EconS491_Recitation5_Spring2011

Giventhischoicetheinquisitorchooses do not torture

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Unformatted text preview: 2, 4, 2 2, 4, 2 6 The Nash equilibria are: • (DNR, DNC/DNC, torture), (R, C/C, torture), (R, C/DNC, torture), and • (DNR, DNC/C, do not torture), (DNR, DNC/DNC, do not torture). b. Find all of the subgame perfect Nash equilibria. In his last decision node (which is associated with the path refer do not confess torture), Galileo chooses do not confess. Given this choice, the Inquisitor chooses do not torture. At his first decision node (associated with Urban VIII having chosen refer), Galileo chooses do not confess. Finally, using the result just shown, Urban VIII chooses do not refer, as it produces payoff 3, which is greater than payoff 2 from playing refer. Hence, the unique subgame perfect Nash equilibrium is (DNR, DNC/DNC, do not torture). c. For each Nash equilibrium that is not a subgame perfect Nash equilibrium, explain why it is not a subgame perfect Nash equilibrium. There are four Nash equilibria that are not subgame perfect Nash equilibria. In Nash equilibria (DNR, DNC/DNC, torture) and (R, C/DNC, torture), the Inquisitor is making a nonoptimal decision by choosing to torture Galileo given Galileo plays do not confess in his last decision node. In Nash equilibria (R, C/C, torture) and (DNR, DNC/C, do not torture), Galileo is making a nonoptimal decision at his last decision node. He should play do n...
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