On the Grey Obligation Rules

In this paper, we extend obligation rules by using grey calculus. We introduce grey obligation rules for minimum grey cost spanning tree (mgcst) situations. It turns out that the grey obligation rule and the grey Bird rule are equal under suitable conditions. Further, we show that such rules are grey cost monotonic and induce population monotonic grey allocation schemes (pmgas). Moreover, if the game is concave, its (extended) grey Shapley value is a PMGAS. Some examples of pmgas, grey obligation rules and grey Shapley value for mgcst situations are also given.