Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (eBook)

Preface 6
Contents 10
Economic modelling and financial markets 12
Agent-based models of economic interactions 13
1 Introduction 13
2 Order books 15
3 Wealth distributions 22
4 Minority games 28
5 Final remarks 33
6 Acknowledgements 34
References 34
On kinetic asset exchange models and beyond: microeconomic formulation, trade network, and all that 40
1 Introduction 40
2 Gas-like models 41
3 A microeconomic formulation 46
4 Models on directed networks 51
5 Preferential transactions and weighted trade network 55
6 Discussions and outlook 57
7 Acknowledgements 57
References 58
Microscopic and kinetic models in financial markets 60
1 Introduction 60
2 Microscopic models 61
3 Kinetic models 67
References 88
A mathematical theory for wealth distribution 90
1 Introduction 90
2 Kinetic wealth distribution models and mathematical tools 92
3 Results for the one-dimensional models 100
4 Results in the two-dimensional case 113
5 Conclusions 119
Acknowledgements 119
References 120
Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences 123
1 Tolstoy’s dream 123
2 Statistical equilibrium in economics 124
3 An example: the taxation-redistribution game 127
Appendix: the P´olya distribution 134
References 141
Social modelling and opinion formation 142
New perspectives in the equilibrium statistical mechanics approach to social and economic sciences 143
1 Introduction 144
2 A brief introduction to many-body dynamics 145
3 Equilibrium behavior 149
4 Equilibrium statistical mechanics of the “ 2- body” model 151
5 Beyond detailed balance: diffusive strategic dynamics 165
6 Statics of many body interactions 168
7 A simple application to trading in markets 177
8 Conclusions and Outlooks 178
References 179
Kinetic modelling of complex socio- economic systems 181
1 Introduction 181
2 Some reasonings on the mathematical modelling of complex socio- economic systems 182
3 Mathematical tools 185
4 An example of application: competition for a secession under influence of media 192
5 Simulations 198
6 Conclusions 204
References 206
Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion 208
1 Opinion dynamics 208
2 Binary opinion dynamics and beyond 213
3 Agents based model and discrete dynamical systems 218
4 The kinetic approach 220
5 New opportunities: an opinion 223
References 223
Global dynamics in adaptive models of collective choice with social influence 227
1 Introduction 227
2 Galam’s model 229
3 A mathematical formalization of Schelling model 231
4 The case of impulsive agents 238
5 A general model with different switching propensity 243
6 Conclusion 246
References 247
Modelling opinion formation by means of kinetic equations 249
1 Sociophysics 249
2 Kinetic approach in sociophysics: tools and methods 252
3 The main phenomenon: the compromise 256
4 Other sociological phenomena 264
5 Conclusion 270
References 271
Human behavior and swarming 275
On the modelling of vehicular traffic and crowds by kinetic theory of active particles 276
1 Introduction 276
2 Common features of vehicular traffic and crowds 278
3 Mathematical representation and structures 280
4 On the modelling of vehicular traffic 285
5 On the modelling of crowds 289
6 Critical analysis and perspectives 292
References 297
Particle, kinetic, and hydrodynamic models of swarming 300
1 Introduction 300
2 Particle models 302
3 Kinetic models 306
4 Hydrodynamic models 315
5 Variations on the theme 322
6 Numerical experiments 329
References 335
Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints 340
1 Self-organization in many-particle systems 340
2 Classical vs. intelligent particles 344
3 What mechanics for intelligent systems? 346
4 Mathematical modeling by time-evolving measures 348
5 Numerical results 356
6 Conclusions and research perspectives 363
Acknowledgements 364
References 364
Statistical physics and modern human warfare 368
1 Introduction 368
2 Two-population conflict model 370
3 Encounter fragmentation model 382
4 Outlook 391
Appendix: derivation of analytic solution for encounter fragmentation ( EF) model 392
References 398
Diffusive and nondiffusive population models 400
1 Introduction 400
2 Initial-value population models 401
3 Reaction–diffusion population models 403
4 Cross-diffusion population models 406
5 Structured population models 416
6 Time-delayed population models 420
References 421
Index 429