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week7_answ

# week7_answ - Department of Economics University of...

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Page 1 of 5 Department of Economics, University of California, Davis Ecn 122 - Game Theory - Professor Giacomo Bonanno ANSWERS TO PRACTICE PROBLEMS for WEEK 7 1. (1) No, because the information set containing a is { a,b,c } which is not contained in E = { a,b,d,k,n }. (2) No, because the information set containing c is { a,b,c } which is not contained in E = { a,b,d,k,n }. (3) Yes, because the information set containing d is { d } which is contained in E = { a,b,d,k,n }. (4) No, because the information set containing h is { e,f,g,h } which is not contained in E = { a,b,d,k,n }. (5) No, because the information set containing k is { k,m } which is not contained in E = { a,b,d,k,n }. (6) Yes, because the information set containing n is { n } which is contained in E = { a,b,d,k,n }. (7) KE = { d,n }. (8) ¬ KE = { a,b,c,e,f,g,h,k,m }. K ¬ KE = { a,b,c,e,f,g,h,k,m }. 2. (1) K Ann E = {a,b,c} , K Bob E = {a,b,f}, K Carol E = {b,c,f,g}, K Carol K Ann E = K Carol {a,b,c} = {b,c}, K Bob K Carol K Ann E = K Bob {b,c} = (this is the symbol for the empty set) , K Ann ¬ K Bob K Carol E = K Ann ¬ K Bob {b,c,f,g} = K Ann ¬ {f} = K Ann {a,b,c,d,e,g,h} = {a,b,c,d,h}. (2) The common knowledge partition is: a b c d e f g h (3) CKE = (4) If F = { a,b,c,d,e,g } then CKF = { a,b,c,d }. 3. We can describe a state by the number of socks you have taken out and the color of each sock. After you have taken out only one sock: 1 B 1 W (the information set capture the fact that you cannot see the color of the sock because it is dark) After you have taken out two socks: 2 B B 2 B W 2 W B 2 W W After you have taken out three socks: 3 B B B 3 B B W 3 B W B 3 B W W 3 W B B 3 W B W 3 W W B 3 W W W Now in every state there are (at least) two socks of the same color, thus you know that you have

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week7_answ - Department of Economics University of...

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