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Discuss the advantages and disadvantages of being on a team.
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.
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.
Dynamic Game - Consider a game in which player 1 first selects between I and O. Represent this game in the extensive form. Find the reduced normal form and find the pure-strategy Nash equilibria of this game
Depict this situation as a Harsanyi game with incomplete information, and for each pair of parameters p and q, find all the Bayesian equilibria.
Construct a game with payoffs that corresponds to situation - Can you solve the game through iterated dominance?
Figure 10-13 demonstrate the payoff matrix for the only 2-auto dealerships in a community, Jim's Autos and Tim's Autos. The matrix demonstrate the profits that each company would earn from selecting either a low price or a high price.
Prove that the nucleolus is covariant under strategic equivalence: for every coalitional game (N; v), for every set K ⊆ RN , for every a > 0, and every set b ∈ RN ,
Describe this as a strategic-form game, and find all the Nash equilibria of the game. What would be your strategy in this game? Why?
Suppose 70% of kids who visit the doctor have a fever, and 15% of kids with a fever have a sore throat. Whats the probability that a kid who goes to the doctor has a fever and a sore throat?
Recall the trust game depicted in Figure. We argued that for δ ≥ 1/2 the following pair of strategies is a sub game perfect equilibrium.
Show that under the median voter rule, it is a Nash equilibrium for each committee member i to vote truthfully, so that yi = xi .
Specify each game precisely and find its subgame perfect equilibrium outcomes. Study the degree to which the governing coalition is cohesive (i.e. all its members vote in the same way).
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