An etude in modeling the definability of equilibrium

We analyse the object assignment model enriched with a set of orderings over the set of agents. These orderings provide potential criteria for determining the suitability of agents to be assigned to an object. A candidate for a definable equilibrium is an assignment of the agents to the objects and an attachment of a single criterion to each object. In equilibrium, each agent is better-suited to his assigned object than any agent who envies him, according to the criterion attached to that object. We analyze the equilibrium notion and provide some examples.