Efficient and strategy‐proof mechanism under general constraints

This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints—ordered accessibility—for which the serial dictatorship (SD) mechanism is Pareto‐efficient (PE), individually rational (IR), and group strategy‐proof (GSP). Then we prove that accessibility is a necessary condition for the existence of PE, IR, and GSP mechanisms. Moreover, we show an example where the SD mechanism with a dynamically constructed order satisfies PE, IR, and GSP if one school has an arbitrary accessible constraint and each of the other schools has a capacity constraint. Second, we examine a setting with endowments. We find that the generalized matroid is a necessary and sufficient condition on the constraint structure for the existence of a mechanism that is PE, IR, and strategy‐proof. We also demonstrate that a top trading cycles mechanism satisfies PE, IR, and GSP under any generalized matroid constraint. Finally, we observe that any two out of the three properties—PE, IR, and GSP—can be achieved under general constraints.