Games and Dynamics in Economics (Essays in Honor of Akio Matsumoto) ||

This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly--but not solely--based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact. Nonlinear dynamical systems, represented by difference and differential and functional equations, are extensively used to simulate the behavior of time-evolving economic systems, also in the presence of time lags, discontinuities, and hysteresis phenomena. In addition, some theoretical issues and particular applications are discussed, as well. The contributions gathered here offer an up-to-date review of the latest research in this rapidly developing research area Preface 1 5 Preface 2 7 Introduction 7 Summary of the Scientific Works of Prof. Matsumoto 7 A Note on Akio’s Passion for the Beatles 9 Contributions of This Volume 10 Papers on Economic Dynamics 10 Papers on Game Theory 11 Papers on Related Area 12 Preface 3 13 Magical Mystery Tour from Linearity to Nonlinearity 10 Contents 19 Contributors 21 Dynamics 24 Coupled Chaotic Systems and Extreme Ecologic-Economic Outcomes 25 1 Introduction 25 2 A Coupled Climate-Economy Model 26 3 Flare Attractors and Extreme Ecologic-Economic Outcomes 28 4 Coupled Chaotic Dynamics in Renewable Resource Markets 30 5 Policy in Complex Multi-level Hierarchies with Bounded Rationality 32 6 Conclusions 34 References 34 A Co-evolutionary Model for Human Capital and Innovative Firms 38 1 Introduction 39 2 Setup of the Model 41 2.1 Firms and Labor Market 43 2.2 Firms and Workers Evolutionary Dynamics 45 3 Evolutionary Dynamics of the Economy 47 3.1 The Feasible Transition Paths 48 4 Conclusion 51 References 52 Path Dependence in Models with Fading Memory or Adaptive Learning 54 1 Introduction 55 2 From Beliefs to Realizations: Rational Expectations and Learning Dynamics 57 2.1 Adaptive Learning and Reduction to One-Dimensional Dynamics 58 2.2 Statistical Learning and Reduction to Two Dimensional Dynamics 60 3 Limit Sets and Basins of Attraction for Statistical Learning With fading Memory 65 3.1 Global Properties and Structure of the Basins of The two-Dimensional Triangular Map 67 3.2 Increasing Maps 72 3.3 The Particular Case of Bray Learning 73 4 Examples 74 4.1 Unimodal Maps: A Cobweb Model 74 4.2 Bimodal Maps: Coexisting Stable REEs and the Problem Of equilibrium Selection 81 4.3 An O.G. Forward Looking Model Represented by an Increasing Map 83 5 Conclusions and Further Research 86 References 86 Come Together: The Role of Cognitively Biased Imitators in a Small Scale Agent-Based Financial Market 89 1 Introduction 89 2 The Benchmark Model 92 2.1 Steady States and Local Stability 93 3 The Model with Imitators 96 3.1 The Complete Model 98 4 Imitators and Local Stability of the Fundamental Steady State 100 4.1 The Strong Fundamentalists Dominance Scenario 101 4.2 The Weak Fundamentalists Dominance Scenario 102 4.3 The Weak Chartists' Dominance Scenario 103 4.4 The Strong Chartists' Dominance Scenario 104 5 Conclusions 105 References 106 Evolutionary Tax Evasion, Prospect Theory and Heterogeneous Taxpayers 109 1 Introduction 109 2 Model 112 2.1 Agents Preferences 113 2.2 Evolutionary Setup 113 2.3 Optimal Enforcement 114 3 Dynamic Analysis 115 4 Concluding Remarks 120 References 120 On Dynamics of a Three-Country Kaldorian Model of Business Cycles with Fixed Exchange Rates 123 1 Introduction 123 2 Formulation of the Model 125 3 Mathematical Analysis of a Special Case 129 4 Numerical Simulations 132 5 Concluding Remarks 141 References 143 Eductive Stability, Heterogeneous Information Costs and Period-Two Cycle Multiplicity 145 1 Introduction 146 2 The Model with Two Types of Biased Fundamentalists 148 3 The Model with Several Types of Biased Fundamentalists 154 4 Conclusion 160 References 160 Nöther’s Theorem and the Lie Symmetries in the Goodwin-Model 162 1 Introduction 163 2 The Generalized Nöther’s Theorem and the Conservation Laws 164 3 Goodwin’s Non-linear Dynamic System 166 4 The Lagrangian and Hamiltonian of Goodwin’s Non-linear Dynamic System 167 5 The Lie Symmetries of Goodwin’s Non-linear Dynamic System 168 6 Numerical Study 169 7 Conclusions 172 References 172 Games 174 Mixed Duopolies with Advance Production 175 1 Introduction 175 2 The Framework 177 3 The Strong Private Firm Case 180 3.1 Simultaneous Moves 181 3.2 Public Firm Moves First 185 3.3 Private Firm Moves First 186 4 The Weak Private Firm Case 187 4.1 Simultaneous Moves 188 4.2 Public Firm Moves First 191 4.3 Private Firm Moves First 192 5 The High Unit Cost Case 193 5.1 Simultaneous Moves 193 5.2 Public Firm Moves First 196 5.3 Private Firm Moves First 197 6 Solution of the Timing Game 198 7 Corollaries and Concluding Remarks 200 References 201 Necessary Conditions for Concave and Cournot Oligopoly Games 203 1 Introduction 203 2 A General Framework for Necessary Conditions in Mathematical programming and Game Theory 204 3 Joó-type Necessary Conditions for Concave Games 206 4 Necessary Conditions for Cournot Oligopoly Games to Have a Pure Nash Equilibrium 209 5 Conclusion 211 References 211 Set-Valued Techniques in Dynamic Economic Models 213 1 Introduction 213 2 Nonconvex Control Problems 214 3 Conjugate Functions 214 4 Differential Inclusions 215 5 The Existence of Optimal Control 216 6 Implicit Differential Schemes 218 7 A Set-Valued Inverse-Continuity Theorem 219 8 Application to a Generalized Dynamic Input-Output Economic Model 219 References 221 Agent Behavior and Transitions in N-Person Social Dilemma Games 222 1 Introduction 223 2 Agent Behavior on the Plateaus 230 2.1 Prisoners' Dilemma Plateau 230 2.2 Leader/Battle of the Sexes Plateau 232 2.3 Harmony/Deadlock Plateau 234 3 Analysis of Transitions Between Plateaus 236 4 Impacts of Changing Parameters 241 5 Conclusions 244 References 245 Related Topics 247 Optimizing Imperfect Preventive Maintenance Policy for a Multi-unit System with Different Virtual Ages 248 1 Introduction 248 2 Problem Definition 250 2.1 Problem Formulation 251 3 Numerical Examples 255 3.1 Example 1 255 3.2 Example 2 259 3.3 Case Study 259 4 Conclusion 269 References 269 Newton-Type Solvers Using Outer Inverses for Singular Equations 271 1 Introduction 271 2 Mathematical Background 272 3 Semilocal Convergence 273 4 Local Convergence 280 5 Conclusion 282 References 282 Properties of Linear Time-Dependent Systems 284 1 Introduction 284 2 Preliminaries 285 2.1 The Kalman-Type Reachability Theorem 286 2.2 The Kalman-Type Duality Theorem 287 3 Lie-Algebras 288 3.1 Application for Solving System States 288 3.2 Determination of Terminal State 291 4 General Reachability Conditions 294 5 Conclusions 302 References 302