Exchange of indivisible goods under matroid constraints

We study the problem of reallocating indivisible goods among a set of strategic agents by generalizing the original Sharpley-Scarf market to the setting where an object can be allocated to multiple agents but subject to an associated matroid constraint. We refer to this modified market as the matroid Sharpley-Scarf market. For this general market, we present a Pareto-optimal, individually rational and group strategy-proof mechanism. Our mechanism is simple and natural generalization of the Top Trading Cycle mechanism and the Serial Dictator mechanism. In our analysis, we demonstrate that the weak core may be absent in the matroid Sharpley-Scarf market, while a relaxed version called the constrained core does exist. Furthermore, we extend the concept called competitive equilibrium to the matroid Sharpley-Scarf market and show that an allocation is a competitive equilibrium if and only if it can be produced by our mechanism.