Contemporary Conflicts and Crises

Abstract

In this thesis, we use mathematical models to assist the Dutch Ministry of Defence with understanding and decision-making within contemporary conflicts and crises. We explore ways to reduce the spread of COVID-19, study dynamics in the Sino-Indian border dispute, and investigate the value of scouting in conflicts involving autonomous systems.
The first two chapters of this thesis are introductory. In Chapter 1, we discuss how this thesis came to be and provide a comprehensive overview of its contents. In Chapter 2,we introduce concepts and tools from game theory, network science and uniform distribution theory, fundamental to subsequent chapters in this thesis. Specifically, we discuss the concept of discrepancy, necessary for Chapter 3, introduce small-world models, applied in Chapter 4, and present concepts fromgame theory, which we use in Chapters 5, 6 and 7.
Part I of the thesis involves mathematical sociology, applied to reduce the spread of COVID-19. In Chapter 3, we study the distribution of points on a circle, with the aim of maximizing the minimum distance between them. We delve into previous work and introduce an novel adaptation to finite sequences, for which we provide an optimal solution. This work has applications in optimizing social distancing. Chapter 4 focuses on modeling the spread of the COVID-19 pandemic using network science. We show that some specific social contacts are especially dangerous for virus spread. Our analysis supports strategies aimed at reducing these high-risk social interactions, thereby allowing for increased social contacts per person while still reducing the spread of the virus.
Part II of this thesis involves the application of game theory to contemporary conflicts. In Chapter 5, we study the value of manpower versus intelligence, as seen in the Russo- Ukrainian War. To model this dynamic, we introduce General Lotto games with scouts, an adaptation of the well established General Lotto game. We provide optimal solutions for this game, which leads to interesting insights about the value of manpower versus intelligence. In Chapter 6, we study the Sino-Indian Border conflict. We examine the trends of the last 15 years, and show they are not random. We use game theory to provide a possible explanation for the observed behaviour. In Chapter 7 we study search games on a partially ordered set.