Reference no: EM131333279
In this exercise, we present an algorithm for computing a solution concept. Given a coalitional game (N; v):
(a) Choose a coalition whose worth is not 0, and divide this worth equally among the members of the coalition (this is called the dividend given to the members of the coalition).
(b) Subtract the worth of this coalition from the worth of every coalition containing it, or equal to it. This defines a new coalitional function (where subtracting a negative number is understood to be equivalent to adding the absolute value of that number).
(c) Repeat this process until there are no more coalitions whose worth is not 0.
For example, consider the game (N; v) defined by the set of players N = {1, 2, 3}, and the coalitional function
v(1) = 6, v(2) = 12, v(3) = 18, v(1, 2) = 30, v(1, 3) = 60, v(2, 3) = 90, v(1, 2, 3) = 120.
The following table summarizes a stage of the algorithm in each row, and includes the coalitional function at the beginning of that stage, the chosen coalition (whose worth is not 0), and the payoff given to each player at that stage. The last line presents the sum total of all payoffs received by each player.
Prove the following claims:
(a) This process always terminates.
(b) The total payoffs received by the players are the Shapley value of the game (and are therefore independent of the order in which the coalitions are chosen).
|
Conduct several searches using any of the databases
: Conduct several searches using any of the databases in the Ashford University Library - Select at least five credible and scholarly, peer-reviewed sources from your library search that support the topics and arguments you plan to present in your F..
|
|
How you would redesign an existing organization to have high
: Explain how you would redesign an existing organization to have higher performance. Explain how you would design a new organization to achieve high performance and learning.
|
|
Calculate the number of grams of calcium carbonate
: Calculate the number of grams of calcium carbonate in the following solutions--you must show all work in detail to receive credit: (a) 25.0 mL of 0.997 M CaCO3, (b) 10.0 mL of 2.50 M CaCO3, (c) 525.0 mL of 0.501 M CaCO3, (d) 1.25 L of 3.42 M CaCO3
|
|
Realities of the underlying science
: Please do a bit of research on how dietary recommendations around fat and cholesterol have changed in the past 30-40 year. Can you explain how such a swing has happened? Is it related to the realities of the underlying science? How?
|
|
Prove the given process always terminates
: Prove the process always terminates.- The total payoffs received by the players are the Shapley value of the game
|
|
Develop a crisis communication plan for an organization
: MSL 5200- Develop a crisis communication plan for an organization of your choice. Include a social media policy. You should combine the sections of the plan that you have already worked on throughout this course.
|
|
Kissing in public may receive disapproving looks
: A same-sex couple holding hands or kissing in public may receive disapproving looks or even abusive comments from other people. This is an example of:
|
|
Leaves the store and decides to go home
: While shopping for clothes, a black woman is followed around the store by a white sales associate. Frustrated, she leaves the store and decides to go home. Her husband, on seeing her enter the house, asks: "What's for dinner?" What concept could w..
|
|
Why a companys strategy needs to pass ethical scrutiny
: Explain why a company's strategy needs to pass ethical scrutiny. Analyze the impact of the Foreign Corrupt Practices Act (FCPA) on the operation of American businesses in competition with international competitors.
|