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Unformatted text preview: Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2008 Midterm Exam Solutions Economics 713 1. (i) The subgame is a coordination game with three Nash equilibria. Combining these with best responses at the initial node, we find three subgame perfect equilibria: (( I , T ) , L ), (( O , B ) , R ), and (( O , 1 2 T + 1 2 B ) , 1 4 L + 3 4 R ). (ii) All of the subgame perfect equilibria are sequential equilibria when combined with appropriatebeliefs. Labelthenodesin2sinformationset x and y . Then(( I , T ) , L )has ( x ) = 1 (since x is reached), (( O , B ) , R ) has ( y ) = 1 (by parsimony), and (( O , 1 2 T + 1 2 B ) , 1 4 L + 3 4 R ) has ( x ) = 1 2 (which is easy to compute directly). (iii) All three subgame perfect equilibria correspond to proper equilibria of the reduced normal form. For (( I , T ) , L ), an -proper equilibrium is ( O + (1- - 2 ) T + 2 B , (1- ) L + R ), for (( O , B ) , R ), an -proper equilibrium is ((1- - 2 ) O + 2 T + B , (1- ) L + R ), and for (( O , 1 2 T + 1 2 B ) , 1 4 L + 3 4 R ), an -proper equilibrium is ((1- 2 ) O +...
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