Pseudomarkets with Priorities in Large Random Assignment Economies

I study large random assignment economies with a continuum of agents and a \u85nite number of object types. I consider the existence of weak priorities discriminating among agents with respect to their rights concerning the \u85nal assignment. The respect for priorities ex ante (ex-ante stability) usually precludes ex-ante envy-freeness. Therefore I de\u85ne a new concept of fairness, called no unjusti\u85ed lower chances: priorities with respect to one object type cannot justify di¤erent achievable chances regarding another object type. This concept, which applies to the assignment mechanism rather than to the assignment itself, implies ex-ante envy-freeness among agents of the same priority type. I propose a variation of Hylland and Zeckhausers (1979) pseudomarket that meets ex-ante stability, no unjusti\u85ed lower chances and ex-ante e ¢ ciency among agents of the same priority type. Assuming enough richness in preferences and priorities, the converse is also true: any random assignment with these properties could be achieved through an equilibrium in a pseudomarket with priorities. If priorities are acyclical (the orderin