Coral Games and the Core of Cores

Casual observation reveals that groups of people interact on many levels simultaneously. Examples include political party formation and interaction; the interaction of Sunnis, Shias and Kurds in the Government of Iraq; and labor union and confederation formation. In this paper, a model of hierarchical group structures is developed. The model generalizes the existing coalitional theory in several ways and reveals a new connection between characteristic and partition function theories; that they are both valuable components of an overall theory. The stability concept that emerges is called the core of cores. Several results are presented, including necessary and sufficient conditions for the existence of the core of cores and a theorem that demonstrates the relationship between the cores of each level of the organizational structure and the core of cores. The results establish that stability can arise from any combination of stable and unstable components, and suggest a re-thinking of existing coalitional models, taking into account the effect of “nearby” games. The framework developed here has immediate applications to various topics in political economy and industrial organization, such as representative voting and corporate mergers. JEL classification codes: C62, C71, C79, D72