Pseudomarkets with Priorities in Large Random Assignment Economies

I study large random assignment economies with a continuum of agents and a …nite number of object types. I consider the existence of weak priorities discriminating among agents with respect to their rights concerning the …nal assignment. The respect for priorities ex ante (ex-ante stability) usually precludes ex-ante envy-freeness. Therefore I de…ne a new concept of fairness, called no unjusti…ed 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 Zeckhauser’s (1979) pseudomarket that meets ex-ante stability, no unjusti…ed 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 ordering [email protected]. I am grateful to Yeon-Koo Che, Piero Gottardi, Jordi Massó, Massimo Morelli and Fernando Vega-Redondo for previous comments and suggestions. For the same reason, I would also like to thank the attendants at seminars at the European University Institute, the University of Barcelona and the University of Siena. I also acknowledge the …nancial support provided by the Spanish Ministry of Science and Innovation (ECO2009-06946 and ECO2008-04756).