A monotone solution to the problem of bargaining with transfers

Abstract: We propose a solution to the problem of bargaining with transfers, along with an axiomatisation of the solution. Each player receives a weighted average of her contributions to each coalition's claim, where a coalition's claim is determined by its best allocation in the bargaining set. The key axioms are additivity and a property we call marginal monotonicity, which states that increasing a player's payoff in an allocation of the bargaining set, either outright or by means of transfers from other players, must benefit that player.