Approaches to Geo-mathematical Modelling

Chapter 17A General Framework for Static, Spatially Explicit Games of Search and Concealment

Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith

17.1 Introduction

In recent years, there has been a growing appreciation of the potential role of game theory as an analytical tool, enabling public and private organisations to make more informed strategic decisions on questions of security and the deployment of resources. Simultaneously, the significant expansion in the field of digital mapping through the development of geographic information systems (GIS) has allowed for an unprecedented degree of spatial sophistication in our approach to a huge variety of real-world problems. The combination of these two areas – the application of game theory to security questions and the development of spatial technologies – offers an opportunity for the development of a new suite of spatially explicit mathematical modelling solutions for security scenarios. However, it also highlights the need for the creation of a broad modelling framework for the field of spatial game theory, which would act as a foundation upon which such new tools could be built.¹

In this chapter, our goal is take steps towards providing a framework of the sort described here. We will define a general search and concealment game that takes full account of the spatial structure of the space over which it is played; it is suitable for application in a wide range of security scenarios. The game is static in the sense ...