Abstract
We analyze centralized markets for indivisible objects without money through pairwise exchange when each agent initially owns a single object. We consider rules that for each profile of agents preferences select an assignment of the objects to the agents. We present a family of domains of preferences (minimal reversal domains) that are maximal rich domains for the existence of rules that satisfy individual rationality, efficiency, and strategy-proofness. Each minimal reversal domain is defined by a common ranking of the set of objects, and agents’ preferences over admissible objects coincide with such common ranking but for a specific pair of objects.
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