The Berge equilibrium: a game-theoretic framework for the golden rule of ethics
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Birkhäuser
[2020]
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| Series: | Static & dynamic game theory: foundations & applications
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxvi, 272 Seiten Illustrationen |
| ISBN: | 9783030255459 |
| ISSN: | 2363-8516 |
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| 245 | 1 | 0 | |a The Berge equilibrium |b a game-theoretic framework for the golden rule of ethics |c Mindia E. Salukvadze, Vladislav I. Zhukovskiy |
| 264 | 1 | |a Cham |b Birkhäuser |c [2020] | |
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Record in the Search Index
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| adam_text | Contents 1 What Is the Golden Rule of Ethics? .......................................................... 1.1 Scribitur ad narrandum, non ad probandum....................................... 1.2 World Religions About the Golden Rule........................................... 1.3 The Golden Rule and Philosophy........................................................ 1.4 What Does the Golden Rule Suggest?................................................ 1.5 The Golden Rule as the Key Principle of Social Life........................ 1.6 Moral Decline of Modern Society..................................................... 1.7 The Golden Rule and Policy.............................................................. 1.8 Is Ethical Policy Possible?................................................................. 1 1 2 4 5 7 10 12 13 2 Static Case of the Golden Rule................................................................... 2.1 What is the Content of the Golden Rule?............................................ 2.2 Main Notions...................................................................................... 2.2.1 Preliminaries......................................................................... 2.2.2 Elements of the Mathematical Model.................................. 2.2.3 Nash Equilibrium................................................................. 2.2.4 Berge Equilibrium........................................ 2.3 Compactness of the Set XB................................................................ 2.4 Internal Instability of the Set Xs
....................................................... 2.5 No Guaranteed Individual Rationality of the Set XB ....................... 2.6 Two-Player Game................................................................................ 2.7 Comparison of Nash and Berge Equilibria...................... 2.8 Sufficient Conditions.......................................................................... 2.8.1 Continuity of the Maximum Function of a Finite Number of Continuous Functions........................................ 2.8.2 Reduction to Saddle Point Design ...................................... 2.8.3 Germeier Convolution.......................................................... 2.9 Mixed Extension of a Noncooperative Game................................... 2.9.1 Mixed Strategies and Mixed Extension of a Game............ 2.9.2 Préambule............................................................................. 2.9.3 Existence Theorem................................................................ 17 17 18 18 21 25 27 28 30 32 34 36 37 37 38 40 44 44 47 48 xxiii
xxiv 3 4 Contents 2.10 Linear-Quadratic Two-Player Game................................................... 2.10.1 Preliminaries......................................................................... 2.10.2 Berge Equilibrium................................................................ 2.10.3 Nash Equilibrium................................................................. 2.10.4 Auxiliary Lemma................................................................. 2.10.5 Concluding Remarks............................................................. 51 52 53 55 56 58 The Golden Rule Under Uncertainty................. ..................................... 3.1 Uncertainty and Types of Uncertainty................................................ 3.1.1 Conceptual Meaning of Uncertainty................................... 3.1.2 Uncertainty in Economic Systems...................................... 3.1.3 Uncertainty in Mechanical Control Systems ..................... 3.1.4 Uncertainty in Decision-Making......................................... *3.1.5 Classification of Uncontrolled Factors................................. 3.1.6 Classification of Uncertainty................................................ 3.2 General Notions and Obtained Results.............................................. 3.2.1 Saddle point and maximin.................................................... 3.2.2 Auxiliary Results from Operations Research, Theory of Multicriteria Choice and Game Theory............ 3.3 Balanced Equilibrium as an Analog of Saddle Point....................... 3.3.1 Analogs of Saddle Point:
The Idea and Formalization...... 3.3.2 Pro et contra of Balanced Equilibrium................................ 3.3.3 Games with Separated Payoff Functions............................. 3.3.4 Existence in Mixed Strategies and One Remark................. 3.4 Strongly-Guaranteed Berge Equilibrium........................................... 3.4.1 Introduction........................................................................... 3.4.2 Maximin and Its Interpretation Using Two-Level Game... 3.4.3 Drawback of Balanced Equilibrium as Solution of Noncooperative Game Under Uncertainty..................... 3.4.4 Formalization......................................................................... 3.4.5 Existence in Mixed Strategies.............................................. 3.4.6 Linear-Quadratic Setup of Game......................................... 3.5 Slater-Guaranteed Equilibria.............................................................. 3.5.1 Definition and Properties.............................. 3.5.2 Existence of Guaranteed Equilibrium in Mixed Strategies................................ 3.5.3 Existence Theorem................................................................ 61 61 62 62 63 64 64 65 69 69 Applications to Competitive Economic Models........................................ 4.1 The Cournot Oligopoly Model............................................................ 4.1.1 Introduction ........................................................................... 4.1.2 Basic Notations and Definitions........................................... 4.1.3 The Cournot
Oligopoly and Equilibrium Strategies........... 4.1.4 Comparison of Payoffs: Berge Equilibrium vs. Nash Equilibrium ........................................................... 70 76 76 78 79 85 87 88 88 90 91 96 102 108 108 Ill 115 119 119 120 121 122 126
xxv Contents 4.2 4.3 4.4 5 The Cournot Duopoly with Import.................................................... 4.2.1 Mathematical Model............................................................. 4.2.2 Strongly-Guaranteed Equilibrium............... ....................... 4.2.3 Pareto-Guaranteed Equilibrium.......................................... The Bertrand Duopoly Model............................................................ 4.3.1 Mathematical Model............ ................................................ 4.3.2 Main Notions......................................................................... 4.3.3 Explicit Design of Berge and Nash Equilibria.................... 4.3.4 Use of Berge Equilibrium...... ............................................. 4.3.5 Choice of Appropriate Equilibrium on the Boundaries of the Constructed Domains................. 4.3.6 Compromising Behavioral Principles for Higher Benefits................................................................ The Bertrand Model with Import....................................................... 4.4.1 Mathematical Model............................................................. 4.4.2 Consideration of Import....................................................... 4.4.3 Calculation of Inner Pareto Minimum................................ 4.4.4 Design of Nash Equilibrium................................................. 4.4.5 Calculation of the Corresponding Profits............... ............ New Approaches to the Solution of Noncooperative Games and Multicriteria Choice
Problems........................................................... 5.1 A New Approach to Optimal Solutions of Multicriteria Choice Problems: Consideration of Savage-Niehans Risk.............. 5.1.1 The Savage-Niehans Principle of Minimax Regret........... 5.1.2 Strong Guarantees and Transition from Гс to 2/V-Criteria Choice Problem...................................... 5.1.3 Formalization of a Guaranteed Solution in Outcomes and Risks for Problem Гс..................................................... 5.1.4 Risks and Outcomes for Diversification of a Deposit into Sub-deposits in Different Currencies .......................... 5.2 A New Approach to Optimal Solutions of Noncooperative Games: Accounting for Savage-Niehans Risk.................................. 5.2.1 Principia Universalia............................................................. 5.2.2 How Can We Combine the Objectives of Each Player to Increase the Payoff and Simultaneously Reduce the Risk?................................................................... 5.2.3 Formalization of Guaranteed Equilibrium in Payoffs and Risks for Game (5.2.1).................................................. 5.2.4 Existence of Pareto Equilibrium in Mixed Strategies........ 5.2.5 De omni re scibili et quibusdam aliis................... 5.2.6 A la fin des fins........................................ 5.3 Cooperation in a Conflict of N Persons Under Uncertainty............ 5.3.1 Introduction.......................................................................... 5.3.2 Game of
Guarantees........................................................... 131 131 133 137 142 143 144 146 148 157 162 164 164 166 168 169 172 175 175 177 178 180 184 191 191 193 198 206 211 214 214 215 216
xxvi Contents 5.3.3 5.3.4 5.3.5 5.4 6 Coalitional Equilibrium........................................................ Sufficient Condition.............................................................. Existence of Coalitional Equilibrium in Mixed Strategies............................................................................... 5.3.6 Concluding Remarks.......................................... How Can One Combine the Altruism of Berge Equilibrium with the Selfishness of Nash Equilibrium? Hybrid Equilibrium .... 5.4.1 Introduction.......................................................................... 5.4.2 Formalization of Hybrid Equilibrium................................. 5.4.3 Properties of Hybrid Equilibria............................................ 5.4.4 Sufficient Conditions .......... 5.4.5 Existence of Pareto Hybrid Equilibrium in Mixed Strategies............................................................................... 5.4.6 Hybrid Equilibrium in Games Under Uncertainty.............. Conclusion........................ 216 217 218 224 225 225 226 228 230 232 239 245 Short Biographies................................................................................................ 251 References............................................................................................................. 259
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| adam_txt |
Contents 1 What Is the Golden Rule of Ethics? . 1.1 Scribitur ad narrandum, non ad probandum. 1.2 World Religions About the Golden Rule. 1.3 The Golden Rule and Philosophy. 1.4 What Does the Golden Rule Suggest?. 1.5 The Golden Rule as the Key Principle of Social Life. 1.6 Moral Decline of Modern Society. 1.7 The Golden Rule and Policy. 1.8 Is Ethical Policy Possible?. 1 1 2 4 5 7 10 12 13 2 Static Case of the Golden Rule. 2.1 What is the Content of the Golden Rule?. 2.2 Main Notions. 2.2.1 Preliminaries. 2.2.2 Elements of the Mathematical Model. 2.2.3 Nash Equilibrium. 2.2.4 Berge Equilibrium. 2.3 Compactness of the Set XB. 2.4 Internal Instability of the Set Xs
. 2.5 No Guaranteed Individual Rationality of the Set XB . 2.6 Two-Player Game. 2.7 Comparison of Nash and Berge Equilibria. 2.8 Sufficient Conditions. 2.8.1 Continuity of the Maximum Function of a Finite Number of Continuous Functions. 2.8.2 Reduction to Saddle Point Design . 2.8.3 Germeier Convolution. 2.9 Mixed Extension of a Noncooperative Game. 2.9.1 Mixed Strategies and Mixed Extension of a Game. 2.9.2 Préambule. 2.9.3 Existence Theorem. 17 17 18 18 21 25 27 28 30 32 34 36 37 37 38 40 44 44 47 48 xxiii
xxiv 3 4 Contents 2.10 Linear-Quadratic Two-Player Game. 2.10.1 Preliminaries. 2.10.2 Berge Equilibrium. 2.10.3 Nash Equilibrium. 2.10.4 Auxiliary Lemma. 2.10.5 Concluding Remarks. 51 52 53 55 56 58 The Golden Rule Under Uncertainty. . 3.1 Uncertainty and Types of Uncertainty. 3.1.1 Conceptual Meaning of Uncertainty. 3.1.2 Uncertainty in Economic Systems. 3.1.3 Uncertainty in Mechanical Control Systems . 3.1.4 Uncertainty in Decision-Making. '*3.1.5 Classification of Uncontrolled Factors. 3.1.6 Classification of Uncertainty. 3.2 General Notions and Obtained Results. 3.2.1 Saddle point and maximin. 3.2.2 Auxiliary Results from Operations Research, Theory of Multicriteria Choice and Game Theory. 3.3 Balanced Equilibrium as an Analog of Saddle Point. 3.3.1 Analogs of Saddle Point:
The Idea and Formalization. 3.3.2 Pro et contra of Balanced Equilibrium. 3.3.3 Games with Separated Payoff Functions. 3.3.4 Existence in Mixed Strategies and One Remark. 3.4 Strongly-Guaranteed Berge Equilibrium. 3.4.1 Introduction. 3.4.2 Maximin and Its Interpretation Using Two-Level Game. 3.4.3 Drawback of Balanced Equilibrium as Solution of Noncooperative Game Under Uncertainty. 3.4.4 Formalization. 3.4.5 Existence in Mixed Strategies. 3.4.6 Linear-Quadratic Setup of Game. 3.5 Slater-Guaranteed Equilibria. 3.5.1 Definition and Properties. 3.5.2 Existence of Guaranteed Equilibrium in Mixed Strategies. 3.5.3 Existence Theorem. 61 61 62 62 63 64 64 65 69 69 Applications to Competitive Economic Models. 4.1 The Cournot Oligopoly Model. 4.1.1 Introduction . 4.1.2 Basic Notations and Definitions. 4.1.3 The Cournot
Oligopoly and Equilibrium Strategies. 4.1.4 Comparison of Payoffs: Berge Equilibrium vs. Nash Equilibrium . 70 76 76 78 79 85 87 88 88 90 91 96 102 108 108 Ill 115 119 119 120 121 122 126
xxv Contents 4.2 4.3 4.4 5 The Cournot Duopoly with Import. 4.2.1 Mathematical Model. 4.2.2 Strongly-Guaranteed Equilibrium. . 4.2.3 Pareto-Guaranteed Equilibrium. The Bertrand Duopoly Model. 4.3.1 Mathematical Model. . 4.3.2 Main Notions. 4.3.3 Explicit Design of Berge and Nash Equilibria. 4.3.4 Use of Berge Equilibrium. . 4.3.5 Choice of Appropriate Equilibrium on the Boundaries of the Constructed Domains. 4.3.6 Compromising Behavioral Principles for Higher Benefits. The Bertrand Model with Import. 4.4.1 Mathematical Model. 4.4.2 Consideration of Import. 4.4.3 Calculation of Inner Pareto Minimum. 4.4.4 Design of Nash Equilibrium. 4.4.5 Calculation of the Corresponding Profits. . New Approaches to the Solution of Noncooperative Games and Multicriteria Choice
Problems. 5.1 A New Approach to Optimal Solutions of Multicriteria Choice Problems: Consideration of Savage-Niehans Risk. 5.1.1 The Savage-Niehans Principle of Minimax Regret. 5.1.2 Strong Guarantees and Transition from Гс to 2/V-Criteria Choice Problem. 5.1.3 Formalization of a Guaranteed Solution in Outcomes and Risks for Problem Гс. 5.1.4 Risks and Outcomes for Diversification of a Deposit into Sub-deposits in Different Currencies . 5.2 A New Approach to Optimal Solutions of Noncooperative Games: Accounting for Savage-Niehans Risk. 5.2.1 Principia Universalia. 5.2.2 How Can We Combine the Objectives of Each Player to Increase the Payoff and Simultaneously Reduce the Risk?. 5.2.3 Formalization of Guaranteed Equilibrium in Payoffs and Risks for Game (5.2.1). 5.2.4 Existence of Pareto Equilibrium in Mixed Strategies. 5.2.5 De omni re scibili et quibusdam aliis. 5.2.6 A la fin des fins. 5.3 Cooperation in a Conflict of N Persons Under Uncertainty. 5.3.1 Introduction. 5.3.2 Game of
Guarantees. 131 131 133 137 142 143 144 146 148 157 162 164 164 166 168 169 172 175 175 177 178 180 184 191 191 193 198 206 211 214 214 215 216
xxvi Contents 5.3.3 5.3.4 5.3.5 5.4 6 Coalitional Equilibrium. Sufficient Condition. Existence of Coalitional Equilibrium in Mixed Strategies. 5.3.6 Concluding Remarks. How Can One Combine the Altruism of Berge Equilibrium with the Selfishness of Nash Equilibrium? Hybrid Equilibrium . 5.4.1 Introduction. 5.4.2 Formalization of Hybrid Equilibrium. 5.4.3 Properties of Hybrid Equilibria. 5.4.4 Sufficient Conditions . 5.4.5 Existence of Pareto Hybrid Equilibrium in Mixed Strategies. 5.4.6 Hybrid Equilibrium in Games Under Uncertainty. Conclusion. 216 217 218 224 225 225 226 228 230 232 239 245 Short Biographies. 251 References. 259 |
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| index_date | 2024-07-03T17:10:24Z |
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| issn | 2363-8516 |
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| spelling | Salukvadze, M. E. 1933- Verfasser (DE-588)1206884819 aut The Berge equilibrium a game-theoretic framework for the golden rule of ethics Mindia E. Salukvadze, Vladislav I. Zhukovskiy Cham Birkhäuser [2020] © 2020 xxvi, 272 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Static & dynamic game theory: foundations & applications 2363-8516 Game Theory, Economics, Social and Behav. Sciences Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Game theory Operations research Management science Calculus of variations Zhukovskii, Vladislav Iosifovich Verfasser (DE-588)1067826157 aut Erscheint auch als Online-Ausgabe 978-3-030-25546-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032662272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Salukvadze, M. E. 1933- Zhukovskii, Vladislav Iosifovich The Berge equilibrium a game-theoretic framework for the golden rule of ethics Game Theory, Economics, Social and Behav. Sciences Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Game theory Operations research Management science Calculus of variations |
| title | The Berge equilibrium a game-theoretic framework for the golden rule of ethics |
| title_auth | The Berge equilibrium a game-theoretic framework for the golden rule of ethics |
| title_exact_search | The Berge equilibrium a game-theoretic framework for the golden rule of ethics |
| title_exact_search_txtP | The Berge equilibrium a game-theoretic framework for the golden rule of ethics |
| title_full | The Berge equilibrium a game-theoretic framework for the golden rule of ethics Mindia E. Salukvadze, Vladislav I. Zhukovskiy |
| title_fullStr | The Berge equilibrium a game-theoretic framework for the golden rule of ethics Mindia E. Salukvadze, Vladislav I. Zhukovskiy |
| title_full_unstemmed | The Berge equilibrium a game-theoretic framework for the golden rule of ethics Mindia E. Salukvadze, Vladislav I. Zhukovskiy |
| title_short | The Berge equilibrium |
| title_sort | the berge equilibrium a game theoretic framework for the golden rule of ethics |
| title_sub | a game-theoretic framework for the golden rule of ethics |
| topic | Game Theory, Economics, Social and Behav. Sciences Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Game theory Operations research Management science Calculus of variations |
| topic_facet | Game Theory, Economics, Social and Behav. Sciences Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Game theory Operations research Management science Calculus of variations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032662272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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