Efficient Combinatorial Allocations: Individual Rationality versus Stability

We investigate combinatorial allocations with opt-out types and clarify the possibility of achieving efficiency under incomplete information. We introduce two distinct collective decision procedures. The first procedure assumes that the central planner designs a mechanism and players have the option to exit. The mechanism requires interim individual rationality. The second procedure assumes that players design a mechanism by committing themselves to participate. The mechanism requires marginal stability against blocking behavior by the largest proper coalitions. We show that the central planner can earn non-negative revenue in the first procedure, if and only if he cannot do so in the second.