TY - JOUR
T1 - Potentials and weighted values of nonatomic games
AU - Hart, Sergiu
AU - Monderer, Dov
PY - 1997
Y1 - 1997
N2 - The `potential approach' to value theory for finite games was introduced by Hart and Mas-Colell (1989). Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley (1974) value. As a corollary we obtain the uniqueness of the Aumann-Shapley value on certain subspaces of games. Next, the potential approach is applied to the weighted case, leading to `weighted non-atomic values.' It is further shown that the asymptotic weighted value is well-defined, and that it coincides with the weighted value generated by the potential.
AB - The `potential approach' to value theory for finite games was introduced by Hart and Mas-Colell (1989). Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley (1974) value. As a corollary we obtain the uniqueness of the Aumann-Shapley value on certain subspaces of games. Next, the potential approach is applied to the weighted case, leading to `weighted non-atomic values.' It is further shown that the asymptotic weighted value is well-defined, and that it coincides with the weighted value generated by the potential.
UR - http://www.scopus.com/inward/record.url?scp=0031209381&partnerID=8YFLogxK
U2 - 10.1287/moor.22.3.619
DO - 10.1287/moor.22.3.619
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AN - SCOPUS:0031209381
SN - 0364-765X
VL - 22
SP - 619
EP - 630
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
IS - 3
ER -