Second-best incentive compatible allocation rules for multiple-type indivisible objects

We consider the problem of allocating several types of indivisible goods when preferences are separable and monetary transfers are not allowed. Our finding is that the coordinatewise application of strategy-proof and non-wasteful rules yields a strategy-proof rule with the following efficiency property: no strategy-proof rule Pareto-dominates the rule. Such rules are abundant as they include the coordinate-wise use of the two well-known priority-based rules of the top trading cycles (TTC) and the deferred acceptance (DA). Moreover, our result supports the current practice in Market Design that separately treats each type of market for its design.