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A fight with imperfect information about strengths:-
Two people are involved in a dispute. Person 1 does not know whether person 2 is strong or weak; she assigns probability α to person 2's being strong. Person 2 is fully informed. Each person can either fight or yield.
Each person's preferences are represented by the expected value of a Bernoulli payoff function that assigns the payoff of 0 if she yields (regardless of the other person's action) and a payoff of 1 if she fights and her opponent yields; if both people fight then their payoffs are (-1, 1)if person 2 is strong and (1, -1)if person 2 is weak. Formulate this situation as a Bayesian game and find its Nash equilibria if α < ½ and if α > ½.
Finally profiles in which the winner obtains three or more votes more than the loser.) Is there any equilibrium in which no player uses a weakly dominated action?
Do you have enough information to calculate the probability that player 2 selects X in equilibrium? If so, what is this probability?
Find the Nash revision strategies for Ann and Bob which form a SGPNE with the δ identified in part (a) - Verify that the strategies found in part (b) do form a SGPNE
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Planning Parenthood, a national organization that assists teenage mothers with pregnancy, estimates that approximately 37% of the women coming into the center had contracted a sexually transmitted infection. They wish to plan a study to obtain a m..
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It costs each company Brokely $3,000 per period to use filters that avoid polluting the lake. However, each company must use the lake's water in production
A 5-card poker hand is said to be a full house if it consists of 3 cards of the same denomination and two other cards of the same denomination(of course,different from the first denomination). How many hands of full house are possible?
We expect two proportions to be about 0.20 and 0.30, and we want an 80% chance of detecting a difference between them using a two-sided 0.05 level test.
Dynamic Game - Consider a game in which player 1 first selects between I and O. Represent this game in the extensive form. Find the reduced normal form and find the pure-strategy Nash equilibria of this game
Draw the extensive form of this game. - What are the Bayesian Nash equilibria of this game? - What are the perfect Bayesian equilibria?
Solve for the Nash equilibrium of G. What if the game is repeated for two periods. Find the SPNE. Is cooperation (C, C) sustainable for some value of x
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