The Manipulability of Matching Rules via Segmentation

Our matching problems feature agents with endowments facing certain division rules. At any matching, the endowments of agents are reallocated between the matched pairs according to some given division rule, and this opens doors to an iterated matching problem and rematching, and to manipulation of some matching rules via segmentation. In this form of manipulation a coalition breaks off from the rest, matches within itself and rejoins the complementary coalition for a rematching at the new endowment profile. Under certain division rules this may benefit the coalition who breaks off without hurting the complementary coalition. Furthermore, both may benefit by first matching internally and then rejoining for a new match.