5,400 research outputs found
Ensuring the boundedness of the core of games with restricted cooperation
The core of a cooperative game on a set of players is one of the most
popular concept of solution. When cooperation is restricted (feasible
coalitions form a subcollection \cF of ), the core may become unbounded,
which makes it usage questionable in practice. Our proposal is to make the core
bounded by turning some of the inequalities defining the core into equalities
(additional efficiency constraints). We address the following mathematical
problem: can we find a minimal set of inequalities in the core such that, if
turned into equalities, the core becomes bounded? The new core obtained is
called the restricted core. We completely solve the question when \cF is a
distributive lattice, introducing also the notion of restricted Weber set. We
show that the case of regular set systems amounts more or less to the case of
distributive lattices. We also study the case of weakly union-closed systems
and give some results for the general case
The restricted core of games on distributive lattices: how to share benefits in a hierarchy
ED EPSInternational audienceFinding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, the core in its usual formulation may be unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes efficiency of the allocation at each level of the hierarchy, is always bounded, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness
The core of games on ordered structures and graphs
In cooperative games, the core is the most popular solution concept, and its
properties are well known. In the classical setting of cooperative games, it is
generally assumed that all coalitions can form, i.e., they are all feasible. In
many situations, this assumption is too strong and one has to deal with some
unfeasible coalitions. Defining a game on a subcollection of the power set of
the set of players has many implications on the mathematical structure of the
core, depending on the precise structure of the subcollection of feasible
coalitions. Many authors have contributed to this topic, and we give a unified
view of these different results
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