A General Mathematical Theory of the Dynamic Global Political Economy

William Jevons (1866 and 1871) established a ground-breaking milestone with "A General Mathematical Theory of Political Economy" for economic analysis. Jevons' work was praised as the start of the mathematical method in the discipline of economics, which is inherently a subject involved with mathematics and quantities. This book focuses on the most fast-evolving and encompassing area in political economy — the dynamic global political economy. Under the high level of globalization currently, intertemporal and cross-boundary interactive elements are present in political-economic encounters. Indeed, almost all studies in the political economy may fall into the study of dynamic global political economy. Since the world has changed significantly, new mathematics developed by the authors of this book is used to formulate a general mathematical theory for the dynamic global political economy nowadays. A distinctive feature of the current book is that it combines advanced mathematics, game-theoretic concepts, and economics to develop a general mathematical theory supporting the study of the dynamic global political economy. The book covers mathematical theory for different areas of the dynamic global political economy. In addition, it explicates the application of the mathematical theory in real-world scenarios, including (i) environmental degradation under an uncoordinated interaction scenario, (ii) global climate accords with collaboration and cooperation, (iii) trade network involving the Belt-Road Initiative (BRI) and Build Back Better World (B3W) Initiative, and (iv) random termination of international joint ventures. Contents Preface About the Authors 1. Introduction 1. Pressing Issues in Global Political Economy 1.1. Nuclear weapons and threats 1.2. Environmental degradation and climate change 1.3. Space race with militarization of new frontier 1.4. Development of artificial intelligence 1.5. Cyberattacks 1.6. Global water crisis 1.7. Spread of false information on social media 1.8. Biotechnological developments 1.9. Trade war 2. Mathematical Structure of the Global Political Economy 3. Organization of this Book References 2. A Disquisition on Global Political Economy 1. Political Economic Systems 2. An Overview of the Development of Political Economy 2.1. Before the 16th century 2.2. From 16th to early 20th century 2.3. Schools of political-economic thought in the 20th century 2.3.1. The Austrian School 2.3.2. The Keynesian School 2.3.3. The Chicago School 2.4. Original mathematics in economics 3. Rise of Global Political Economy 4. Toward Time-consistent GPE: Theoretical Underpinning 4.1. Time consistency and subgame consistency 4.2. Approaches of GPE Policy formulation 5. A General Mathematical Theory of Political Economy Revisited 5.1. Economics is inherently mathematical 5.2. Pain, pleasure, and motivation 5.3. Quantity of feeling and utility References 3. Uncoordinated Interaction in a Dynamic World: Mathematical Theory and Explication in Environmental Degradation 1. Description of the Dynamic GPE 1.1. The state of the economy and its evolution 1.2. Target controls/strategies 1.3. Evolution of the state 1.4. The payoffs of the nations 1.5. Government policy instruments 2. Game Formulation and Mathematical Solution Theory 2.1. Mathematical representation of constituent elements 2.2. Mathematical solution theory 3. Policy Analysis and Cost of Individually Rational Self-Seeking 4. An Explication in Environmental Degradation 4.1. Environmental degradation 4.2. Damaging anthropogenic impacts 4.3. Modeling the uncoordinated environmental problem 4.3.1. The set of target controls 4.3.2. State variables and evolution dynamics 4.3.3. Government objectives and payoffs 4.3.4. Characterization of uncoordinated environmental management 5. A Computational Illustration 5.1. Problem formulation 5.2. Equilibrium outcome 5.3. Policy instruments and implementation 6. Notes References 4. Coordination and Cooperation: Mathematical Theory and Explication in Global Climate Agreement 1. Theoretical Underpinnings for Coordination and Cooperation 2. Mathematical Theory for Cooperative Optimization 2.1. Pareto optimal target controls under coordination 2.2. Subgame-consistent sharing 3. Subgame-Consistent Payoff Distribution 3.1. Payoff distribution procedure 3.2. Other gain-sharing optimality principle considerations 4. Price of Anarchy and Cost of Delay 5. Explication in Global Climate Agreement 5.1. Existing challenges in global climate agreement 5.2. Modelling global climate agreement 5.2.1. The set of target controls 5.2.2. State variables and evolution dynamics 5.2.3. Government objectives and payoffs 5.2.4. Sustainable technology 5.2.5. Cooperative curtailment of pollution 6. Subgame-Consistent Cooperation 6.1. Gain-distribution optimality principle 6.2. Subgame-consistent payoff distribution 7. A Computational Illustration 7.1. Problem formulation 7.2. Collaborative outcome 7.3. Global policy instruments and implementation 7.4. Subgame-consistent payoff distribution among nations 7.5. Other subgame-consistent payoff distributions 8. Chapter Notes References 5. Coalition and Blocs: Mathematical Theory and Explication in Trade Networks 1. Coalition and Bloc Formation 2. Mathematical Foundation of GPE with Coalitions 2.1. Characterization of GPE with coalitions 2.2. Coalitional equilibrium 2.3. Intra-coalition payoff distribution 3. Grand Coalition Cooperation 3.1. Pareto optimal target controls 3.2. Coalition payoff distribution 4. Explication in Trade Networks 4.1. China’s Belt-Road Initiative 4.2. Build Back Better World (B3W) Initiative 4.3. Coalitional equilibrium and intra-coalition payoff distribution 4.3.1. Coalition equilibrium 4.3.2. Intra-coalition payoff distribution 5. Grand Coalition Cooperation Analysis 5.1. Pareto optimal target controls 5.2. Coalition payoff distribution 5.3. Intra-coalition payoff distribution 6. A Computational Illustration 6.1. Game equilibrium 6.2. Intra-coalition payoff distribution 6.3. Grand coalition cooperation and efficient outcomes 7. Chapter Notes References 6. Random Termination Mathematical Theory and Explication in International Joint Venture 1. Termination of International Institutions 2. Game Formulation and Mathematical Solution Theory 2.1. Characterization of the game 2.2. Mathematical solution theory 3. Dynamic Cooperation under Random Termination 3.1. Group optimality and individual rationality 3.2. Subgame-consistent solutions and payment mechanism 4. An Explication in International Joint Venture 4.1. Maximization of joint venture profits 4.2. Subgame-consistent sharing of venture payoff 5. A Computational Illustration: Part I 5.1. Game formulation 5.2. Game equilibrium outcome 6. A Computational Illustration: Part II 6.1. Game formulation and group payoff maximization 6.2. Subgame-consistent payoff distribution 7. Chapter Notes References 7. Mathematical Solution Mechanisms 1. Durable-Strategies Dynamic Optimization (Theorem I) 2. Solution of Durable-Strategies Dynamic Games (Theorem II) 3. Dynamically Consistent Solutions and Payment Mechanism (Theorem III) 4. Random Horizon Dynamic Optimization under Durable Strategies (Theorem IV) 5. Solution for Random Horizon Dynamic Games with Durable Strategies (Theorem V) 6. Subgame-Consistent Payment Mechanism under Random Termination (Theorem VI) References Mathematical Appendices for Computational Illustrations Appendix A: Proof of Proposition 5.1 in Chapter 3 Appendix B: Proof of Proposition 8.1 in Chapter 4 Appendix C: Proof of Propositions 6.1 and 6.2 in Chapter 5 Appendix D: Proof of Propositions 6.5 and 6.6 in Chapter 5 Appendix E: Proof of Proposition 5.1 in Chapter 6 Appendix F: Proof of Proposition 6.1 in Chapter 6 Index