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Let (N; v) be the three-player coalitional game with the following coalitional function:
v(S) = 0 ⇐⇒ |S| ≤ 1, (20.208)
v(S) = 1 ⇐⇒ |S| ≥ 2. (20.209)
Let K be the triangle in R3 whose vertices are (1, 0, 0), (0, 1, 0), and (0, 0, 1), and let K0 be its boundary. Compute the nucleolus of the game (N; v) relative to K and relative to K0.
However, when I run "./random2 1 100 20" for example it seg faults after displaying largest number and smallest number without displaying mean and median.
Is this a weighted majority game? If you answer yes, write down the quota and weights of the game. If you answer no, prove that it is not a weighted majority game.
Does every correlated equilibrium lie in the convex hull of the product distributions that correspond to pairs of optimal strategies?
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?
Prove the process always terminates.- The total payoffs received by the players are the Shapley value of the game
A manufacturer of a new, less expensive type of light bulb claims that this product is very well made and even more reliable than the higher priced competitive light bulbs.
The following hypothetical data demonstrate the relationship. The dependent variable is a measure of language skill at age 3 for each child. Do the data indicate any significant differences? Test with α=0.05.
Prove that every game is strategically equivalent to a monotonic game. It follows that the property of monotonicity is not invariant under strategic equivalence.
Radon levels in a house vary from week to week. In one house a sample of 8 weeks had the following readings for radon level ( in pCi/L): 1.9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
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?
Discuss a real-world example of a contractual situation with limited verifiability. - How do the parties deal with this contractual imperfection?
Determine whether this game has a symmetric mixed-strategy Nash equilibrium in which each player selects X with probability p. If you can find such an equilibrium, what is p?
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