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Econ398_HW1Solutions - Econ 398 Homework 1 Sketch of...

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Econ 398 Homework 1 Sketch of Solutions 1. For Olaf and Phil, it is handy to number the nodes like this: Then Olaf’s strategies specify what he does at node 1 and what he does at node 5. His strategy set is {(U,T), (M,T), (D,T), (U,B), (M,B), (D,B)}. Phil’s strategies specify what he does at nodes 2, 3, then 4. His strategy set is {(L,L,L), (L,L,R), (L,R,L), (R,L,L), (L,R,R), (R,L,R), (R,R,L), (R,R,R)}. The rollback equilibria are ((U,B), (L,L,R)), ((U,B), (R,L,R)), ((M,B), (R,L,R)), and ((D,B), (R,L,R)). 2. Michigan’s strategies list Michigan’s initial play, whether Michigan switches following Ohio’s blitz to the run offense, then whether Michigan switches following Ohio’s blitz to the pass offense, in that order. Ohio’s strategies list what Ohio does after Michigan’s run offense, and then what Ohio does following Michigan’s pass offense, in that order. Michigan’s strategies: (Run offense, Stay with Run, Switch to Run), (Run offense, Stay with Run, Stay with Pass), (Run offense, Switch to Pass, Switch to Run), (Run offense, Switch to Pass, Stay with Pass),
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