Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions

The game-theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market (e.g., firms or workers) to be simultaneously maximized. This is shown to follow from the lattice structure of the set of stable outcomes. However it is shown that in a more general class of problems the optimality results persist, but the lattice structures do not. Thus this paper raises as many questions as it answers.