New axiomatizations of the Priority value for cooperative games with priority structure

The principle of gain-loss imposes that whenever the total worth generated does not change, a player can only gain at the expense of another one. In this paper we provide two new axiomatizations of the Priority value using the axiom of gain-loss and the other standard properties serving as axiomatizations of the Shapley value. Also, we introduce the axiom of equal treatment of priority players among necessary players and we show that this axiom, jointly with the standard properties of additivity, null player and priority player out, characterizes the Priority value without relying on efficiency. In addition, we obtain a charaterization of the Priority value inspired by a more general result for the weighted Priority values in Béal et al. (2023) [2].