The idea of using the core as a model for predicting the formation of coalitions and the sharing of benefits to coordinated activities has been studied extensively. Basic to the concept of the core is the idea of group rationality as embodied by the blocking condition. The predictions given by the core may run into difficulties if some individuals or coalitions may benefit from not blocking truthfully. This paper investigates this question in games in some games that generalize assignment games. Some positive results are given, and relationships with Vickrey-Clarke-Groves mechanisms are drawn.
