Gale's Fixed Tax for Exchanging Houses

We consider the taxation of exchanges among a set of agents where each agent owns one object. Agents may have different valuations for the objects and they need to pay taxes for exchanges. Using basic properties, we show that if pairwise (or some) exchanges of objects are allowed, then all exchanges (in any possible manner) must be feasible. Furthermore, whenever any agent exchanges his object, he pays the same fixed tax (a lump sum payment which is identical for all agents) independently of which object he consumes. Gale's top trading cycles algorithm finds the final allocation using the agents' valuations adjusted with the fixed tax. Our mechanisms are in stark contrast to Clarke-Groves taxation schemes or the max-med schemes proposed by Sprumont (2013).