Generalizing Top Trading Cycles for Housing Markets with Fractional Endowments

摘要

The housing market setting constitutes a fundamental model of exchangeeconomies of goods. In most of the work concerning housing markets, it isassumed that agents own and are allocated discrete houses. The drawback of thisassumption is that it does not cater for randomized assignments or allocationof time-shares. Recently, house allocation with fractional endowment of houseswas considered by Athanassoglou and Sethuraman (2011) who posed the openproblem of generalizing Gale's Top Trading Cycles (TTC) algorithm to the caseof housing markets with fractional endowments. In this paper, we address theproblem and present a generalization of TTC called FTTC that is polynomial-timeas well as core stable and Pareto optimal with respect to stochastic dominanceeven if there are indifferences in the preferences. We prove that if each agentowns one discrete house, FTTC coincides with a state of the art strategyproofmechanism for housing markets with discrete endowments and weak preferences. We show that FTTC satisfies a maximal set of desirable properties by provingtwo impossibility theorems. Firstly, we prove that with respect to stochasticdominance, core stability and no justified envy are incompatible. Secondly, weprove that there exists no individual rational, Pareto optimal and weakstrategyproof mechanism, thereby answering another open problem posed byAthanassoglou and Sethuraman (2011). The second impossibility implies a numberof results in the literature.