During previous pandemics, social distancing was organized top-down, through the imposition of a minimum distance. An alternative approach toward social distancing asks individuals to try to maximize their distance to others. Here, we ask whether people can thus efficiently self-organize spatial arrangements. We studied 953 social distancing decisions made in 150 groups under controlled conditions. Results show that subject behavior approximates what optimal mathematical strategies achieve. At scale, the observed behavior produces greater distancing than the mere respecting of an externally imposed minimum distance. These findings suggest that the encouragement of maximal distancing may reduce the propagation of viruses that spread through close-range contact beyond what is achieved with minimum-distance policies alone.

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.

The China-India border is the longest disputed border in the world. The countries went to war in 1962 and there have been recurring border skirmishes ever since. Reports of Chinese incursions into Indian territory are now a frequent occurrence. This rising tension between the world’s most populous countries not only poses risks for global security and the world economy, but also has a negative impact on the unique ecology of the Himalayas, because of the expanding military infrastructure. We have assembled a unique data set of the dates and locations of the major incursions over the past 15 years. We find that the conflict can be separated into two independent conflicts, the western and eastern sectors. The incursions in these sectors are statistically independent. However, major incidents do lead to an increased tension that persists for years all along the entire Line of Actual Control (LAC). This leads us to conclude that an agreement on the exact location of a limited number of contested regions, such as the Doklam plateau on the China-Bhutan border, has the potential to significantly defuse the conflict, and could potentially settle the dispute at a further date. Building on insights from game theory, we find that the Chinese incursions in the west are strategically planned and may aim for a more permanent control over specific contested areas. This finding is in agreement with other studies into the expansionist strategy of the current Chinese government.

This paper repurposes the classic insight from network theory that long-distance connections drive disease propagation into a strategy for controlling a second wave of Covid-19. We simulate a scenario in which a lockdown is first imposed on a population and then partly lifted while long-range transmission is kept at a minimum. Simulated spreading patterns resemble contemporary distributions of Covid- 19 across EU member states, German and Italian regions, and through New York City, providing some model validation. Results suggest that our proposed strategy may significantly reduce peak infection. We also find that post-lockdown flare-ups remain local longer, aiding geographical containment. These results suggest a tailored policy in which individuals who frequently travel to places where they interact with many people are offered greater protection, tracked more closely, and are regularly tested. This policy can be communicated to the general public as a simple and reasonable principle: Stay nearby or get checked.