Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market

In the multiple-partners job market, introduced in ( Sotomayor, 1992 ), each firm can hire several workers and worker be hired by firms, up to a given quota. We show that, contrast what happens simple assignment game, this extension, firms-optimal stable rules are neither valuation monotonic nor pairwise monotonic. However, we that satisfy weaker property, call firm-covariance , property characterizes these among all rules. This allows us shed some light on how firms (and cannot) manipulate particular, cannot them constantly over-reporting their valuations. Analogous results hold when focusing workers. Finally, extend market known characterization of fair-division domain games.