A player i is called a null player in a game (N, w) if he contributes nothing

Question:

A player i is called a null player in a game (N, w) if he contributes nothing to any coalition, that is, if
w(S ∪ {i}) = w(S) for every S ⊆ N
Verify that the Shapley value of a null player is zero, that is,
i null ⇒ ϕiw = 0

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:40 AM

See More Questions

Tournament Play The directed graph in Fig. 3.1.7 is called a tournament graph because every node is connected to every other node exactly once. The nodes represent players, and an arc from node i to...
In a strategic game, a strategy of player i is justifiable if it is a best response to some possible (mixed) strategy (example 1.98) of the other players, that is, si is justifiable si Bi (-i)...
A and B play the following game: A writes down either number 1 or number 2, and B must guess which one. If the number that A has written down is i and B has guessed correctly, B receives i units from...
Can someone please help me with sections d, e, and f? Black and Shannon trave decided to fom a partnership. They have agreed that Black is to invest $ \$ 243,000 $ and that 5 hannon is to invest...
The following percentages come from a national survey of the ages of prerecorded-music shoppers. A local survey produced the observed values. Does the evidence in the observed data indicate that we...
The disaccharide Î±, Î²-trehalose differs from the Î±, Î± structure in Figure 9.14(a) by having an (a1Î²1) linkage. Draw its structure as...
A model for a hemodialyser with simulation of the patient-artificial-kidney system: a case-study problem. A useful case study is the paper by Ramachandran and Mashelkar (1980), where a mesoscopic...
Consider the perpendicular rectangles shown schematically. (a) Determine the shape factor F 12 . (b) For rectangle widths of X = 0.5, 1.5, and 5 m, plot F 12 as a function of Z b for 0.05 Z b 0.4m....
Your client want to have $168,313 in 20 years, how much money should he put in a savings account today? Assume that the savings account pays you 5.5 percent and it is compounded annually.
The following data were obtained from a study of the times required to conduct a consumer test panel study: Costs are given in thousands of dollars, time in weeks. (a) Find the all-normal schedule...
A function f : X Y is linear if and only if f (1x1 + 2x2) = 1f(x1) + 2f(x2) for all x1, x2 X, and 1, 2 .
The set of solutions to a nonhomogeneous system of linear equations Ax = c is an affine set. The converse is also true.
(a) What concentration (in moles per liter) of Ag + ions is required for the formation of a precipitate in 1.0 * 10 5 m NaCl(aq)? (b) What mass (in micrograms) of solid AgNO 3 needs to be added for...
Define propriety audit. What are its objectives?
Can dividend be paid under the following circumstances: (a) Out of current profit without making good past losses? (b) Out of a capital profit. (c) Out of past profit when there is neither profit nor...
You have just been appointed as auditor of Hindalco Engineering Company Ltd. to fill up a casual vacancy created by the death of the previous auditor, Mr. V. K. Rattan, a sole practitioner. He has...
State the circumstances when a person will be disqualified for being appointed as company auditor.
How do you verify the following items: (a) Raw material stock (b) Land (c) Preliminary expenses (d) Investment (e) Work-in-progress (f) Copyright (g) Machine purchased on H. P. System (h) Patterns...
The data show the average wind speed for 30 days in a large city. Construct an ungrouped frequency distribution for the data. 8 15 8 10 12 9 9 13 13 8 9 13 9 98 14 8 8 13 10 11 11 9 9 9 8 9 9 8...
Air pollution generated by a steel mill is an example of a) a positive production externality. b) a negative production externality. c) a public good. d) the free-rider problem. State and local taxes...
A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: (a)...
Rework Exercise 8-27 to compute a 95% lower confidence bound on rod diameter. Compare this bound with the lower limit of the two-sided confidence limit from Exercise 8-27. Discuss why they are...
The wall thickness of 25 glass 2-liter bottles was measured by a quality-control engineer. The sample mean was x = 4.05 millimeters, and the sample standard deviation was s = 0.08 millimeter. Find a...
As of June 30, Year 1, the bank statement showed an ending balance of $16,878. The unadjusted Cash account balance was $15,239. The following information is available: 1. Deposit in transit, $2,190....
Superior Company provided the following data for the year ended December 31 (all raw materials are used in production as direct materials): Selling expenses Purchases of raw materials Direct labor...
Marin Company produces two software products (Cloud-X and Cloud-Y) in two separate departments (A and B). These products are highly regarded network maintenance programs. Cloud-X is used for small...

A player i is called a null player in a game (N, w) if he contributes nothing

Question:

Step by Step Answer:

For any null play...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions