David Pérez-Castrillo

In the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides with the set of stable payoffs, may be empty. We introduce the idea of tradewise-stable (t-stable) outcomes: they are individually rational outcomes where all trades are stable; that is, no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of constrained-optimal (optimal) t-stable outcomes, the set of the maximal elements of the set of t-stable outcomes, as a natural solution concept for this game. We prove that this set is non-empty, it coincides with the set of stable outcomes when the core is non-empty, and it satisfies similar properties to the set of stable outcomes even when the core is empty. We propose a partnership formation process that starts with the outcome where every player stands alone, goes through steps where the set of active players expands, always forming t-stable outcomes, and ends in an (in any) optimal t-stable outcome. Finally, we also use the new concept to establish conditions under which the core is non-empty.

The theory of incentives and matching theory can complement each other. In particular, matching theory can be a tool for analyzing optimal incentive contracts within a general equilibrium framework. We propose several models that study the endogenous payoffs of principals and agents as a function of the characteristics of all the market participants, as well as the joint attributes of the principal–agent pairs that partner in equilibrium. Moreover, considering each principal–agent relationship as part of a market may strongly influence our assessment of how the characteristics of the principal and the agent affect the optimal incentive contract. Finally, we discuss the effect of the existence of moral hazard on the nature of the matching between principals and agents that we may observe at equilibrium, compared to the matching that would happen if incentive concerns were absent.