Department of Economics. University of Melbourne. Parkville Victoria 3052 Australia
ABSTRACT
The paper considers an extension of the original Shapley and Shubik
(1972) two-sided matching problem to the case of multisided matching with
transfereable utility. We investigate existence and properties of stable
matchings using the approach of cooperative game theory. In general, cores
of multisided matching games are empty. However, stable matchings are shown
to exist when characteristic functions are supermodular as in Topkis (1978).
We analyze the structure of the core of supermodular matching games and
suggest an algorithm for constructing its extreme payoff vectors. Although
supermodular matching games are not convex as in Shapley (1971/72), we
find some interesting similarities between supermodular matching and convex
games. The results suggest that supermodular games are of special interest
not only in non-cooperative, but also in cooperative game theory.
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