The priority value for cooperative games with a priority structure

We study cooperative games with a priority structure modeled by a poset on the agent set. We introduce the Priority value, which splits the Harsanyi dividend of each coalition among the set of its priority agents, i.e. the members of the coalition over which no other coalition member has priority. This allocation shares many desirable properties with the classical Shapley value: it is efficient, additive and satisfies the null agent axiom, which assigns a null payoff to any agent with null contributions to coalitions. We provide two axiomatic characterizations of the Priority value which invoke both classical axioms and new axioms describing various effects that the priority structure can impose on the payoff allocation. Applications to queueing and bankruptcy problems are discussed.