Please solve in 30 minute 4. King Leonidas and King Xerxes assemble their armies for a battle against each other. The kingwho brings more warriors wins the battle and gets control over Sparta. Both kings value thethrone of Sparta the same amount.King Leonidas can equip x warriors per 1000 gold coins spent and King Xerxes can equipy warriors per 1000 gold coins spent. Let E and y be drawn independently from a uniformdistribution with the support (0, z], z > 0.(a) Suppose that both z and y are observable. Show that there is no equilibrium in purestrategies in this game.(b) Suppose that Leonidas privately learns z and Xerxes privately learns y. How many warriorsfight in the battle between Leonidas and Xerxes?(c) Keep the assumptions made in 4b. Suppose that the god of war Ares loves large battles.Mighty Ares threatens to keep Sparta for himself if both kings bring less than a warriorseach. Find a that maximizes the size of the winning army on average.

Above game has following specifications - Two player - King Leonid & Xerxes Strategy set of…

4. King Leonidas and King Xerxes assemble their armies for a battle against each other. The king who brings more warriors wins the battle and gets control over Sparta. Both kings value the throne of Sparta the same amount. King Leonidas can equip r warriors per 1000 gold coins spent and King Xerxes can equip y warriors per 1000 gold coins spent. Let x and y be drawn independently from a uniform distribution with the support [0, z], z > 0. (a) Suppose that both r and y are observable. Show that there is no equilibrium in pure strategies in this game. (b) Suppose that Leonidas privately learns r and Xerxes privately learns y. How many warriors Gebt in the httle

4. King Leonidas and King Xerxes assemble their armies for a battle against each other. The king who brings more warriors wins the battle and gets control over Sparta. Both kings value the throne of Sparta the same amount. King Leonidas can equip r warriors per 1000 gold coins spent and King Xerxes can equip y warriors per 1000 gold coins spent. Let x and y be drawn independently from a uniform distribution with the support [0, z], z > 0. (a) Suppose that both r and y are observable. Show that there is no equilibrium in pure strategies in this game. (b) Suppose that Leonidas privately learns r and Xerxes privately learns y. How many warriors Gebt in the httle

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please solve in 30 minute

4. King Leonidas and King Xerxes assemble their armies for a battle against each other. The king
who brings more warriors wins the battle and gets control over Sparta. Both kings value the
throne of Sparta the same amount.
King Leonidas can equip x warriors per 1000 gold coins spent and King Xerxes can equip
y warriors per 1000 gold coins spent. Let E and y be drawn independently from a uniform
distribution with the support (0, z], z > 0.
(a) Suppose that both z and y are observable. Show that there is no equilibrium in pure
strategies in this game.
(b) Suppose that Leonidas privately learns z and Xerxes privately learns y. How many warriors
fight in the battle between Leonidas and Xerxes?
(c) Keep the assumptions made in 4b. Suppose that the god of war Ares loves large battles.
Mighty Ares threatens to keep Sparta for himself if both kings bring less than a warriors
each. Find a that maximizes the size of the winning army on average.

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