18) Mordor is considering invading and conquering Gondor. Gondor has an alliance withRohan, however it is unclear whether or not Rohan will maintain the alliance. Assumethat there is a 30% probability that Rohan is a loyal ally that would help Gondor, and a70% probability that they would abandon Gondor. Neither Gondor nor Mordor knowwhether Rohan is a loyal ally, although of course Rohan knows their own type. Afternature chooses whether Rohan is a loyal ally, Gondor can either surrender or not. IfGondor surrenders, the game ends. If Gondor does not surrender, Mordor can invade ornot. If Mordor does not invade, the game ends. If Mordor does invade, Rohan can eitherride to Gondor's aid or not. If Rohan aids Gondor, the alliance will prevail. If they donot, Mordor will prevail. Gondor gets -80 utility for surrendering, -100 utility from beingconquered, 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 utilityfor not invading and -20 utility trying to conquer and losing. Rohan gets -20 utility ifGondor surrenders or is conquered, and 0 utility if Gondor is not invaded. The loyal allygets 30 utility from winning the war, and the disloyal ally gets -30 utility from choosingto fight. Draw the game. Then solve it to find its SPNE. What will happen?

A sub game perfect nash euilibrium is a concept in game theory where every player has the best plan…

Answered: Draw the game.

Math

Probability

Draw the game.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...

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