Question: Show that a TP-coalitional game (N; w) is convex if and only if w(T {i}) - w (T) w (S {i}) - w(S)

Show that a TP-coalitional game (N; w) is convex if and only if
w(T ∪{i}) - w (T) ≥ w (S ∪ {i}) - w(S)
for every i ∊ N and for every S ⊂ T ⊂ N / {i}
The marginal contribution of every player increases with the size of the coalition to which the player is joined.

Step by Step Solution

★★★★★

3.40 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Rewriting 218 this implies for every 234 Let and let Substituting in 234 Since Subst... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (394).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

A TP-coalitional game (N, w) is called 0-1 normalized if w({i}) = 0 for every i N and w(N) = 1 Show that 1. To every essential game (N, w) there is a corresponding 0-1 normalized game (N, w0) 2. Core...

The core of a TP-coalitional game is convex.

The set of imputations of an essential TP-coalitional game (N, w)is an(n - 1)-dimensional simplex in

For any TP-coalitional game (N; w) the potential function is defined to be where t =| T | and Î±T are the coefficients in the basic expansion of w (exercise 1.75). Show that P(N, w) = E...

Let (N, w) be a 0-1 normalized TP-coalitional game, and let G be the corresponding two-person zero-sum game described in the previous exercise with value Î´. Show that Î´...

could tou read these papers and do half paper abstract... I UN LUMIYU TIL JUULI ULI How professional ethics impact construction quality: Perception and evidence in a fast developing economy Hamzah...

EE 127 / EE 227AT Homework Assignment #4 A Due date: 3/15/16 11AM. Please L TEX or scan your homework solution and submit the pdf on bCourses. Exercise 1 (A Boolean problem of maximal margin) We have...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

Let (N, w) be a 0-1 normalized TP-coalitional game, and let A be the set of all nontrivial coalitions A = {S N : w(S) > 0}. Consider the following two-player zero-sum game. Player 1 chooses a player...

Let (N, w) be a TP-coalitional game with a compact set of outcomes X. For every outcome x X, let d (x) be a list of coalitional deficits arranged in decreasing order (example 1.49). Let di (x)...

What are the underlying ethical issues in this situation?

Birch Park Senior Center has a weekly payroltl of 55,000. December 31 falls on Wednesday, and Birch Park Senior Center will pay its employees the folowing Monday (January 5) for the previous u wesk....

3. An element X, with electronic configuration 2,8,1, reacts with element Y, with electronic configuration 2,8,6, to form an ionic compound. The likely formula of the compound is (a) XY (b) XY (c) XY...

State and discuss the rules of the dual simplex algorithm. In particular, explain the meaning (and the algebraic representation) of a dual basic feasible solution.

Show that the following function satisfies the properties of a joint probability mass function: f(x, y) 1/4 1/8 1/8 1 1/4 1/4 1 2.

Continuation of Exercise 5-96. Determine the following probabilities: (a) P(X 0.5, Y

Continuation of Exercise 5-96. Determine the following: (a) Marginal probability distribution of the random variable X (b) Conditional probability distribution of Y given that X = 1 (c) E(Y|X = 1)...

One year ago, your company purchased a machine used in manufacturing for $95,000. You have learned that a new machine is available that offers many advantages and that you can purchase it for...

(1) The equation of the regression line is Y = a + bX. Match the following symbols to the description to the right. (1) Denotes the variable plotted on the horizontal axis and called the explanatory...

The following data represents the percentages of family income allocated to groceries for a random sample of 12 shoppers: 26 28 30 37 33 30 29 39 49 31 40 For these data, Calculate: 6.1 the mean (4)...