Abstract
Hart and Kurz (1983) introduced four stability concepts, called α-, β-, γ-, and δ-stability. In contrast to the intensive studies on their conceptual aspects, these notions have rarely been adopted to analyze stable coalition structures in an application because the definitions consist of multiple intermediate steps. The purpose of this paper is to solve these practical difficulties. We provide an explicit form for each of the four stability concepts and reformulate each concept without using any intermediate steps. Moreover, we offer some sufficient conditions that guarantee the existence of stable coalition structures and the inclusion relation among the four stability notions. In addition, we propose a new approach to characterize the notions of stability. An application of our results to Cournot oligopoly is also provided.
