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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.8P

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C D C D 2, 2-3, 3 3, -3 1, 1 For the following parts, suppose this game is played for infinitely many times with discount factor for both players & € [0, 1). 6. Let both players adopt the following strategy: start with cooperation; cooperate if both players cooperated or both players defected in the previous period; defect if one player defected and another player cooperated in the previous period. In other words, the punishment for deviating from cooperation only lasts for one period, and both players revert to cooperation immediately after. What is the condition on d for this strategy profile to be a SPNE? (a) 8 > 0 (b) 8 ≥ 1/4 (c) 8 > 1/3 (d) 8 > 1/2 (e) There is no d underwhich an SPNE can be supported
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