Динамические модели эколого-экономических проблем с переключением режимов: Коллективная монография / Отв. ред. Д.В. Кузютин и А.В. Тур.— СПб.: Изд-во РХГА, 2023. — 232 с.
ISBN 978-5-907613-24-9
В монографии представлены результаты исследований различных динамических теоретико-игровых моделей эколого-экономического менеджмента с возможностью переключения режимов в процессе развития игры и при наличии неопределенностей различного вида. В частности, рассмотрены модели с сезонными (периодическими) переключениями значений параметров моделируемых динамических систем; модели добычи природных ресурсов со случайной продолжительностью и возможными изменениями структуры вероятностного распределения; динамические модели добычи невозобновляемых ресурсов с неопределенностью относительно начального запаса ресурса; многошаговые и многокритериальные модели добычи возобновляемых ресурсов с возможностью переключения режима с кооперативного сценария на некооперативный, а также с неопределенностью относительно коэффициентов относительной важности используемых игроками критериев. С использованием методов теории оптимального управления, динамической теории игр, теории вероятностей и теории многокритериальной оптимизации построены некооперативные и кооперативные решения, изучены их свойства и предложены механизмы имплементации.
Книга адресована специалистам в области теории динамических игр, оптимального управления, экологии и экономики природопользования.
УДК 519.837:502.131
ББК 22.18:20.18:65.28
Д46
Рецензенты:
д.ф.-м.н., профессор, декан факультета прикладной математики-процессов управления
Санкт-Петербургского государственного университета Л.А. Петросян;
д.ф.-м.н., зам.директора по научной работе Института прикладных математических исследований
Карельского научного центра РАН А.Н. Реттиева
Ответственные редакторы:
к.ф.-м.н., доц. Д.В. Кузютин, доцент кафедры МТИиСР СПбГУ, доцент НИУ ВШЭ;
к.ф.-м.н., доц. А.В. Тур, доцент кафедры МТИиСР СПбГУ.
Авторский коллектив:
Балас Т.Н., Бондарев А.В., Громова Е.В., Кузютин Д.В., Липко И.В.,
Марова Е.В., Марченко И.В., Панкратова Я.Б., Светлов Р.В., Смирнова Н.В.,
Скородумова Ю.В., Тантлевский И.Р., Тур А.В., Заремба А.В.
Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта
№ 21-51-12007 «Гибридное оптимальное управление в задачах эколого-экономического
менеджмента с переключением режимов»
© Коллектив авторов, 2023
© АНО ВО РХГА им. Ф.М. Достоевского, 2023
The reported study was funded by RFBR and DFG, project number 21-51-12007
Contributors:
Tatyana Balas, Anton Bondarev, Ekaterina Gromova, Denis Kuzyutin,
Ivan Lipko, Ekaterina Marova, Irina Marchenko,Yaroslavna Pankratova,
Yulia Skorodumova, Nadezhda Smirnova, Roman Svetlov, Igor Tantlevskij,
Anna Tur, Anastasiia Zaremba
Dynamical models of ecological-economic problems with regime shifts: Collective monograph / Ed. by D.V. Kuzyutin and A.V. Tur. — St. Petersburg: Тhe Russian Christian Academy for the Humanities named after Fyodor Dostoevsky Publ., 2023. — 232 p.
ISBN 978-5-907613-24-9
The monograph presents the results of studies of various dynamic game-theoretic models of environmental and economic management with the possibility of regime shifts during the game evolution and in the presence of uncertainties of various types. In particular, models with seasonal (periodic) switchings of parameter values of the simulated dynamic systems are considered; models of natural resource extraction with random duration and possible changes in the structure of the probability distribution; dynamic models of non-renewable resource extraction with uncertainty regarding the initial resource stock; multistage and multi-criteria models for the extraction of renewable resources with the ability to switch modes from a cooperative to a non-cooperative scenario, as well as with uncertainty regarding the coefficients of the relative importance of different objectives used by the players. Using methods of optimal control theory, dynamic game theory, probability theory and multicriteria optimization theory, non-cooperative and cooperative solutions are constructed, their properties are studied and some implementation mechanisms are proposed.
The book is addressed to specialists in the field of dynamic game theory, optimal control, ecology and environmental economics.
© Contributing authors, 2023
© ANO «RCAH», 2023
Contents
Preface 11
1 Bi-modal resource management problems with regime switches 13
1.1 Resource management problems with exogenous regime switches 13
1.1.1 Pollution control problem with a switch of seasonable component 13
1.1.2 Seasonal periodic solution 17
1.1.3 Differential game with random time horizon and composite distribution function 21
1.1.4 Hybrid optimal control problem 23
1.1.5 Resource extraction problem with a switch of the hazard function 27
1.2 Resource management problems with endogenous regime switches 34
1.2.1 Differential game of pollution control. Comparison analysis of cooperative and non-cooperative scenarios 34
1.2.2 Value of Cooperation 39
1.2.3 Reclamation of a Resource Extraction Site Model with Random Components. Comparison analysis of cooperative and non-cooperative scenarios 40
2 Non-renewable resource extraction games with switches and uncertainties 57
2.1 The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon 57
2.1.1 Introduction 57
2.1.2 Problem Statement 58
2.1.3 System of Hamilton–Jacobi–Bellman Equations 60
2.1.4 Example 61
2.1.5 Time-Dependent Switch 61
2.1.6 State-Dependent Switch 65
2.1.7 Conclusions 68
2.2 On the Estimation of the Initial Stock in the Problem of Resource Extraction 72
2.2.1 Introduction 72
2.2.2 Problem Statement 72
2.2.3 Nash Equilibrium 76
2.2.4 Optimal Estimate for the Initial Resource Stock 77
2.2.5 Conclusions 79
3 Extensive-form games in economics and ecology management 83
3.1 Long-term implementation of the cooperative solution in a multistage multicriteria game 83
3.1.1 Introduction 83
3.1.2 Multistage multicriteria game with perfect information 85
3.1.3 Pareto optimal solution 87
3.1.3.1 Strong time consistency property 87
3.1.3.2 The Minimal Sum of Relative Deviations rule 88
3.1.4 Constructing a characteristic function for multicriteria game 89
3.1.5 Long-term implementation of the cooperative solution 91
3.1.5.1 The imputation distribution procedure and its properties 91
3.1.5.2 Choice of supporting imputation for the core 93
3.1.6 Example. Implementation of three payment schedules for given multicriteria game 95
3.1.7 Conclusion 97
3.2 A-Subgame Concept and the Solutions Properties for Multistage Games with Vector Payoffs 101
3.2.1 Introduction 101
3.2.2 Multistage game with vector payoffs 102
3.2.3 Pareto equilibria and its properties 104
3.2.4 Designing a cooperative solution 106
3.2.5 The sustainability of a cooperative agreement 108
3.2.6 Implementation of the A-incremental IDP 110
3.2.7 Conclusion 111
3.3 Cooperation enforcing in multistage multicriteria game: new algorithm and its implementation 115
3.3.1 Introduction 115
3.3.2 Multistage game with vector payoffs 116
3.3.3 Designing a cooperative solution 117
3.3.4 Imputation distribution procedure and its properties 120
3.3.5 A-incremental IDP may imply negative current payments 122
3.3.6 Refined A-incremental IDP and its implementation 124
3.3.7 Conclusion 126
3.4 Minimal Current Payments Algorithm for Sustainable Cooperation in Multicriteria Game 128
3.4.1 Introduction 128
3.4.2 A cooperative solution for multistage multicriteria game 129
3.4.3 The properties of a payment schedule 130
3.4.4 The minimal current payments IDP 131
3.4.5 Conclusion 132
4 Extensive-form games with chance moves. _-subgame-perfect Core 135
4.1 On the Cooperative Behavior in Multistage Multicriteria Game with Chance Moves 135
4.1.1 Introduction 135
4.1.2 Multistage game with chance moves and vector payoffs 136
4.1.3 Cooperative behavior 138
4.1.4 Sustainability of the Shapley value 141
4.1.5 Conclusion 144
4.2 Subgame Consistent Cooperative Behavior in an Extensive form Game with Chance Moves 146
4.2.1 Introduction 147
4.2.2 Extensive-form game with chance moves 149
4.2.3 Refined backwards induction procedure to construct a unique SPE 151
4.2.4 Cooperative strategies and trajectories 154
4.2.5 Subgame consistency and incremental IDP 157
4.2.6 Conclusion 162
4.3 Subgame Perfect Pareto Equilibria for Multicriteria Game with Chance Moves 165
4.3.1 Introduction 165
4.3.2 Pareto equilibria in multicriteria game 166
4.3.3 Choosing a unique subgame perfect Pareto equilibrium 167
4.3.4 The algorithm implementation 168
4.3.5 Conclusion 169
4.4 A novel payoff distribution procedure for sustainable cooperation in an extensive game with payoffs at all nodes 172
4.4.1 Introduction 172
4.4.2 Extensive-form game with current payoffs at each node 173
4.4.3 Payoff distribution procedure and the subgame-perfect core concept. 174
4.4.4 Properties and implementation of the β-S-P Core 175
4.4.5 β-S-P Core for fishery-management extensive-form model 178
4.4.6 Concluding remarks 180
5 Multistage and multi-objective models 185
5.1 A cooperation scheme in multistage game of renewable resource extraction with asymmetric players 185
5.1.1 Introduction 185
5.1.2 The Model. Non-cooperative behavior 186
5.1.3 Cooperative behavior. β-S-P Core 188
5.1.4 An algorithm for choosing unique PDP from β-S-P Core 190
5.1.5 Numerical example 191
5.1.6 Concluding remarks 193
5.2 A dynamic multicriteria game of renewable resource extraction with environmentally concerned players 196
5.2.1 Introduction 197
5.2.2 The Model. Non-cooperative behavior 197
5.2.2.1 Model specification 197
5.2.2.2 Pareto equilibria 198
5.2.2.3 Single-criterion game with an economic objective 199
5.2.2.4 Non-cooperative solution for a multicriteria game 200
5.2.3 Cooperative behavior 201
5.2.3.1 Cooperation in a single-criterion game with an economic objective 201
5.2.3.2 Cooperation in a bicriteria game 202
5.2.4 Concluding remarks 204
5.3 Sustainable Cooperation in a Bicriteria Game of Renewable Resource Extraction 207
5.3.1 Introduction 207
5.3.2 The Model 208
5.3.3 Non-Cooperative Solution 209
5.3.4 Cooperative Solution 211
5.3.5 Sustainability Of A Cooperative Agreement 213
5.3.6 Numerical Example 215
5.3.7 Concluding Remarks 217
5.4 A multistage bicriteria production game with pollution control 221
5.4.1 Introduction 221
5.4.2 The Model 221
5.4.3 Single-criterion game with only economic objective 223
5.4.3.1 Non-cooperative behavior 223
5.4.3.2 Cooperation in a single-criterion game 224
5.4.4 Bicriteria game analysis 225
5.4.5 Numerical Example 227
5.4.6 Concluding Remarks 227
Научное издание
Динамические модели
эколого—экономических проблем
с переключением режимов
Коллективная монография
Ответственные редакторы
Денис Вячеславович Кузютин, Анна Викторовна Тур
Dynamical models
of ecological-economic problems
with regime shifts
Collective monograph
Ed. by D.V.Kuzyutin and A.V.Tur
Директор издательства А. А. Галат
Макет Н. В. Смирнова
Дизайн обложки О. Д. Курта
Печатается без издательского редактирования
Подписано в печать 01.12.2023. Формат 60×90 1/8
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