This paper introduces a model of coalition formation with claims.
It assumes that agents have claims over the outputs they could produce
by forming coalitions. Outputs, insufficient to meet the claims and
are rationed by a rule whose proposals of division induce each agent
to rank the coalitions in which she can participate. As a result, a
hedonic game of coalition formation emerges. Using resource
monotonicity and consistency, we characterize the continuous rationing rules
that induce hedonic games that admit core-stability.