On the number of employed in the matching model

This study analyzes the number of matches in stable and efficient matchings. The benchmark number of matches is the largest one among the matchings in which no agent can be better off by itself. We show that, in the one-to-one matching model, the number of matches in any stable matching is more than or equal to the smallest integer that is not less than half of the benchmark number. This result is satisfied even if “stable matching” is replaced by “efficient matching”. We extend the model to the many-to-one matching one and provide the sets of preference profiles in which each of the above results continues to hold.