On identifying efficient, fair and stable allocations in "generalized" sequencing games.

We model sequencing problems as coalitional games and study the Shapley value and the non-emptiness of the core. The ”optimistic” cost of a coalition is its minimum waiting cost when the members are served first in an order. The ”pessimistic” cost of a coalition is its minimum waiting cost when the members are served last. We take the weighted average of the two extremes and define the class of ”weighted optimistic pessimistic (WOP)” cost games. If the weight is zero, we get the optimistic scenario and if it is one, we get the pessimistic scenario. We find a necessary and sufficient condition on the associated weights for the core to be non-empty. We also find a necessary and sufficient condition on these weights for the Shapley value to be an allocation in the core. We impose ”upper bounds” to protect agents against arbitrarily high disuilities from waiting. If an agent’s disutility level is his Shapley payoff from the WOP cost game, we find necessary and sufficient conditions on the upper bounds for the Shapley value to conform to them.