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Prove that a three-player 0-normalized game whose core is nonempty, and satisfying v(S) ≥ 0 for every coalition S, is monotonic.
Is this true also for games with more than three players? Justify your answer.
Does it hold true without the condition that v(S) ≥ 0 for every coalition? Justify your answer.
Is this a weighted majority game? If you answer yes, write down the quota and weights of the game. If you answer no, prove that it is not a weighted majority game.
Explain how a person can choose freely, but his or her choices are caused by past events - Draw the causal tree for Newcomb's Problem when Eve cannot perfectly detect Adam's causal history.
Please review the problem and explain each step of the solution listed below, and give me an example of an application which this property would be undesirable in a hash function.
This is your exception category. In response to your classmates' posts, explain what circumstances would have to change to move a case from the rule category to the exception category, or vice versa.
Suppose that a pair of 14-sided dice are rolled (the sides are numbered 1-14 and yes, these do actually exist).
What are the pure-strategy Bayesian Nash equilibria of this game? - Which of the Bayesian Nash equilibria that you found in (a) are perfect Bayesian equilibria?
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
Construct a 95% confidence interval estimate for the population proportion of social media users who would say it is not okay to friend their boss.
Suppose that in some two-player game, s1 is a rationalizable strategy for player 1. If, in addition, you know that s1 is a best response to s2 , can you conclude that s2 is a rationalizable strategy for player 2? Explain.
Determine whether the process of iterated elimination of strictly dominated strategies yields a single strategy vector when it is completed.
In the following two-player zero-sum game, find the optimal behavior strategies of the two players. (Why must such strategies exist?)
Suppose your friend is creating a game about Lewis and Clark's expedition. Provide a list of 10 possible elements she should include in the game in order to make it as informative and exciting as possible
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