Compute the Shapley value for the games represented by the following MC-Nets:

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Welcome to Ask Sage.

It would make sense to provide references for the vocabulary and notation.

It seems the context is coalitional game theory, and "mc-net" means "marginal contribution net".

Are these the references you have in mind?

• "Shapley value" on Wikipedia
• Samuel Ieong, Yoav Shoham. Marginal contribution nets: a compact representation scheme for coalitional games
• Edith Elkind, Leslie Ann Goldberg, Paul W. Goldberg, Michael Wooldridge. A tractable and expressive class of marginal contribution nets and its applications

For example you could change the title to "Shapley values for games". Then, inside the question, you could give a little introduction such as:

In game theory, games can be represented by "marginal contribution nets", also known as "MC-Nets". Using the notation introduced in the book ... / the article ..., consider the game represented by the MC-Net:

a1 ∧ a2 → 6

Is it possible to compute the Shapley value of this game with SageMath?

In particular, an algorithm is described in ... and I would like to know if it is implemented in Sage.

Please adapt to your case. As it is, my guess is that few users would be able to answer your question.

Note that the reference manual for game theory in Sage, in html and pdf, is at

• https://doc.sagemath.org/html/en/reference/game_theory/
• https://doc.sagemath.org/pdf/en/reference/game_theory/game_theory.pdf

Maybe you could say if there is something there that is close to your question.

Possibly related:

• cs.stackexchange question "Solving problems related to marginal contribution nets"