Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Model the foregoing decision problem as a cooperative transferable utility game (N, v) that is the minimum of two inessential games and compute and describe the core of (N, v) and its vertices. 2. Describe and compute the nucleolus and the prenucleolus of (N, v). 3. Describe and compute the Shapley value of (N, v).

1. Model the foregoing decision problem as a cooperative transferable utility game (N, v) that is the minimum of two inessential games and compute and describe the core of (N, v) and its vertices. 2. Describe and compute the nucleolus and the prenucleolus of (N, v). 3. Describe and compute the Shapley value of (N, v).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Please no written by hand and no emage

Make a detailed explanation, of each question (especially 2 and 3) 

Suppose that each wind turbine needs an area of one acre and produces electricity that can be sold for one money unit. Our partial market has six agents 1,...,6. Agent i, i = 1, 2, 3, has i acres of land (i.e., Agent 1 has one, Agent 2 has two, and Agent 3 has three acres) and no turbine. Each of the remaining agents 4, 5, 6 has two wind turbines, but no land. The payoff of a coalition is the number of turbines that the members can run. For instance, if Agent 3 agrees with one turbine owner to produce energy, then two wind turbines can run and the profit of two units is generated, but if the same agent convinces two or three of the turbine owners to produce energy exclusively on her land, then the resulting profit would be three units of money. 1. Model the foregoing decision problem as a cooperative transferable utility game (N, v) that is the minimum of two inessential games and compute and describe the core of (N, v) and its vertices. 2. Describe and compute the nucleolus and the prenucleolus of (N, v). 3. Describe and compute the Shapley value of (N, v). 4. Assume now that each of the landowners has exactly one acre of land and nothing else is changed. Describe the core, the nucleolus, the prenucleolus, and the Shapley value in this case.
Transcribed Image Text:Suppose that each wind turbine needs an area of one acre and produces electricity that can be sold for one money unit. Our partial market has six agents 1,...,6. Agent i, i = 1, 2, 3, has i acres of land (i.e., Agent 1 has one, Agent 2 has two, and Agent 3 has three acres) and no turbine. Each of the remaining agents 4, 5, 6 has two wind turbines, but no land. The payoff of a coalition is the number of turbines that the members can run. For instance, if Agent 3 agrees with one turbine owner to produce energy, then two wind turbines can run and the profit of two units is generated, but if the same agent convinces two or three of the turbine owners to produce energy exclusively on her land, then the resulting profit would be three units of money. 1. Model the foregoing decision problem as a cooperative transferable utility game (N, v) that is the minimum of two inessential games and compute and describe the core of (N, v) and its vertices. 2. Describe and compute the nucleolus and the prenucleolus of (N, v). 3. Describe and compute the Shapley value of (N, v). 4. Assume now that each of the landowners has exactly one acre of land and nothing else is changed. Describe the core, the nucleolus, the prenucleolus, and the Shapley value in this case.
Expert Solution
steps

Step by step

Solved in 5 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS