Core structure and comparative statics in a hybrid matching market

Flexible firms compete by means of wages in the Assignment market while rigid firms have no flexibility over terms of appointment in the Marriage market. Workers trade with both kinds of firms in the hybrid market.Examples show that standard results that characterize the core of the Marriage market (respectively, Assignment market) are not robust to the entrance of flexible (respectively, rigid) firms to this market. A new algebraic structure provides a different characterization for the core of the hybrid model and reflects a sort of robustness to the exit of rigid (respectively, flexible) firms from this market. Meaningful comparative static results are derived.