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Table of Contents
Intro; Preface; Contents; 1 Introduction; 1.1 General Background; 1.2 Few Notes on Game Theory; 1.2.1 Nash Equilibrium; 1.2.2 Two-Strategy Games; 1.2.2.1 The Prisoner's Dilemma; 1.2.2.2 The Public Goods Game; 1.3 Evolutionary Game Theory; 1.3.1 Strategy Revision Phase; 1.3.2 Cooperation: Motivations and Mechanisms; Bibliography; 2 Modeling Complex Systems; 2.1 Population Dynamics; 2.1.1 Replicator Dynamics; 2.2 The Ising Model; 2.2.1 Mean Field; 2.2.2 Curie-Weiss Model; 2.2.3 Landau Theory of Phase Transitions; 2.2.4 Numerical Simulations; 2.3 Complex Networks: A Very Short Overview.
2.3.1 Network Structures2.3.1.1 Classical Random Networks; 2.3.1.2 Scale-Free Networks; 2.3.1.3 Small-World Networks; Bibliography; 3 Evolutionary Games I: Statistical Physics; 3.1 Phase Transitions in the Prisoner's Dilemma; 3.1.1 Model; 3.1.1.1 Mean Field Approach; 3.1.1.2 Mapping Agents to Gas Particles; 3.1.2 Results; 3.1.3 Order-Disorder Phase Transitions in the Agent Population; 3.2 The Role of the Temperature in the Spatial Public Goods Game; 3.2.1 Model; 3.2.1.1 The Noise and the General Setup of the Model; 3.2.2 Results; 3.2.3 Conclusion; Bibliography.
4 Evolutionary Games II: Applications4.1 The Role of Conformity in the Public Goods Game; 4.1.1 Model; 4.1.2 Results; 4.1.3 Conclusion; 4.2 Solving Optimization Problems by the Public Goods Game; 4.2.1 Model; 4.2.2 Results; 4.2.3 Conclusion; Appendix 1; Appendix 2; Bibliography; 5 Conclusions; 5.1 Summary; 5.2 Perspectives; Bibliography.
2.3.1 Network Structures2.3.1.1 Classical Random Networks; 2.3.1.2 Scale-Free Networks; 2.3.1.3 Small-World Networks; Bibliography; 3 Evolutionary Games I: Statistical Physics; 3.1 Phase Transitions in the Prisoner's Dilemma; 3.1.1 Model; 3.1.1.1 Mean Field Approach; 3.1.1.2 Mapping Agents to Gas Particles; 3.1.2 Results; 3.1.3 Order-Disorder Phase Transitions in the Agent Population; 3.2 The Role of the Temperature in the Spatial Public Goods Game; 3.2.1 Model; 3.2.1.1 The Noise and the General Setup of the Model; 3.2.2 Results; 3.2.3 Conclusion; Bibliography.
4 Evolutionary Games II: Applications4.1 The Role of Conformity in the Public Goods Game; 4.1.1 Model; 4.1.2 Results; 4.1.3 Conclusion; 4.2 Solving Optimization Problems by the Public Goods Game; 4.2.1 Model; 4.2.2 Results; 4.2.3 Conclusion; Appendix 1; Appendix 2; Bibliography; 5 Conclusions; 5.1 Summary; 5.2 Perspectives; Bibliography.