{"product_id":"approaches-to-geo-mathematical-modelling-isbn-9781118922279","title":"Approaches to Geo-mathematical Modelling","description":"\u003cp\u003e\u003cb\u003eGeo-mathematical modelling: models from complexity science\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSir Alan Wilson, Centre for Advanced Spatial Analysis, University College London\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMathematical and computer models for a complexity science tool kit\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eGeographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eIn this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to ‘emerge’, and hence the current notion of ‘emergent behaviour’. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing ‘war’, agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003ci\u003eGeo-mathematical modelling:\u003c\/i\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePresents mathematical models with spatial dimensions.\u003c\/li\u003e \u003cli\u003eProvides representations of path dependence and phase changes.\u003c\/li\u003e \u003cli\u003eIllustrates complexity science using models of trade, migration, security and development aid.\u003c\/li\u003e \u003cli\u003eDemonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eThis book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.\u003c\/p\u003e \u003cp\u003eNotes on Contributors xv\u003c\/p\u003e \u003cp\u003eAcknowledgements xxi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Approaches\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The Toolkit 3\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAlan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Estimating Missing Data: Bi-proportional Fitting and Principal Components Analysis\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe 9\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAdam Dennett\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 9\u003c\/p\u003e \u003cp\u003e2.2 The Approach 12\u003c\/p\u003e \u003cp\u003e2.3 Data 12\u003c\/p\u003e \u003cp\u003e2.4 Preliminary Analysis 13\u003c\/p\u003e \u003cp\u003e2.5 Multinomial Logit Regression Analysis 15\u003c\/p\u003e \u003cp\u003e2.6 Discussion 22\u003c\/p\u003e \u003cp\u003e2.7 Conclusions 24\u003c\/p\u003e \u003cp\u003eReferences 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Test of Bi-Proportional Fitting Procedure Applied to International Trade 26\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSimone Caschili and Alan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 26\u003c\/p\u003e \u003cp\u003e3.2 Model 27\u003c\/p\u003e \u003cp\u003e3.3 Notes of Implementation 28\u003c\/p\u003e \u003cp\u003e3.4 Results 30\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Estimating Services Flows 33\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRobert G. Levy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 33\u003c\/p\u003e \u003cp\u003e4.2 Estimation Via Iterative Proportional Fitting 34\u003c\/p\u003e \u003cp\u003e4.2.1 The Method 34\u003c\/p\u003e \u003cp\u003e4.2.2 With All Initial Values Equal 35\u003c\/p\u003e \u003cp\u003e4.2.3 Equivalence to Entropy Maximisation 36\u003c\/p\u003e \u003cp\u003e4.2.4 Estimation with Some Known Flows 37\u003c\/p\u003e \u003cp\u003e4.2.5 Drawbacks to Estimating Services Flows with IPF 37\u003c\/p\u003e \u003cp\u003e4.3 Estimating Services Flows Using Commodities Flows 37\u003c\/p\u003e \u003cp\u003e4.3.1 The Gravity Model 37\u003c\/p\u003e \u003cp\u003e4.3.2 Splitting Up Value Added 40\u003c\/p\u003e \u003cp\u003e4.4 A Comparison of The Methods 40\u003c\/p\u003e \u003cp\u003e4.4.1 Unbalanced Row and Column Margins 42\u003c\/p\u003e \u003cp\u003e4.4.2 Iterative Proportional Fitting 42\u003c\/p\u003e \u003cp\u003e4.4.3 Gravity Model 42\u003c\/p\u003e \u003cp\u003e4.4.4 Gravity Model Followed by IPF 44\u003c\/p\u003e \u003cp\u003e4.5 Results 45\u003c\/p\u003e \u003cp\u003e4.5.1 Selecting a Representative Sector 45\u003c\/p\u003e \u003cp\u003e4.5.2 Estimated in-Sample Flows 46\u003c\/p\u003e \u003cp\u003e4.5.3 Estimated Export Totals 47\u003c\/p\u003e \u003cp\u003e4.6 Conclusion 49\u003c\/p\u003e \u003cp\u003eReferences 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 A Method for Estimating Unknown National Input–Output Tables Using Limited Data 51\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eThomas P. Oléron Evans and Robert G. Levy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Motivation and Aims 51\u003c\/p\u003e \u003cp\u003e5.2 Obstacles to The Estimation of National Input–Output Tables 52\u003c\/p\u003e \u003cp\u003e5.3 Vector Representation of Input–Output Tables 53\u003c\/p\u003e \u003cp\u003e5.4 Method 54\u003c\/p\u003e \u003cp\u003e5.4.1 Concept 54\u003c\/p\u003e \u003cp\u003e5.4.2 Estimation Procedure 55\u003c\/p\u003e \u003cp\u003e5.4.3 Cross-Validation 57\u003c\/p\u003e \u003cp\u003e5.5 In-Sample Assessment of The Estimates 58\u003c\/p\u003e \u003cp\u003e5.5.1 Summary Statistics 58\u003c\/p\u003e \u003cp\u003e5.5.2 Visual Comparison 61\u003c\/p\u003e \u003cp\u003e5.6 Out-of-Sample Discussion of The Estimates 63\u003c\/p\u003e \u003cp\u003e5.6.1 Final Demand Closeness 63\u003c\/p\u003e \u003cp\u003e5.6.2 Technical Coefficient Clustering 65\u003c\/p\u003e \u003cp\u003e5.7 Conclusion 67\u003c\/p\u003e \u003cp\u003eReferences 68\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Dynamics in Account-based Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour 71\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eHannah M. Fry, Alan G. Wilson and Frank T. Smith\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 71\u003c\/p\u003e \u003cp\u003e6.2 Definition of Variables for System Description 73\u003c\/p\u003e \u003cp\u003e6.3 The Pricing and Trade Flows Algorithm 73\u003c\/p\u003e \u003cp\u003e6.4 Initial Setup 75\u003c\/p\u003e \u003cp\u003e6.5 The Algorithm to Determine Farming Trade Flows 77\u003c\/p\u003e \u003cp\u003e6.5.1 The Accounts for the Farming Industry 79\u003c\/p\u003e \u003cp\u003e6.5.2 A Final Point on The Farming Flows 79\u003c\/p\u003e \u003cp\u003e6.6 The Algorithm to Determine The Natural Resources Trade Flows 80\u003c\/p\u003e \u003cp\u003e6.6.1 The Accounts for The Natural Resources Sector 80\u003c\/p\u003e \u003cp\u003e6.7 The Algorithm to Determine Manufacturing Trade Flows 81\u003c\/p\u003e \u003cp\u003e6.7.1 The Accounts for The Manufacturing Industry 82\u003c\/p\u003e \u003cp\u003e6.8 The Dynamics 83\u003c\/p\u003e \u003cp\u003e6.9 Experimental Results 84\u003c\/p\u003e \u003cp\u003e6.9.1 Concluding Comments 88\u003c\/p\u003e \u003cp\u003eReferences 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Global Dynamical Input–Output Modelling 91\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAnthony P. Korte and Alan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Towards a Fully Dynamic Inter-country Input–Output Model 91\u003c\/p\u003e \u003cp\u003e7.2 National Accounts 92\u003c\/p\u003e \u003cp\u003e7.2.1 Definitions 92\u003c\/p\u003e \u003cp\u003e7.2.2 The Production Account 94\u003c\/p\u003e \u003cp\u003e7.2.3 The Commodity Markets Account 94\u003c\/p\u003e \u003cp\u003e7.2.4 The Household Account 94\u003c\/p\u003e \u003cp\u003e7.2.5 The Capital Markets Account 94\u003c\/p\u003e \u003cp\u003e7.2.6 The Rest of the World (RoW) Account 94\u003c\/p\u003e \u003cp\u003e7.2.7 The Government Account 95\u003c\/p\u003e \u003cp\u003e7.2.8 The Net Worth of an Economy and Revaluations 95\u003c\/p\u003e \u003cp\u003e7.2.9 Overview of the National Accounts 95\u003c\/p\u003e \u003cp\u003e7.2.10 Closing the Model: Making Final Demand Endogenous 96\u003c\/p\u003e \u003cp\u003e7.3 The Dynamical International Model 97\u003c\/p\u003e \u003cp\u003e7.3.1 Supply and Demand 97\u003c\/p\u003e \u003cp\u003e7.3.2 The National Accounts Revisited 99\u003c\/p\u003e \u003cp\u003e7.4 Investment: Modelling Production Capacity: The Capacity Planning Model 100\u003c\/p\u003e \u003cp\u003e7.4.1 The Multi-region, Multi-sector Capacity Planning Model 100\u003c\/p\u003e \u003cp\u003e7.5 Modelling Production Capacity: The Investment Growth Approach 103\u003c\/p\u003e \u003cp\u003e7.5.1 Multi-region, multi-sector Investment Growth Models with Reversibility 103\u003c\/p\u003e \u003cp\u003e7.5.2 One-country, One-sector Investment Growth Model with Reversibility 104\u003c\/p\u003e \u003cp\u003e7.5.3 Two-country, Two-sector Investment Growth Model with Reversibility 106\u003c\/p\u003e \u003cp\u003e7.5.4 A Multi-region, Multi-sector, Investment Growth Model without Reversibility 108\u003c\/p\u003e \u003cp\u003e7.5.5 A Multi-region, Multi-sector, Investment Growth Model without Reversibility, with Variable Trade Coefficients 111\u003c\/p\u003e \u003cp\u003e7.5.6 Dynamical Final Demand 114\u003c\/p\u003e \u003cp\u003e7.5.7 Labour 115\u003c\/p\u003e \u003cp\u003e7.5.8 The Price Model 118\u003c\/p\u003e \u003cp\u003e7.6 Conclusions 121\u003c\/p\u003e \u003cp\u003eReferences 122\u003c\/p\u003e \u003cp\u003eAppendix 123\u003c\/p\u003e \u003cp\u003eA.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Space–Time Statistical Analysis\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Space–Time Analysis of Point Patterns in Crime and Security Events 127\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eToby P. Davies, Shane D. Johnson, Alex Braithwaite and Elio Marchione\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 127\u003c\/p\u003e \u003cp\u003e8.1.1 Clustering 127\u003c\/p\u003e \u003cp\u003e8.1.2 Clustering of Urban Crime 129\u003c\/p\u003e \u003cp\u003e8.1.3 The Knox Test 130\u003c\/p\u003e \u003cp\u003e8.2 Application in Novel Areas 132\u003c\/p\u003e \u003cp\u003e8.2.1 Maritime Piracy 132\u003c\/p\u003e \u003cp\u003e8.2.2 Space–Time Clustering of Piracy 134\u003c\/p\u003e \u003cp\u003e8.2.3 Insurgency and Counterinsurgency in Iraq 136\u003c\/p\u003e \u003cp\u003e8.3 Motif Analysis 138\u003c\/p\u003e \u003cp\u003e8.3.1 Introduction 138\u003c\/p\u003e \u003cp\u003e8.3.2 Event Networks 140\u003c\/p\u003e \u003cp\u003e8.3.3 Network Motifs 140\u003c\/p\u003e \u003cp\u003e8.3.4 Statistical Analysis 141\u003c\/p\u003e \u003cp\u003e8.3.5 Random Network Generation 142\u003c\/p\u003e \u003cp\u003e8.3.6 Results 143\u003c\/p\u003e \u003cp\u003e8.4 Discussion 147\u003c\/p\u003e \u003cp\u003eReferences 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Real-Time Response Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The London Riots –1: Epidemiology, Spatial Interaction and Probability of Arrest 153\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eToby P. Davies, Hannah M. Fry, Alan G. Wilson and Steven R. Bishop\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 153\u003c\/p\u003e \u003cp\u003e9.2 Characteristics of Disorder 156\u003c\/p\u003e \u003cp\u003e9.3 The Model 158\u003c\/p\u003e \u003cp\u003e9.3.1 Outline 158\u003c\/p\u003e \u003cp\u003e9.3.2 General Concepts 158\u003c\/p\u003e \u003cp\u003e9.3.3 Riot Participation 159\u003c\/p\u003e \u003cp\u003e9.3.4 Spatial Assignment 160\u003c\/p\u003e \u003cp\u003e9.3.5 Interaction between Police and Rioters 162\u003c\/p\u003e \u003cp\u003e9.4 Demonstration Case 162\u003c\/p\u003e \u003cp\u003e9.5 Concluding Comments 166\u003c\/p\u003e \u003cp\u003eReferences 166\u003c\/p\u003e \u003cp\u003eAppendix 168\u003c\/p\u003e \u003cp\u003eA.1 Note on Methods: Data 168\u003c\/p\u003e \u003cp\u003eA.2 Numerical Simulations 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The London Riots –2: A Discrete Choice Model 170\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePeter Baudains, Alex Braithwaite and Shane D. Johnson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 170\u003c\/p\u003e \u003cp\u003e10.2 Model Setup 170\u003c\/p\u003e \u003cp\u003e10.3 Modelling the Observed Utility 172\u003c\/p\u003e \u003cp\u003e10.4 Results 176\u003c\/p\u003e \u003cp\u003e10.5 Simulating the 2011 London Riots: Towards a Policy Tool 181\u003c\/p\u003e \u003cp\u003e10.6 Modelling Optimal Police Deployment 187\u003c\/p\u003e \u003cp\u003eReferences 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI The Mathematics of War\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Richardson Models with Space 195\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePeter Baudains\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 195\u003c\/p\u003e \u003cp\u003e11.2 The Richardson Model 196\u003c\/p\u003e \u003cp\u003e11.3 Empirical Applications of Richardson’s Model 202\u003c\/p\u003e \u003cp\u003e11.4 A Global Arms Race Model 204\u003c\/p\u003e \u003cp\u003e11.5 Relationship to a Spatial Conflict Model 206\u003c\/p\u003e \u003cp\u003e11.6 An Empirical Application 207\u003c\/p\u003e \u003cp\u003e11.6.1 Two Models of Global Military Expenditure 207\u003c\/p\u003e \u003cp\u003e11.6.2 The Alliance Measure C ij 208\u003c\/p\u003e \u003cp\u003e11.6.3 A Spatial Richardson Model of Global Military Expenditure 210\u003c\/p\u003e \u003cp\u003e11.6.4 Results 211\u003c\/p\u003e \u003cp\u003e11.7 Conclusion 212\u003c\/p\u003e \u003cp\u003eReferences 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VII Agent-based Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Agent-based Models of Piracy 217\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eElio Marchione, Shane D. Johnson and Alan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 217\u003c\/p\u003e \u003cp\u003e12.2 Data 219\u003c\/p\u003e \u003cp\u003e12.3 An Agent-based Model 221\u003c\/p\u003e \u003cp\u003e12.3.1 Defining Maritime Piracy Maps 221\u003c\/p\u003e \u003cp\u003e12.3.2 Defining Vessel Route Maps 222\u003c\/p\u003e \u003cp\u003e12.3.3 Defining Pirates’, Naval Units’ and Vessels’ Behaviours 224\u003c\/p\u003e \u003cp\u003e12.3.4 Comparing Risk Maps 227\u003c\/p\u003e \u003cp\u003e12.4 Model Calibration 232\u003c\/p\u003e \u003cp\u003e12.5 Discussion 232\u003c\/p\u003e \u003cp\u003eReferences 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 A Simple Approach for the Prediction of Extinction Events in Multi-agent Models 237\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eThomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 237\u003c\/p\u003e \u003cp\u003e13.2 Key Concepts 238\u003c\/p\u003e \u003cp\u003e13.2.1 Binary Classification 238\u003c\/p\u003e \u003cp\u003e13.2.2 Measures of Classifier Performance 238\u003c\/p\u003e \u003cp\u003e13.2.3 Stochastic Processes 240\u003c\/p\u003e \u003cp\u003e13.3 The NANIA Predator–prey Model 241\u003c\/p\u003e \u003cp\u003e13.3.1 Background 241\u003c\/p\u003e \u003cp\u003e13.3.2 An ODD Description of the NANIA Model 241\u003c\/p\u003e \u003cp\u003e13.3.3 Behaviour of the NANIA Model 245\u003c\/p\u003e \u003cp\u003e13.3.4 Extinctions in the NANIA Model 246\u003c\/p\u003e \u003cp\u003e13.4 Computer Simulation 247\u003c\/p\u003e \u003cp\u003e13.4.1 Data Generation 247\u003c\/p\u003e \u003cp\u003e13.4.2 Categorisation of the Data 249\u003c\/p\u003e \u003cp\u003e13.5 Period Detection 249\u003c\/p\u003e \u003cp\u003e13.6 A Monte Carlo Approach to Prediction 252\u003c\/p\u003e \u003cp\u003e13.6.1 Binned Data 252\u003c\/p\u003e \u003cp\u003e13.6.2 Confidence Intervals 257\u003c\/p\u003e \u003cp\u003e13.6.3 Predicting Extinctions using Binned Population Data 257\u003c\/p\u003e \u003cp\u003e13.6.4 ROC and Precision-recall Curves for Monte Carlo Prediction of Predator Extinctions 260\u003c\/p\u003e \u003cp\u003e13.7 Conclusions 263\u003c\/p\u003e \u003cp\u003eReferences 264\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VIII Diffusion Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Urban Agglomeration Through the Diffusion of Investment Impacts 269\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMinette D’Lima, Francesca R. Medda and Alan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 269\u003c\/p\u003e \u003cp\u003e14.2 The Model 270\u003c\/p\u003e \u003cp\u003e14.3 Mathematical Analysis for Agglomeration Conditions 272\u003c\/p\u003e \u003cp\u003e14.3.1 Introduction 272\u003c\/p\u003e \u003cp\u003e14.3.2 Case: r \u0026lt; c 274\u003c\/p\u003e \u003cp\u003e14.3.3 Case: r ≥ c 274\u003c\/p\u003e \u003cp\u003e14.4 Simulation Results 275\u003c\/p\u003e \u003cp\u003e14.5 Conclusions 279\u003c\/p\u003e \u003cp\u003eReferences 279\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IX Game Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 From Colonel Blotto to Field Marshall Blotto 283\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePeter Baudains, Toby P. Davies, Hannah M. Fry and Alan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 283\u003c\/p\u003e \u003cp\u003e15.2 The Colonel Blotto Game and its Extensions 285\u003c\/p\u003e \u003cp\u003e15.3 Incorporating a Spatial Interaction Model of Threat 286\u003c\/p\u003e \u003cp\u003e15.4 Two-front Battles 288\u003c\/p\u003e \u003cp\u003e15.5 Comparing Even and Uneven Allocations in a Scenario with Five Fronts 289\u003c\/p\u003e \u003cp\u003e15.6 Conclusion 292\u003c\/p\u003e \u003cp\u003eReferences 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Modelling Strategic Interactions in a Global Context 293\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJanina Beiser\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 293\u003c\/p\u003e \u003cp\u003e16.2 The Theoretical Model 294\u003c\/p\u003e \u003cp\u003e16.3 Strategic Estimation 295\u003c\/p\u003e \u003cp\u003e16.4 International Sources of Uncertainty in the Context of Repression and Rebellion 297\u003c\/p\u003e \u003cp\u003e16.4.1 International Sources of Uncertainty Related to Actions 297\u003c\/p\u003e \u003cp\u003e16.5 International Sources of Uncertainty Related to Outcomes 299\u003c\/p\u003e \u003cp\u003e16.6 Empirical Analysis 301\u003c\/p\u003e \u003cp\u003e16.6.1 Data and Operationalisation 301\u003c\/p\u003e \u003cp\u003e16.7 Results 303\u003c\/p\u003e \u003cp\u003e16.8 Additional Considerations Related to International Uncertainty 304\u003c\/p\u003e \u003cp\u003e16.9 Conclusion 304\u003c\/p\u003e \u003cp\u003eReferences 305\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 A General Framework for Static, Spatially Explicit Games of Search and Concealment 306\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eThomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 306\u003c\/p\u003e \u003cp\u003e17.2 Game Theoretic Concepts 307\u003c\/p\u003e \u003cp\u003e17.3 Games of Search and Security: A Review 310\u003c\/p\u003e \u003cp\u003e17.3.1 Simple Search Games 310\u003c\/p\u003e \u003cp\u003e17.3.2 Search Games with Immobile Targets 311\u003c\/p\u003e \u003cp\u003e17.3.3 Accumulation Games 311\u003c\/p\u003e \u003cp\u003e17.3.4 Search Games with Mobile Targets 311\u003c\/p\u003e \u003cp\u003e17.3.5 Allocation Games 312\u003c\/p\u003e \u003cp\u003e17.3.6 Rendez-vous Games 312\u003c\/p\u003e \u003cp\u003e17.3.7 Security Games 313\u003c\/p\u003e \u003cp\u003e17.3.8 Geometric Games 313\u003c\/p\u003e \u003cp\u003e17.3.9 Motivation for Defining a New Spatial Game 314\u003c\/p\u003e \u003cp\u003e17.4 The Static Spatial Search Game (SSSG) 314\u003c\/p\u003e \u003cp\u003e17.4.1 Definition of the SSSG 314\u003c\/p\u003e \u003cp\u003e17.4.2 The SSSG and other Games 316\u003c\/p\u003e \u003cp\u003e17.4.3 The SSSG with Finite Strategy Sets 317\u003c\/p\u003e \u003cp\u003e17.4.4 Dominance and Equivalence in the SSSG 318\u003c\/p\u003e \u003cp\u003e17.4.5 Iterated Elimination of Dominated Strategies 323\u003c\/p\u003e \u003cp\u003e17.5 The Graph Search Game (GSG) 324\u003c\/p\u003e \u003cp\u003e17.5.1 Definition of the GSG 324\u003c\/p\u003e \u003cp\u003e17.5.2 The GSG with r ≠ 1 326\u003c\/p\u003e \u003cp\u003e17.5.3 Preliminary Observations 327\u003c\/p\u003e \u003cp\u003e17.5.4 Bounds on the Value of the GSG 330\u003c\/p\u003e \u003cp\u003e17.6 Summary and Conclusions 335\u003c\/p\u003e \u003cp\u003eReferences 336\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart X Networks\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Network Evolution: A Transport Example 343\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eFrancesca Pagliara, Alan G. Wilson and Valerio de Martinis\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 343\u003c\/p\u003e \u003cp\u003e18.2 A Hierarchical Retail Structure Model as a Building Block 344\u003c\/p\u003e \u003cp\u003e18.3 Extensions to Transport Networks 345\u003c\/p\u003e \u003cp\u003e18.4 An Application in Transport Planning 347\u003c\/p\u003e \u003cp\u003e18.5 A Case Study: Bagnoli in Naples 350\u003c\/p\u003e \u003cp\u003e18.6 Conclusion 360\u003c\/p\u003e \u003cp\u003eReferences 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 The Structure of Global Transportation Networks 363\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSean Hanna, Joan Serras and Tasos Varoudis\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 363\u003c\/p\u003e \u003cp\u003e19.2 Method 364\u003c\/p\u003e \u003cp\u003e19.3 Analysis of the European Map 366\u003c\/p\u003e \u003cp\u003e19.4 Towards a Global Spatial Economic Map: Economic Analysis by Country 368\u003c\/p\u003e \u003cp\u003e19.5 An East-west Divide and Natural Economic Behaviour 373\u003c\/p\u003e \u003cp\u003e19.6 Conclusion 376\u003c\/p\u003e \u003cp\u003eReferences 377\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Trade Networks and Optimal Consumption 378\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRobert J. Downes and Robert G. Levy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 378\u003c\/p\u003e \u003cp\u003e20.2 The Global Economic Model 379\u003c\/p\u003e \u003cp\u003e20.2.1 Introduction 379\u003c\/p\u003e \u003cp\u003e20.2.2 Data Sources 380\u003c\/p\u003e \u003cp\u003e20.2.3 Model Overview 380\u003c\/p\u003e \u003cp\u003e20.3 Perturbing Final Demand Vectors 380\u003c\/p\u003e \u003cp\u003e20.3.1 Introduction 380\u003c\/p\u003e \u003cp\u003e20.3.2 Perturbation Process 382\u003c\/p\u003e \u003cp\u003e20.4 Analysis 384\u003c\/p\u003e \u003cp\u003e20.4.1 Introduction 384\u003c\/p\u003e \u003cp\u003e20.4.2 A Directed Network Representation 384\u003c\/p\u003e \u003cp\u003e20.4.3 A Weighted Directed Network Representation 389\u003c\/p\u003e \u003cp\u003e20.4.4 Communities in the Network of Improvements 390\u003c\/p\u003e \u003cp\u003e20.5 Conclusions 393\u003c\/p\u003e \u003cp\u003eAcknowledgements 394\u003c\/p\u003e \u003cp\u003eReferences 394\u003c\/p\u003e \u003cp\u003eAppendix 396\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart XI Integration\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Research Priorities 399\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAlan G. Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eIndex 403\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eAlan Geoffrey Wilson\u003c\/strong\u003e, Centre for Advanced Spatial Analysis, University College London, UK. His research interests have been concerned with many aspects of mathematical modelling and the use of models in planning in relation to all aspects of cities and regions - including demography, economic input-output modelling, transport and locational structures. He was responsible for the introduction of a number of model building techniques which are now in common use internationally. These models have been widely used in areas such as transport planning. He made important contributions through the rigorous deployment of accounts' concepts in demography and economic modelling. In recent years he has been particularly concerned with applications of dynamical systems theory in relation to the task of modelling the evolution of urban structure, initially described in Catastrophe theory and bifurcation: applications to urban and regional systems. His current research, supported by ESRC and EPSRC grants of around ?3M, is on the evolution of cities and the dynamics of global trade and migration.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988755628261,"sku":"NP9781118922279","price":139.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118922279.jpg?v=1761781466","url":"https:\/\/k12savings.com\/es\/products\/approaches-to-geo-mathematical-modelling-isbn-9781118922279","provider":"K12savings","version":"1.0","type":"link"}