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Draw the game.

Draw the game.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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18) Mordor is considering invading and conquering Gondor. Gondor has an alliance with Rohan, however it is unclear whether or not Rohan will maintain the alliance. Assume that there is a 30% probability that Rohan is a loyal ally that would help Gondor, and a 70% probability that they would abandon Gondor. Neither Gondor nor Mordor know whether Rohan is a loyal ally, although of course Rohan knows their own type. After nature chooses whether Rohan is a loyal ally, Gondor can either surrender or not. If Gondor surrenders, the game ends. If Gondor does not surrender, Mordor can invade or not. If Mordor does not invade, the game ends. If Mordor does invade, Rohan can either ride to Gondor's aid or not. If Rohan aids Gondor, the alliance will prevail. If they do not, Mordor will prevail. Gondor gets -80 utility for surrendering, -100 utility from being conquered, and 30 utility for winning the war, and 70 utility if Mordor does not invade. Mordor gets 100 utility if Gondor surrenders, 50 utility for conquering Mordor, 0 utility for not invading and -20 utility trying to conquer and losing. Rohan gets -20 utility if Gondor surrenders or is conquered, and 0 utility if Gondor is not invaded. The loyal ally gets 30 utility from winning the war, and the disloyal ally gets -30 utility from choosing to fight. Draw the game. Then solve it to find its SPNE. What will happen?
Transcribed Image Text:18) Mordor is considering invading and conquering Gondor. Gondor has an alliance with Rohan, however it is unclear whether or not Rohan will maintain the alliance. Assume that there is a 30% probability that Rohan is a loyal ally that would help Gondor, and a 70% probability that they would abandon Gondor. Neither Gondor nor Mordor know whether Rohan is a loyal ally, although of course Rohan knows their own type. After nature chooses whether Rohan is a loyal ally, Gondor can either surrender or not. If Gondor surrenders, the game ends. If Gondor does not surrender, Mordor can invade or not. If Mordor does not invade, the game ends. If Mordor does invade, Rohan can either ride to Gondor's aid or not. If Rohan aids Gondor, the alliance will prevail. If they do not, Mordor will prevail. Gondor gets -80 utility for surrendering, -100 utility from being conquered, and 30 utility for winning the war, and 70 utility if Mordor does not invade. Mordor gets 100 utility if Gondor surrenders, 50 utility for conquering Mordor, 0 utility for not invading and -20 utility trying to conquer and losing. Rohan gets -20 utility if Gondor surrenders or is conquered, and 0 utility if Gondor is not invaded. The loyal ally gets 30 utility from winning the war, and the disloyal ally gets -30 utility from choosing to fight. Draw the game. Then solve it to find its SPNE. What will happen?
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