Fair Payoffs Distribution in Linear Production Game by Shapley Value

Shapley value is regarded as a fair payoff distribution concept for cooperative agents. While traditional cooperative game assume superadditivity and non-externalty, real world environments do not hold this assumption. We show that in linear production game, the environment is non-superadditive is with externalties. In such environment, grand coalition does not provide optimal solution to the system. Consequently, applying traditional shapley value does not provide an attractive payoff to agents. In addition, fairness may also be lost because individual payoffs are less than singleton coalition values. We show how this environments may occur and how we can propose a more attractive and, still, fair payoffs to agents.