Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.Authors acknowledge financial support from the Spanish Ministry of Education and Science, through the projects ECO2009-11213 and ECO2009-12836, from Basque Government through the project GIC07/146-IT-377-07, from Andalusian Government through the project P07.SEJ.02547 and from Belgian Federal Government through the IAP Project (contract 6/09)