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Boris believes that "it is common belief among me and Alex that Bruce Jenner won a gold medal at the Montreal Olympics," while Alex believes that "it is common belief among me and Boris that Bruce Jenner won a silver medal at the Montreal Olympics."
(a) Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
(b) Prove that, in any belief space in which the set of states of the world is a finite set and contains a state ω describing the situation in this exercise, ω is not contained in the support of the beliefs of either Boris or Alex, at any state of the world. In other words, ω ∉ supp(πi(ω" )) for any state of the world ω" , for i ∈ {Boris, Alex}.
Draw the table for this game. What are the Nash equilibria in pure strategies? Can one of the equilibria be a focal point? Which one? Why?
Draw the extensive-form version of this game and find all pure-strategy sub-game perfect Bayes Nash equilibrium.
Establish whether there exists a two-player game in extensive form with perfect information, and possible outcomes.
Which of these applications are well-suited for the minimalist Internet multicast service model? Why
In the years 2000 and 2001, the bubble burst for many Internet and computer firms. - Describe the equilibrium strategies and briefly explain why this is an equilibrium.
Find a real-world example where the uncertain quantity you are interested in can be modeled as a random variable with exponential distribution. Explain why the memoryless property indeed holds.
Each player in any given match can condition her action on whether she was the first to suggest getting together. - Assume that for any given player the probability of being the first is one half. Find the ESSs of this game.
Show that under the median voter rule, it is a Nash equilibrium for each committee member i to vote truthfully, so that yi = xi .
Draw this game's extensive-form tree for k = 5. - Use backward induction to find the subgame perfect equilibrium.- Describe the backward induction outcome of this game for any finite integer k.
Analyze the renewable resource problem for N players. Is it true that all of the resource is extracted in the first period if N approaches infinity?
Suppose that player 1 selects the strategy p = 50 and player 2 selects the cutoff-rule strategy with p - = 50. Verify that these strategies form a Nash equilibrium of the game. Do this by describing the payoffs players would get from deviating.
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.
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