On coalitional stability of anonymous interim mechanisms

In a situation where agents have private information, we investigate the st ability of mechanisms with respect to coalitional deviations. In the cooper ative tradition, we first extend the notion of Core, taking into account th e information a coalition may have when it forms and the conjectures of out siders. This leads us to propose a family of Cores rather than a single one . Secondly, we study the stability of Core mechanisms to secession proposal s in simple noncooperative games. The two different stability analyses, nor mative and strategic, tend to give support to the more natural extension of the Core, called Statistical Core, only in situations where some strong fo rm of increasing returns to coalition is met. Without this property, argume nts for a concept of Core that is non empty in a reasonably large class of problems are less compelling. Applications to taxation and insurance are gi ven.