Supermodularity and complementarity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1998
|
| Series: | Frontiers of economic research
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 272 S. |
| ISBN: | 0691032440 9780691032443 |
Staff View
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| 245 | 1 | 0 | |a Supermodularity and complementarity |c Donald M. Topkis |
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Record in the Search Index
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|---|---|
| adam_text | Contents
I
Preface xi
Chapter 1 Introduction 3
Chapter 2 Lattices, Supermodular Functions, and
Related Topics 7
2.1 Introduction 7
2.2 Partially Ordered Sets and Lattices 11
2.2.1 Definitions, Notation, and Some Basic Properties 11
2.2.2 Sublattice Structure 17
2.3 Completeness and Topological Properties 29
2.4 Induced Set Ordering 32
2.5 Fixed Points 38
2.6 Supermodular Functions on a Lattice 42
2.6.1 Characterization and Complementarity 42
2.6.2 Transformations 49
2.6.3 Ordinal Generalizations 58
2.6.4 Log Supermodularity 64
2.7 Maximizing a Supermodular Function 66
2.7.1 Sets of Maximizers 66
2.7.2 Preservation of Supermodularity 70
2.8 Increasing Optimal Solutions 74
2.8.1 Sufficient Conditions 74
2.8.2 Necessary Conditions 83
2.9 Complementarity Equivalences 92
Chapter 3 Optimal Decision Models 94
3.1 Introduction 94
3.2 Matching 95
3.3 Comparative Statics of the Firm 102
3.3.1 Model of the Firm 103
3.3.2 Sufficient Conditions 104
3.3.3 Necessary Conditions 121
viii CONTENTS
3.4 Transportation and Transshipment Problems 125
3.4.1 Transportation Problem 125
3.4.2 Transshipment Problem 129
3.5 Dynamic Economic Lot Size Production Models,
Acyclic Networks 131
3.5.1 Acyclic Networks 132
3.5.2 Dynamic Economic Lot Size Production Models 134
3.6 Production Planning 138
3.7 Minimum Cuts, Maximum Closures, and the Selection
Problem 142
3.7.1 Minimum Cut Problem 143
3.7.2 Maximum Closure Problem 146
3.7.3 Selection Problem 148
3.7.4 Equivalent Combinatorial Structures 150
3.8 Myopic Decisions 151
3.8.1 General Conditions 152
3.8.2 Dynamic Selection Problem 155
3.9 Markov Decision Processes and Property Inducing
Stochastic Transformations 158
3.9.1 Property Inducing Stochastic Transformations 159
3.9.2 Markov Decision Processes 163
3.10 Stochastic Inventory Problems and Supermodularity Preserving
Stochastic Transformations 169
3.10.1 Supermodularity Preserving Stochastic Transformations 169
3.10.2 Stochastic Inventory Problems 170
Chapter 4 Noncooperative Games 175
4.1 Introduction 175
4.2 Existence of an Equilibrium Point, Parametric Properties 179
4.3 Algorithms for Approximating an Equilibrium Point 185
4.3.1 Round Robin Optimization 185
4.3.2 Simultaneous Optimization 190
4.4 Examples of Supermodular Games 195
4.4.1 Pricing Game with Substitute Products 196
4.4.2 Production Game with Complementary Products 198
4.4.3 Multimarket Oligopoly 199
4.4.4 Arms Race Game 200
4.4.5 Trading Partner Search Game 201
4.4.6 Optimal Consumption Game with Multiple Products 202
4.4.7 Facility Location Game 203
4.4.8 Minimum Cut Game 204
CONTENTS ix
Chapter 5 Cooperative Games 207
5.1 Introduction 207
5.2 Convex Games 211
5.2.1 The Core and the Greedy Algorithm 211
i 5.2.2 Games with a Parameter 221
5.2.3 Structure of the Core 223
5.3 Examples of Convex Games 238
5.3.1 Monopoly Firm 238
5.3.2 Monotonic Surplus Sharing 240
5.3.3 Aircraft Landing Fee Game 241
5.3.4 Trading Game 243
5.4 Activity Optimization Games 244
5.5 Examples of Activity Optimization Games 248
5.5.1 General Welfare Game 249
5.5.2 Production Game with Common Procurement of Inputs 250
5.5.3 Investment and Production Game 252
5.5.4 Activity Selection Game 253
5.5.5 Waste Disposal Game 256
5.6 Games with Complementarities That Are Not Convex
Games 258
5.6.1 Network Design Game 258
5.6.2 Max Min Game 261
Bibliography 263
Index 269
|
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| indexdate | 2024-07-09T18:21:09Z |
| institution | BVB |
| isbn | 0691032440 9780691032443 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008171109 |
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| physical | IX, 272 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series2 | Frontiers of economic research |
| spelling | Topkis, Donald M. Verfasser aut Supermodularity and complementarity Donald M. Topkis Princeton, NJ Princeton Univ. Press 1998 IX, 272 S. txt rdacontent n rdamedia nc rdacarrier Frontiers of economic research Besliskunde gtt Jeux non coopératifs (Mathématiques) Prise de décision - Modèles mathématiques Speltheorie gtt Wiskundige economie gtt Wiskundige modellen gtt Mathematisches Modell Decision making Mathematical models Noncooperative games (Mathematics) Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008171109&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topkis, Donald M. Supermodularity and complementarity Besliskunde gtt Jeux non coopératifs (Mathématiques) Prise de décision - Modèles mathématiques Speltheorie gtt Wiskundige economie gtt Wiskundige modellen gtt Mathematisches Modell Decision making Mathematical models Noncooperative games (Mathematics) Mathematisches Modell (DE-588)4114528-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4138606-1 |
| title | Supermodularity and complementarity |
| title_auth | Supermodularity and complementarity |
| title_exact_search | Supermodularity and complementarity |
| title_full | Supermodularity and complementarity Donald M. Topkis |
| title_fullStr | Supermodularity and complementarity Donald M. Topkis |
| title_full_unstemmed | Supermodularity and complementarity Donald M. Topkis |
| title_short | Supermodularity and complementarity |
| title_sort | supermodularity and complementarity |
| topic | Besliskunde gtt Jeux non coopératifs (Mathématiques) Prise de décision - Modèles mathématiques Speltheorie gtt Wiskundige economie gtt Wiskundige modellen gtt Mathematisches Modell Decision making Mathematical models Noncooperative games (Mathematics) Mathematisches Modell (DE-588)4114528-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Besliskunde Jeux non coopératifs (Mathématiques) Prise de décision - Modèles mathématiques Speltheorie Wiskundige economie Wiskundige modellen Mathematisches Modell Decision making Mathematical models Noncooperative games (Mathematics) Entscheidungstheorie |
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