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For each of the following partitions of a two-dimensional simplex, determine whether or not it is a simplicial partition. Justify your answer.
In each case, the partition elements are the two-dimensional polytopes in it, their faces, and their vertices.
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.
Manuel is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. What is the probability that Manuel makes his first free throw on his fifth shot?
Compute the subgame perfect equilibrium of this market game.- Do so by first finding the equilibrium quantities and profits in the Cournot subgames.
Explain how payoff matrices used in Game Theory illustrate mutual interdependence among firms in oligopolies. How can they be used to predict likely outcomes?
A firm incurs production costs C(q) = F + mq, and transportation costs T(q) = aq + ????2, where q is the output of each of its plants. What is the optimal plant size, and how does it vary with the parameters F, m, a and b?
Discuss the interpretation of the core of this game, taking into account that the definition of v(S) makes assumptions about the behavior of the players outside S.
What is the equilibrium outcome to the Stackelberg game if the absolute value of the slope of firm 2's best-response function exceeds 1? Why?
For N = {1, 2, 3}, compute the bargaining set of the coalitional game (N; v) relative to the coalitional structure {{1, 2},{3}}, for each of the given coalitional functions:
Compute the pure-strategy and mixed-strategy Nash equilibria for this game, and note how they depend on x. In particular, what is the difference between x > 1 and x.
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.
Find the Nash equilibrium in mixed strategies of the following static game of complete information. For the following base game determine whether or not (2, 1) is an equilibrium payoff of the corresponding infinitely repeated game
Using two states of the world describe the following situation, specifying how each state differs from the other: "Roger ascribes probability 0.4 to the Philadelphia Phillies winning the World Series."
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