Labor Time Shared In The Assignment Game Generating New Cooperative And Competitive Structures

Aiming to obtain new characterizations for the concepts of core, cooperative equilibrium and competitive equilibrium, and new correlations among these concepts, we introduce labor time into the assignment game. Two many-to-many matching models are obtained, distinguished by the nature of the agreements - rigid and flexible. An example illustrates that the characteristic function form does not always fully represent the cooperative structure of the two markets. Two different notions of demand correspondence generate distinct sets of competitive equilibrium allocations. The connection between the cooperative structures of both markets and the cooperative and competitive structures of each market is established through five cooperative solution sets proved to be non-empty, distinct and correlated by the set inclusion - one set is a superset of the next: the maximal set is the core; the second one characterizes the cooperative equilibria for the rigid market; the third set characterizes the cooperative equilibria for the flexible market; the other two sets characterize the competitive equilibrium allocations for the two competitive markets.