A generalized value for a cooperative game on simplicial complexes with filtration: considering player's bargaining power

In a cooperative game on simplicial complexes with filtration (SF), players can join the grand coalition simultaneously according to a given sequence, but the simplicial value of a cooperative game on SF (SF game) does not consider player's bargaining power in the formation of SF. Considering the influence of player's joining order in the formation of SF, we introduce a relative marginal contribution (RMC) value in this restricted coalition and the generalized simplicial value (the GS value) is proposed as an extension of the simplicial value. Furthermore, because player's joining order is deterministic in SF, which is different from a crisp cooperative game, we examine the effect of players' order on their RMCs and the MCD value is characterized. The MCD value may motivate players to contribute to SF. As extensions of the simplicial value, both the GS value and the MCD value are based on RMC, while the MCD value is friendly to the players who join the cooperation early on.