This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 +...
View
Full
Document
 Spring '08
 SANDHOLM
 Economics, Game Theory

Click to edit the document details