When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads....

The Competitive Equilibrium with Equal Incomes is an especially appealing efficient and envy-free division of private goods when utilities are additive: it maximizes the Nash product of utilities and is single-valued and continuous in the marginal rates of substitution. The CEEI to divide bads...

For the class of cooperative games with transferable utilities an excess function e is defined as a function of two variables increasing in the first variable and decreasing in the first one such that given a TU game (N,v) , a coalition S, and a payoff vector x, the value e(v(S), x(S)) is a...

A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. Each solution from the collection is parametrized by a positive integer k 1 and is called the k-prekernel for properties extending those verifying by the prekernel such that the 2-prekernel...

For cooperative games with transferable utilities (TU games) excess functions e : R2 ! R1 whose values e(x(S); v(S)); S N are relative negative utilities of coalitions S with respect to their payos x(S) = Pi2S xi are dened. The excess values for the class of two-person games are dened as those...

The egalitarian solution for the class of convex TU games was defined by Dutta and Ray [1989] and axiomatized by Dutta 1990. An extension of this solution — the egalitarian split-off set (ESOS) — to the class of non-levelled NTU games is proposed. On the class of TU games it coincides with...

A game with restricted cooperation is a triple (N,v,Ω), where N is a finite set of players, Ω⊂2N is a nonempty collection of feasible coalitions such that N∈Ω, and v:Ω→R is a characteristic function. The definition implies that if Ω=2N, then the game (N,v,Ω)=(N,v) is the classical...

One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by...