Some characterizations of Generalized Top Trading Cycles

Consider object exchange problems when each agent may be endowed with and consume more than one object. For most domains of preferences, no rule satisfies efficiency, the endowment lower bound, and strategy-proofness. Insisting on the first two properties, we explore the extent to which weaker incentive compatibility can be achieved. Motivated by behavioral and computational considerations as well as online mechanisms, we define several forms of manipulation. We consider the lexicographic domain of preferences, and provide several characterizations of Generalized Top Trading Cycles based on properties concerning immunity from heuristic and identity-splitting manipulations. We also show that this establishes a boundary with respect to incentive compatibility—minimal strengthening results in impossibility.