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Compute the prenucleolus of the three-player coalitional game with the following coalitional function:
v(1) = v(2) = v(3) = v(2, 3) = 0, v(1, 2) = v(1, 3) = v(1, 2, 3) = -1.
Find the subgame perfect Nash equilibria of this new model and compare it/them with the subgame perfect equilibrium of the original model.
Could you, please, help me in developing a study that is business oriented, maybe trying to investigate at what point business owners start feeling like they dislike what they do and feel discouraged.
For each game that is equivalent to a two-player zero-sum game, write explicitly the positive affine transformation that proves your answer.
Find the Nash equilibrium (equilibria?) of a variant of the example of Cournot's duopoly game that differs from the one in this section. What happens if each firm maximizes its market share?
Now consider the variant in which each player, on her turn, has the additional option of shooting into the air. Find the subgame perfect equilibria of this game when pA pB. Explain the logic behind A's equilibrium action.
ind firm i's best-response function as a function of Q-i . Graph this function - Compute the Nash equilibrium of this game. Report the equilibrium quantities, price, and total output.
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?
Assume that the relationship between the growth of a fish population and the population size can be expressed as g = 2P - 0.1P, where g is the growth in tons and P is the size of the population (in thousands of tons).
What is the number of subgames in a game whose game tree has eight vertices and one information set, which contains two vertices?
What is the efficient configuration of the price and quantity of chicken once proper account is taken of the cost of all of the negative externalities?
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.
Construct the normal form of game assuming consumers move simultaneously and choose between two strategies: "Adopt" or "Don't Adopt." Solve for any (pure strategy) Nash equilibria.
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