The Rights-Egalitarian Solution for NTU Sharing Problems

The purpose of this paper is to extend the Rights Egalitarian solution (Herrero, Maschler & Villar, 1999) to the context of non-transferable utility sharing problems. Such an extension is not unique. Depending on the kind of properties we want to preserve we obtain two different generalizations. One is the "proportional solution", that corresponds to the Kalai-Smorodinsky solution for surplus sharing problems and the solution in Herrero (1998) for rationing problems. The other is the "Nash solution” that corresponds to the standard Nash bargaining solution for surplus sharing problems and the Nash rationing solution (Mariotti & Villar (2005) for the case of rationing problems.Sharing problems, rights egalitarian solution, NTU problems.

Equal loss under separatorization and egalitarian values

We characterize the equal division value, the equal surplus division value, and the class of their affine combinations for TU-games involving equal loss under separatorization. This axiom requires that, if a player becomes a dummifying player (Casajus and Huettner, 2014), then any two other players are equally affected

Linear, efficient and symmetric values for TU-games

In this paper, we study values for TU-games which satisfy three classical properties: Linearity, efficiency and symmetry. We give the general analytical form of these values and their relation with the Shapley value and the Egalitarian value.

The grand surplus value

We propose a value for games with transferable utility, called the grand surplus value. This new value is an alternative to the Shapley value, especially in games where the worth of a coalition depends on goods that are more or less arbitrarily multipliable or applicable, particularly in the intellectual property domain. Central is the concept of the grand surplus, which is the surplus that results when all coalitions, each lacking one player of the player set, no longer act individually, but only cooperate together as the grand coalition. All the axiomatizations presented have an analogous equivalent for the Shapley value, including the classics by Shapley and Young. A further new concept, called multiple dividends, provides a close connection to the Shapley value

Allocation of fixed costs and the weighted Shapley value

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several approximations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.cost allocation, Shapley value, fixed cost