Modelling Conflict and Cooperation: A Mathematical Approach to International Relations

Contemporary research in international relations necessitates innovative and interdisciplinary approaches that not only deepen our understanding of the complexities of the global system but also contribute to practical solutions for conflict resolution and the advancement of peace and stability. One of these integrated approaches is mathematical modelling, which includes game theory, network analysis, and dynamical system models. The game theory model offers a framework to analyse situations involving mutually dependent decision-making and the impact of these decisions on others. Likewise, network analysis and dynamical system models can be utilised to comprehend various scenarios of conflict and cooperation between states. This paper presents a hypothetical formulation of a game-theoretical model to assess the applicability of mathematical modelling to real-world situations. It discusses the use of utility functions and analyses Nash equilibrium, Pareto optimality, and the security dilemma to grasp the complexities of decision-making. The research focuses on prominent theoretical frameworks of international relations, namely realism and idealism, to demonstrate that mathematical modelling is equally effective in studying the dynamics and behaviour of an international system where sovereign states make strategic choices based on their national interests.