One of the fundamental issues of international relations concerns whether, and under what conditions, stability prevails in anarchic systems, these being systems in which all authority and institutional restraints to action are wholly endogenous. This book uses the tools of game theory to develop a comprehensive theory of such systems and details both necessary and sufficient conditions for stability. The authors first define two forms of stability: system and resource stability. International political systems are said to be stable when no state confronts the possibility of a loss of sovereignty. Resource stability, in contrast, requires that the current distribution of wealth and power among states can change only due to differences in the vitality of economies. The theory developed in this book refines the classic balance-of-power theory and formally incorporates into that theory the consideration of endogenous resource growth, preventive war, war costs and the imperatives of geography, revealing a fundamental conflict between the concepts of 'balancers' and 'central powers'.