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# HW5-answer - Dr Huanxing Yang Econ 601 Game Theory Homework...

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Dr. Huanxing Yang Econ 601 Game Theory Homework Assignment 5 Due May 21, Wednesday 1. Chapter 9, Problem 5 a) Consider the final subgame associated with the letter having been sent. The strategic form is in Figure SOL9.5.1. Defect is a dominant strategy so there is a unique Nash equilibrium of ( Defect , Defect ). Figure SOL9.5.1 Melekhin Re Borodin 4,4 2,3 Re 3,2 1,1 Defect nege Defect nege Next consider the final subgame associated with the letter not having been sent. The strategic form is in Figure SOL9.5.2. It has two Nash equilibria: ( Defect , Defect ) and ( Renege , Renege ). Figure SOL9.5.2 Melekhin Re Borodin 8,8 6,5 Re 5,6 7,7 Defect nege Defect nege Next turn to the subgame which is the game itself. If the Nash equilibrium is ( Defect , Defect ) at both final subgames then the captain prefers to not send the letter - as it results in a payoff of 8 - while sending the letter means a lower payoff of 7. This gives us one subgame perfect Nash equilibrium of ( Do not send letter, Defect/Defect , Defect/Defect ). Now suppose the Nash equilibrium at the subgame in which the letter is not sent is ( Renege , Renege ). If the letter is sent, the captain again earns a payoff of 7 and if the letter is not sent then his payoff is 4 as both officers renege. We then find that ( Send letter, Defect/Renege , Defect/Renege ) is a second subgame perfect Nash equilibrium. b) The payoffs are such that if the letter is sent then it is a dominant strategy for each of the two officers to defect. However, if the letter is not sent then there are two Nash equilibria for that subgame. One in which both officers defect and one in which both renege. If the letter is not sent - so there is the opportunity to return to the Soviet Union without their plan to defect having been discovered - then an officer wants to renege unless everyone else is planning to defect. By sending the letter, the captain ensures that the officers will continue to defect; while if the

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letter is not sent then induced equilibrium play could mean that they renege and the plan to defect fails.
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HW5-answer - Dr Huanxing Yang Econ 601 Game Theory Homework...

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