Calculated Security? Mathematical Modelling of Conflict and Cooperation

The pioneering work of Lewis Fry Richardson on modelling the arms race raised expectations that mathematics can contribute to peace and conflict resolution. Based upon Richardson’s model, various extensions are discussed, with a focus on time-discrete nonlinear models showing chaotic behavior. As a general framework for the modelling of conflict and cooperation in international security a multi-actor dynamic game is introduced, with mathematical conditions for unstable interaction, potentially leading to violent conflict, arms race and war. On the other hand, the approach provides a basis for the evolution of cooperation and coalition formation. In more detail, the case of instabilities in the offense-defense competition is discussed and the role of uncertainties in complex international relations.