Game-Theoretically Secure Protocols for the Ordinal Random Assignment Problem

We study game-theoretically secure protocols for the classical ordinal assignment problem (aka matching with one-sided preference), in which each player has a total preference order on items. To achieve fairness notion of equal treatment equals, conventionally randomness necessary to resolve conflicts between players is assumed be generated by some trusted authority. However, distributed setting, mutually untrusted are responsible generating themselves. In addition standard desirable properties such as and Pareto-efficiency, we investigate game-theoretic maximin security, guarantees that an honest following protocol will not harmed even if corrupted deviate from protocol. Our main contribution impossibility result shows no can both efficiency. Specifically, this implies well-known probabilistic serial (PS) mechanism Bogomolnaia Moulin cannot realized any On other hand, give achieves stability ex-post Pareto-efficiency). Moreover, inspired PS mechanism, show variant known OnlinePSVar (varying rates) fairness, uniform dominance, means guaranteed receive item distribution at least good uniformly random item. sense, best one hope case when all have same order.