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At the state of the world ω, Player I believes that the state of the world is consistent, while Player II believes the state of the world is inconsistent.
Is it possible that ω is a consistent state of the world? Justify your answer.
Critical Thinking: Suppose you and a friend each take different random samples of data pairs (x,y) from the sample population. Assume the samples are the same size.
For which values of the discount factor δ can the players support the pair of actions (T,L) played in every period? Why is your answer different from that for (a)?
Is it a strictly dominant strategy to bid your true valuation in this auction? Is it a weakly dominant strategy to bid your true valuation in this auction?
For what values of p is a 5-component system more likely to operate effectively than a 3-component system?
If this game had only one period, what would be the effort level e and the price p in the unique perfect Bayesian equilibrium?
What are the rationalizable strategies for the players? - Is there a symmetric Nash equilibrium, in which all of the players play the same strategy?
If it is true, explain why. If it is false, provide a game that illustrates that it is false. "If a Nash equilibrium is not strict, then it is not efficient."
Characterize the set of all Nash equilibria of this game.- Which Nash equilibria are perfect?- Find a proper equilibrium of the game.
Firm A and Firm B are the only competitors in market. Each has to decide what price to set for its product. Once prices are set, they cannot be changed for year. Both companies set prices at the same time.
What is the probability that Marie will be ranked number one after this year? What is the probability that Marie will win all 4 games this year against Jan?
Provide an example of a belief space ? with three players, which contains a state of the world ω, such that the minimal belief subspaces of the players at ω are inconsistent, and differ from each other.
In the following game, Describe the set of actions that survive the iterated elimination of strictly dominated actions. Describe the set of actions that survive the iterated elimination of weakly dominated actions
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