Potentials and Weighted Values of Non-Atomic Games
Sergiu Hart and Dov Monderer
Abstract
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.
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Mathematics of Operations Research 22 (1997), 3, 619-630