On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems in which an existing network has to be extended to connect users to a source. This paper generalizes the definition of irreducible core to minimum cost spanning extension problems and introduces an algorithm generating all elements of the irreducible core. Moreover, the equal remaining obligations rule, a one-point refinement of the irreducible core ispresented. Finally, the paper characterizes these solutions axiomatically. The classical Bird tree allocation of minimum cost spanning tree problems is obtained as a particular case in our algorithm for the irreducible core.Networks;Cost Allocation;costs and cost price

Minimum cost spanning extension problems: The proportional rule and the decentralized rule

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems (see Bird 1976) where an existing network has to be extended to connect users to a source. In this paper, we present two cost allocation rules for these problems, viz. the proportional rule and the decentralized rule. We introduce algorithms that generate these rules and prove that both rules are refinements of the irreducible core, as defined in Feltkamp, Tijs and Muto (1994b). We then proceed to axiomatically characterize the proportional rule.Networks;Cost Allocation;costs and cost price

Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes

In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme.As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0-1 cost functions.It turns out that the Subtraction Algorithm is closely related to the famous algorithm of Kruskal for the determination of minimum cost spanning trees.For variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist.operational research;cost allocation;game theory

Bird's tree allocations revisited

Game Theory;Cost Allocation

Hypercubes and compromise values for cooperative fuzzy games

90D12;03E72cooperative games

Monotonic Allocation Schemes in Clan Games

Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition reflecting the decreasing marginal contribution of non-clan members to growing coalitions.This decreasing marginal contribution is incorporated in the notion of a bi-monotonic allocation scheme, where the value of each coalition is divided over its members in such a way that the clan members receive a higher, and the non-clan members a lower share as the coalitions grow larger.Each core element of a total clan game can be extended to both a population monotonic and a bi-monotonic allocation scheme.In total clan games where the clan consists of a single member (the so-called big boss) the use of the nucleolus as an allocation mechanism gives rise to a bi-monotonic allocation scheme.cooperative games;population monotonic allocation scheme;bi-monotonic allocation scheme;clan games;big boss games

Egalitarianism in convex fuzzy games

cooperative games;algorithm

Convex fuzzy games and participation monotonic allocation schemes

90D12;03E72cooperative games

On Cores and Stable Sets for Fuzzy Games

AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy games