Reconciling marginalism and the core in two-sided markets with money

R. vand den Brink, M. Núñez Oliva, F. Robles, L. Robles

The Banzhaf value is not efficient on the domain of two-sided markets with
money. We prove that exactness is a necessary and sufficient condition for the
Banzhaf value to belong to the core of assignment games. This condition is suffi-
cient for the Shapley value to belong to the core of such games, but not necessary.
In addition, we provide a sufficient condition for the Shapley and Banzhaf values
to coincide with the fair-division point.
Moreover, we introduce intra-sector solution concepts: the intra-sector Shap-
ley value and intra-sector Banzhaf value, which capture intra-sector competition
within these markets. We demonstrate that these intra-sector values align with
the core if and only if each agent in the market can be matched with one of his/her preferred counterparts.

Keywords: assignment game, Shapley value, Banzhaf value, core

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