Set #3 (2 pages)

Unformatted text preview:

14 123 Microeconomic Theory III Problem Set 3 The due date for this assignment is Thursday March 11 1 Lecture Notes Chapter 6 4 Exercise 8 2 Alice and Bob seek each other Simultaneously Alice puts e ort sA and Bob puts e ort sB to search The probability of meeting is sA sB the value of the meeting is vA 0 for Alice and vB 0 for Bob and the search costs s3A to Alice and s3B to Bob a Compute the set of all rationalizable strategies b How do the rationalizable search e orts change with vA and vB 3 Consider a game with a nite set N 1 n of players and a nite set S S1 Sn of strategy pro les A general information structure is a list I1 In p1 pn where Ii is the information partition of i and pi is the prior belief of i for every i N For every rationalizable strategy s i Si of every player i show that there exist a general information structure I1 In p1 pn and an adapted strategy pro le s1 sn such that si s i for some and sj arg maxsj Sj Epj uj sj s j Ij for every and j N Hint For every i N and every si Si si is best reply a belief si i on S i Take S 4 Characteruze the set of all correlated equilibrium distributions for the following game L R U 3 1 0 0 D 0 0 1 3 1 MIT OpenCourseWare http ocw mit edu 14 123 Microeconomic Theory III Spring 2010 For information about citing these materials or our Terms of Use visit http ocw mit edu terms