Shapley Value Calculation

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I have a problem using Shapley value. I have a 3-person game. Related to the Shapley value definition, all coalitions are possible (2^3 = 8 coalitions). But my game is in the real world and 2 of my players cannot cooperate and make a coalition.
For example let N=A,B,C
My feasible coalitions (except null) are: A,B,C,AB,C,A,BC and ABC.
I'm wondering if someone could help me how should I calculate the Shapley value for above set of coalitions.
Regards










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up vote
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down vote

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I have a problem using Shapley value. I have a 3-person game. Related to the Shapley value definition, all coalitions are possible (2^3 = 8 coalitions). But my game is in the real world and 2 of my players cannot cooperate and make a coalition.
For example let N=A,B,C
My feasible coalitions (except null) are: A,B,C,AB,C,A,BC and ABC.
I'm wondering if someone could help me how should I calculate the Shapley value for above set of coalitions.
Regards










share|cite|improve this question





















  • Welcome to math.SE! Please see this tutorial and reference on how to typeset math on this site.
    – joriki
    Sep 7 at 23:55












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I have a problem using Shapley value. I have a 3-person game. Related to the Shapley value definition, all coalitions are possible (2^3 = 8 coalitions). But my game is in the real world and 2 of my players cannot cooperate and make a coalition.
For example let N=A,B,C
My feasible coalitions (except null) are: A,B,C,AB,C,A,BC and ABC.
I'm wondering if someone could help me how should I calculate the Shapley value for above set of coalitions.
Regards










share|cite|improve this question













I have a problem using Shapley value. I have a 3-person game. Related to the Shapley value definition, all coalitions are possible (2^3 = 8 coalitions). But my game is in the real world and 2 of my players cannot cooperate and make a coalition.
For example let N=A,B,C
My feasible coalitions (except null) are: A,B,C,AB,C,A,BC and ABC.
I'm wondering if someone could help me how should I calculate the Shapley value for above set of coalitions.
Regards







game-theory






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asked Sep 1 at 7:47









Sahand M.s

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  • Welcome to math.SE! Please see this tutorial and reference on how to typeset math on this site.
    – joriki
    Sep 7 at 23:55
















  • Welcome to math.SE! Please see this tutorial and reference on how to typeset math on this site.
    – joriki
    Sep 7 at 23:55















Welcome to math.SE! Please see this tutorial and reference on how to typeset math on this site.
– joriki
Sep 7 at 23:55




Welcome to math.SE! Please see this tutorial and reference on how to typeset math on this site.
– joriki
Sep 7 at 23:55















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