LABOR TIME SHARED IN THE ASSIGNMENT GAME LENDING NEW INSIGHTS TO THE THEORY OF TWO-SIDED MATCHING MARKETS

We consider two two-sided matching markets, where every agent has an amount of units of a divisible good to be distributed among the partnerships he forms and exchanged for money. Both markets have the same sets of feasible allocations but operate under distinct rules. However they are indistinguishable under their representation in the characteristic function form. The adequate and proposed mathematical model provides the foundation to characterize the cooperative equilibrium concept in each market. Setwise-stability is then shown not to be the general definition of stability. The connection between the cooperative structures of these markets and between the cooperative and competitive structures of each market is established, by focusing on the algebraic structure of the core, the set of cooperative equilibrium allocations and the set of competitive equilibrium allocations. The results obtained and the methodology used in their proofs provide new and useful insights to the theory of two-sided matching markets.