TY - JOUR
T1 - Minimal exact balancedness
AU - Lohmann, E.R.M.A.
AU - Borm, P.E.M.
AU - Herings, P.J.J.
N1 - Appeared earlier as CentER DP 2011-012
PY - 2012
Y1 - 2012
N2 - To verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the definition of balanced collections, the weight vector of a balanced collection must be positive whereas the weight vector for an exact balanced collection may contain one negative weight. We investigate minimal exact balanced collections, and show that only these collections are needed to obtain exactness. The relation between minimality of an exact balanced collection and uniqueness of the corresponding weight vector is analyzed. We show how the class of minimal exact balanced collections can be partitioned into three basic types each of which can be systematically generated.
AB - To verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the definition of balanced collections, the weight vector of a balanced collection must be positive whereas the weight vector for an exact balanced collection may contain one negative weight. We investigate minimal exact balanced collections, and show that only these collections are needed to obtain exactness. The relation between minimality of an exact balanced collection and uniqueness of the corresponding weight vector is analyzed. We show how the class of minimal exact balanced collections can be partitioned into three basic types each of which can be systematically generated.
U2 - 10.1016/j.mathsocsci.2012.01.002
DO - 10.1016/j.mathsocsci.2012.01.002
M3 - Article
VL - 64
SP - 127
EP - 135
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
SN - 0165-4896
IS - 2
ER -