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Ronald and Jimmy are betting on the result of a coin toss. Ronald ascribes probability 1/3 to the event that the coin shows heads, while Jimmy ascribes probability 3/4 to that event. The betting rules are as follows: Each of the two players writes on a slip of paper "heads" or "tails," with neither player knowing what the other player is writing.
After they are done writing, they show each other what they have written. If both players wrote heads, or both players wrote tails, each of them receives a payoff of 0. If they have made mutually conflicting predictions, they toss the coin. The player who has made the correct prediction regarding the result of the coin toss receives $1 from the player who has made the incorrect prediction. This description is common knowledge among the two players.
(a) Depict this situation as a game with incomplete information.
(b) Are the beliefs of Ronald and Jimmy consistent? Justify your answer.
(c) If you answered the above question positively, find the common prior.
(d) Find a Bayesian equilibrium in this game (whether or not the beliefs of the players are consistent).
Compute the rationalizable strategies when m = 5 and n = 100? Prove that xi ? (0, 100) is a strictly dominated strategy for each of the m players.
Assume you are one of two manufactures of tennis balls. Both you and your competitor have zero marginal costs. Total demand for tennis balls is
Manuel is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. What is the probability that Manuel makes his first free throw on his fifth shot?
Formulate problem as a two-person, zero-sum game and use the concept of dominated strategies to determine the best strategy for each side.
Prove that every 2 × 2 game has a Nash equilibrium. - Do this by considering the following general game and breaking the analysis:
Company charges the same $5.00 price for the irmagazines. Each wants to maximize its salesgiven the$5.00price. Eachweek,therearetwopotentialcoverstories. Oneison politics.
Represent the game in normal form and find its Nash equilibria - Draw the best response function for each player using the coordinate system below. Mark Nash equilibria on the diagram.
Suppose the maximum risk value for a particular client is 0.4. What is the optimal allocation of investment funds among stocks, bonds, mutual funds and cash? What is the annual rate of return and the total risk for the optimal portfolio?
Describe the situation as a game with incomplete information, and find all the Bayesian equilibria in the corresponding game.
Find the core of the variant of the horse trading game in which there is a single owner, whose valuation is less than the highest valuation of the non owners.
A fight with imperfect information about strengths:- Formulate this situation as a Bayesian game and find its Nash equilibria if α ½.
you must work alone to complete this quiz. do not share answers or ideas with other students. write your answers
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