One-to-many non-cooperative matching games

We study a strategic model of wage negotiations between …rms and workers. First, we de…ne the stability of an allocation in an environment where …rms can employ more than one worker. Secondly, we develop a one-to-many non-cooperative matching game, which is an extension of Kamecke’s one-to-one non-cooperative matching game. The main result shows that the equivalence between the stable allocations and the outcomes of the subgame equilibria in the matching game: for any stable allocation there is a subgame perfect equilibrium in this game which induces the allocation on the equilibrium path, and every subgame perfect equilibrium induces a stable allocation on the equuilibrium path. Furthermore, as for the existence of a stable allocation, we argue that a stable allocation, so a subgame perfect equilibrium, does not always exist, but it exists under some conditions, using Kelso and Crawford’s modelling.