An Alternative Characterization of Top Trading Cycles

This paper introduces two new characterizations of the Top Trading Cycles algorithm. The key to our characterizations is a new condition, independence of irrelevant rankings (IIR). Intuitively, a mechanism satisfies IIR if whenever an agent’s ranking at an object is irrelevant to her assignment, then it is irrelevant to the assignment of all agents. We demonstrate that a mechanism is Pareto efficient, strategy proof, IIR, and satisfies mutual best if and only if it is Top Trading Cycles. This provides a new insight into what distinguishes Top Trading Cycles from all other efficient and strategy proof assignment mechanisms. We provide a second characterization in terms of †North Carolina State University. Email address: thayer [email protected]. I would like to thank Melinda Morrill and Robert Hammond for their helpful comments. I am grateful to an anonymous referee and editor who noticed an error in a previous version of this paper. This paper changed substantially as a result of their comments.