# 14-086/II (2014-07-08)

Author(s)
Emiliya Lazarova, University of East Anglia, United Kingdom; Peter Borm, Tilburg University, the Netherlands; Arantza Estévez-Fernández, VU University Amsterdam, the Netherlands
Keywords:
matching, Pareto optimal matching, contractually exchange stability, compensation stability, compensation schedule
JEL codes:
C78, C71, D60

In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractually exchange stability and matchings of maximum total reward by means of compensation exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in the sense that there will be no subset of agents who can all by deviation obtain a higher reward. The proof of this
result uses the fact that the core of an associated compensation matching game with constraints is nonempty.