Denote by wmx the set of minimal winning coalitions

Assignment Help Game Theory

Reference no: EM131333378

Let (N; v) be a simple strong game, and let x ∈ X(N; v) be an imputation. Recall that q(x) := minS∈Wm x(S). Answer the following questions:

(a) Show by example that the game [q(x); x] is not necessarily a simple strong game. Which property in the definition of a simple strong game may not hold?

(b) Denote by Wmx the set of minimal winning coalitions in the game [q(x); x].Prove that Wm ⊆ W^m_x.

Reference no: EM131333378

Questions Cloud

Calculate the cpk for machine : C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 3 ± 0.003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of..

Find rabbi nathan solution of given bankruptcy problems : Find the Rabbi Nathan solution of the following bankruptcy problems:- There are four wives, who are owed 100, 200, 300, and 400, respectively, outof an estate of 350.

Chemical components and the proportions : Identify the chemical components and the proportions necessary to achieve a buffer with the desired pH. Include relevant calculations in your answer.

Observations about the products : Assuming the same amounts of potassium and water were used in each experiment, do you expect their observations about the products formed and reaction rate to be the same? Explain your answer.

Denote by wmx the set of minimal winning coalitions : Show by example that the game [q(x); x] is not necessarily a simple strong game. Which property in the definition of a simple strong game may not hold?

Result of excess sulphur dioxide : Explain why acidic rain produced as a result of excess sulphur dioxide in the atmosphere can cause degradation of buidings?

How can the risk of adverse tax consequences be minimized : What issues arise if the partnership distributes $150,000 of cash to Jonathan three months after the property contribution? How can the risk of adverse tax consequences be minimized?

Calculate the equilibrium molar concentration : Consider 1.20 mol of carbon monoxide and 4.00 mol of chlorine sealed in a 5.00 L container at 476oC. The equilibrium constant, Kc, is 2.50 (in M-1) for

Find a weighted majority game that is not constant sum : Find a weighted majority game that is not constant sum, satisfying the property that if S is a losing coalition, then Scis a winning coalition.

User Account

All Pages