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Suppose that (N; v) is a coalitional game such that the set of imputations X(N; v) is nonempty, and such that the nucleolus x∗ differs from the prenucleolus x^.
Prove that the nucleolus is located on the boundary of the set X(N; v).
Depict this situation as a game with incomplete information.- Are the beliefs of Ronald and Jimmy consistent? -If you answered the above question positively, find the common prior.
Job Changes: A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the fol..
Find a mixed strategy of Player I that guarantees him the same payoff against any pure strategy of Player II.- Find a mixed strategy of Player II that guarantees him the same payoff against any pure strategy of Player I.
Find the unique Nash equilibrium of the first-stage game and the two pure-strategy Nash equilibria of the second-stage game.
Show that for each type vi of each player i in a second-price sealed-bid auction with imperfect information about valuations the bid vi weakly dominates all other bids.
Is there any NE in whicheveryone votes? Is there any NE in which there is a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote?
What is the dierence between separating and pooling equilibria in this model? Find the separating equilibrium with the lowest possible education level for the high type and What is the largest level of education that can be chosen by workers with..
Draw the game tree and the matrix of this game, and find all the Nash equilibria. - Find all the subgame-perfect equilibria of this game.
Find all subgame perfect equilibria of this game. Now suppose player 2 has found a way of cheating, getting to observe player 1's hand. Represent the extensive form of this game and find its subgame perfect equilibria.
Specify this situation as a strategic game. - Use the symmetry of the game to show that the unique equilibrium payoff of each player is 0.
First consider the case of Cournot competition, in which each form chooses qi and this game is infinitely repeated with a discount factor δ.
Suppose that there is a payoff-irrelevant event that has a probability e of occurring before this game is played and that, if it occurred, would be observed by players 1 and 3 but not by player 2.
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