Core stability in chain-component additive games

Chain-component additive games are graph-restricted superadditive games, where an exogenously given chain determines the cooperative possibilities of the players. These games can model various multi-agent decision situations, such as strictly hierarchical organisations or sequencing/scheduling related problems, where an order of the agents is fixed by some external factor, and with respect to this order only consecutive coalitions can generate added value. In this paper we characterise core stability of chain-component additive games in terms of polynomially many linear inequalities and equalities that arise from the combinatorial structure of the game. Furthermore we show that core stability is equivalent to essentially extendible. We also obtain that largeness of the core as well as extendibility and exactness of the game are equivalent properties which are all sufficient for core stability. Moreover, we also characterise these properties in terms of linear inequalities.