Matching with restricted trade

Official URL: http://dx.doi.org/10.1007/s00182-019-00667-3

Motivated by various trade restrictions in real-life object allocation problems, we introduce an object allocation with a particular class of trade restrictions model. The set of matchings that can occur through a market-like process under such restrictions is defined, and each such matching is called feasible. We then introduce a class of mechanisms, which we refer to as "Restricted Trading Cycles" (RTC). Any RTC mechanism is feasible, constrained efficient, and respects endowments. An axiomatic characterization of RTC is obtained, with feasibility, constrained efficiency, and a new property that we call hierarchically mutual best. In terms of strategic issues, feasibility, constrained efficiency, and respecting endowments together turns out to be incompatible with strategy-proofness. This in particular implies that no RTC mechanism is strategy-proof. Lastly, we consider a probabilistically restricted trading cycles (PRTC) mechanism, which is obtained by introducing a certain randomness to the RTC class. While PRTC continues to be manipulable, compared to RTC, it is more robust to truncations and reshufflings.