Full substitutability
将可替代性定义扩展到代理人可同时作为买方和卖方的场景，证明各定义等价，并引入一类新的可替代偏好来建模有生产能力的中介，同时证明可替代性在贸易禀赋、合并和有限责任等变换下保持不变。
Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.