Game Theory in Defence Applications: A Review.

This paper presents a succinct review of attempts in the literature to use game theory to model decision-making scenarios relevant to defence applications. Game theory has been proven as a very effective tool in modelling the decision-making processes of intelligent agents, entities, and players. It has been used to model scenarios from diverse fields such as economics, evolutionary biology, and computer science. In defence applications, there is often a need to model and predict the actions of hostile actors, and players who try to evade or out-smart each other. Modelling how the actions of competitive players shape the decision making of each other is the forte of game theory. In past decades, there have been several studies that applied different branches of game theory to model a range of defence-related scenarios. This paper provides a structured review of such attempts, and classifies existing literature in terms of the kind of warfare modelled, the types of games used, and the players involved. After careful selection, a total of 29 directly relevant papers are discussed and classified. In terms of the warfares modelled, we recognise that most papers that apply game theory in defence settings are concerned with Command and Control Warfare, and can be further classified into papers dealing with (i) Resource Allocation Warfare (ii) Information Warfare (iii) Weapons Control Warfare, and (iv) Adversary Monitoring Warfare. We also observe that most of the reviewed papers are concerned with sensing, tracking, and large sensor networks, and the studied problems have parallels in sensor network analysis in the civilian domain. In terms of the games used, we classify the reviewed papers into papers that use non-cooperative or cooperative games, simultaneous or sequential games, discrete or continuous games, and non-zero-sum or zero-sum games. Similarly, papers are also classified into two-player, three-player or multi-player game based papers. We also explore the nature of players and the construction of payoff functions in each scenario. Finally, we also identify gaps in literature where game theory could be fruitfully applied in scenarios hitherto unexplored using game theory. The presented analysis provides a concise summary of the state-of-the-art with regards to the use of game theory in defence applications and highlights the benefits and limitations of game theory in the considered scenarios.

Optimal governance and implementation of vaccination programmes to contain the COVID-19 pandemic.

Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public. We emphasize that decision-making under uncertainty and imperfect information, and with only conditionally optimal outcomes, is a unique forte of established game-theoretic modelling. Therefore, we can use this approach to obtain the best framework for modelling and simulating vaccination prioritization and uptake that will be readily available to inform important policy decisions for the optimal control of the COVID-19 pandemic.

Game theoretic modelling of infectious disease dynamics and intervention methods: a review.

We review research studies which use game theory to model the decision-making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. The literature is classified based on (i) type of population modelling (classical or network-based), (ii) frequency of the game (non-repeated or repeated), and (iii) type of strategy adoption (self-learning or imitation). The choice of model is shown to depend on many factors such as the immunity to the disease, the strength of immunity conferred by the vaccine, the size of population and the level of mixing therein. We highlight that while early studies used classical compartmental modelling with self-learning games, in recent years, there is a substantial growth of network-based modelling with imitation games. The review indicates that game theory continues to be an effective tool to model decision-making by individuals with respect to intervention (vaccination or social distancing).

The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model.

We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the resultant vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number R 0 for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces R 0 and delays the disease prevalence, and thus is essential to containing epidemics.

Assortativity and mixing patterns in international supply chain networks.

As economic globalisation increases, inclination toward domestic protectionism is also increasing in many countries of the world. To improve the productivity and the resilience of national economies, it is important to understand the drivers and the barriers of the internatiolisation of economic activities. While internatiolisation of individual economic actors is difficult to explain using traditional theories, aggregate patterns may be explained to some extent. We take a network-centric perspective to describe the extent of corporate internatiolisation in different countries. Based on Newman's assortativity coefficient, we design a range of assortativity metrics which are appropriate in the firm network context. Using these, we quantify companies' appetite for internatiolisation in relation to the internatiolisation of their partners. We use the Factset Revere dataset, which is provided by FactSet Research Systems Inc., that captures global supply chain relationships between companies. We identify countries where the level of internationalisation is relatively high or relatively low, and we show that subtle differences in the assortativity metrics used change the ranking of countries significantly in terms of the assortativity correlation, highlighting that companies in different countries are prone to different types of internationalisation. Overall, we demonstrate that firms from most countries in the dataset studied have a slight preference to make supply chain relationships with other firms which have undergone a similar level of internationalisation, and other firms from their own country. The implications of our results are important for countries to understand the evolution of international relationships in their corporate environments, and how they compare to other nations in the world in this regard.

Urbanization affects peak timing, prevalence, and bimodality of influenza pandemics in Australia: Results of a census-calibrated model.

We examine salient trends of influenza pandemics in Australia, a rapidly urbanizing nation. To do so, we implement state-of-the-art influenza transmission and progression models within a large-scale stochastic computer simulation, generated using comprehensive Australian census datasets from 2006, 2011, and 2016. Our results offer a simulation-based investigation of a population's sensitivity to pandemics across multiple historical time points and highlight three notable trends in pandemic patterns over the years: increased peak prevalence, faster spreading rates, and decreasing spatiotemporal bimodality. We attribute these pandemic trends to increases in two key quantities indicative of urbanization: the population fraction residing in major cities and international air traffic. In addition, we identify features of the pandemic's geographic spread that we attribute to changes in the commuter mobility network. The generic nature of our model and the ubiquity of urbanization trends around the world make it likely for our results to be applicable in other rapidly urbanizing nations.

The Pagerank-Index: Going beyond Citation Counts in Quantifying Scientific Impact of Researchers.

Quantifying and comparing the scientific output of researchers has become critical for governments, funding agencies and universities. Comparison by reputation and direct assessment of contributions to the field is no longer possible, as the number of scientists increases and traditional definitions about scientific fields become blurred. The h-index is often used for comparing scientists, but has several well-documented shortcomings. In this paper, we introduce a new index for measuring and comparing the publication records of scientists: the pagerank-index (symbolised as π). The index uses a version of pagerank algorithm and the citation networks of papers in its computation, and is fundamentally different from the existing variants of h-index because it considers not only the number of citations but also the actual impact of each citation. We adapt two approaches to demonstrate the utility of the new index. Firstly, we use a simulation model of a community of authors, whereby we create various 'groups' of authors which are different from each other in inherent publication habits, to show that the pagerank-index is fairer than the existing indices in three distinct scenarios: (i) when authors try to 'massage' their index by publishing papers in low-quality outlets primarily to self-cite other papers (ii) when authors collaborate in large groups in order to obtain more authorships (iii) when authors spend most of their time in producing genuine but low quality publications that would massage their index. Secondly, we undertake two real world case studies: (i) the evolving author community of quantum game theory, as defined by Google Scholar (ii) a snapshot of the high energy physics (HEP) theory research community in arXiv. In both case studies, we find that the list of top authors vary very significantly when h-index and pagerank-index are used for comparison. We show that in both cases, authors who have collaborated in large groups and/or published less impactful papers tend to be comparatively favoured by the h-index, whereas the pagerank-index highlights authors who have made a relatively small number of definitive contributions, or written papers which served to highlight the link between diverse disciplines, or typically worked in smaller groups. Thus, we argue that the pagerank-index is an inherently fairer and more nuanced metric to quantify the publication records of scientists compared to existing measures.

Impact of Physician Community Structure on Healthcare Outcomes.

There is a substantial variation in healthcare spending and readmission rate for individuals having admissions to different hospitals. This study assessed how the community structure of physician collaboration networks that evolve during the period of providing healthcare services to hospitalised patients contribute to this variation. A physician collaboration network is said to have a community structure if the nodes (i.e. physicians) of that network can be easily grouped into sets of nodes such that each set of nodes is densely connected internally but sparsely connected between groups. This study constructed physician collaboration networks based on patient-sharing ties among physicians who provided healthcare services to hospitalised patients. An administrative health insurance claim dataset was utilised to extract patient-sharing ties among physicians. Simple linear regression models were estimated to assess the impact of the community structure of physician collaboration networks on the healthcare outcome measures (i.e. readmission rate and hospitalisation cost). From these models, this study found that the structure of a physician community has significant impact on readmission rate and hospitalisation cost. Healthcare administrators or managers could consider this finding in developing effective and efficient healthcare environments in their respective healthcare organisations.

Emergence of scale-free characteristics in socio-ecological systems with bounded rationality.

Socio-ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback--Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio-ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems.

Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks.

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Assortative mixing in directed biological networks.

We analyze assortative mixing patterns of biological networks which are typically directed. We develop a theoretical background for analyzing mixing patterns in directed networks before applying them to specific biological networks. Two new quantities are introduced, namely the in-assortativity and the out-assortativity, which are shown to be useful in quantifying assortative mixing in directed networks. We also introduce the local (node level) assortativity quantities for in- and out-assortativity. Local assortativity profiles are the distributions of these local quantities over node degrees and can be used to analyze both canonical and real-world directed biological networks. Many biological networks, which have been previously classified as disassortative, are shown to be assortative with respect to these new measures. Finally, we demonstrate the use of local assortativity profiles in analyzing the functionalities of particular nodes and groups of nodes in real-world biological networks.