Efficient Combinatorial Exchanges with Opt-Out Types

We investigate combinatorial exchanges as a generalization of auctions and bilateral trades, where multiple heterogeneous commodities are initially possessed not only by a central planner but also by participants. We assume private values, quasi-linearity, risk neutrality, and independent type distribution. Efficiency, Bayesian Incentive Compatibility, and Interim Individual Rationality in a type-dependent manner are required. We introduce a stability notion in the ex-ante term, namely marginal core. By assuming the presence of opt-out types for each player, we show a full characterization in that the central planner inevitably has a deficit if and only if the marginal core is non-empty.