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The Shapley value is a very useful concept to evaluate the importance/contribution of a player based on how he affects different possible coalitions. Now based on this information, is it possible to build a network between players that tells us, for each player $p_i$, which relationships can yield more/less successful outcomes ?

To be clear, let's say that we have a cooperative game with three players : $N=\{p_1,p_2,p_3\}$ and an evaluation function $f$ defined over the power set of players.

  1. I want to know how important each player is with respect to the group (easily done with the Shapley vlue).
  2. I want to be able to draw conclusions that relate each player to the others, something like : Player $p_1$ yields better outcome when cooperating with $p_2$ than with $p_3$, and $p_3$ is better off playing by himself.

Is there any concept that can help evaluate such relashionships or maybe build a whole "social network" between players ?

Thanks !

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  • $\begingroup$ I feel that this should probably be more application-specific. It depends on what you want the edges in this graph to model (in my opinion). I would also guess that aspects of this question have been studied in economics, but I'm not sure where to start looking for references.... $\endgroup$
    – usul
    Commented May 23, 2016 at 14:42

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