Game-theoretical models in biology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla.
CRC Press
2013
|
| Series: | Chapman & Hall/CRC mathematical and computational biology series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 445 - 488 |
| Physical Description: | XXV, 494 Seiten Diagramme 25 cm |
| ISBN: | 1439853215 9781439853214 |
Staff View
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Record in the Search Index
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| adam_text | Chapman amp; Hall/CRC Mathematical and Computational Biology Series
Game-Theoretical
Models in Biology
Mark Broom
Jan Rychtar
CRC Press
Taylor S» Francis Croup
Boca Raton London New York
CRC Press is an imprint of the
Taylor amp; Francis Croup, an informa business
ACHAPMAN amp;HALLBOOK
Contents
Preface xxi
Authors xxv
1 Introduction 1
1 1 The history of evolutionary ga mes 1
111 Early game playing and strategic decisions 3
112 The birth of modern game theory 4
113 The beginnings of evolutionary games 5
1 2 The key mathematical developments 7
121 Static games 7
122 Dynamic games 8
1 3 The range of applications 10
1 4 Reading this book 11
2 What is a game? 13
2 1 Key game elements 14
211 Players 14
212 Strategies 15
2121 Pure strategies 15
2122 Mixed strategies 16
2123 Pure or mixed strategies? 18
213 Payoffs 18
2131 Representation of payoffs by matrices 19
2132 Payoffs from contests between mixed
strategists 20
2133 Generic payoffs 21
214 Games in normal form 23
2 2 Games in biological settings 24
221 Representing the population 25
222 Payoffs in matrix games 26
2 3 Further reading 27
2 4 Exercises 27
ix
X Contents
3 Two approaches to game analysis 29
3 1 The dynamical approach 29
311 Replicator dynamics 29
3111 Discrete replicator dynamics 29
3112 Continuous replicator dynamics 30
312 Adaptive dynamics 31
313 Other dynamics 32
314 Timescales in evolution 33
3 2 The static approach—Evolutionarily Stable
Strategy (ESS) 34
321 Nash equilibria 34
322 Evolutionarily Stable Strategies 37
3221 ESSs for matrix games 38
323 Some differences between polymorphic and
monomorphic populations 39
324 Stability of Nash equilibria and of ESSs 41
3 3 Dynamics versus statics 42
331 ESS and replicator dynamics in matrix games 43
332 Replicator dynamics and finite populations 44
3 4 MATLAB program 4-5
3 5 Further reading 46
3 6 Exercises 46
4 Some classical games 49
4 1 The Hawk-Dove game 49
411 The underlying conflict situation 49
412 The mathematical model 50
413 Mathematical analysis 50
414 An adjusted Hawk-Dove game 51
415 Replicator dynamics in the Hawk-Dove game 51
416 Polymorphic mixture versus mixed strategy 51
4 2 The Prisoner s Dilemma 53
421 The underlying conflict situation 54
422 The mathematical model 54
423 Mathematical analysis 55
424 Interpretation of the results 55
425 The Iterated Prisoner s Dilemma, computer
tournaments and Tit for Tat 56
4 3 The war of attrition 58
431 The underlying conflict situation 58
432 The mathematical model 58
433 Mathematical analysis 59
434 Some remarks on the above analysis and results 61
435A war of attrition game with limited contest duration 61
436A war of attrition with finite strategies 62
Contents xi
437 The asymmetric war of attrition 63
4 4 The sex ratio game 63
441 The underlying conflict situation 64
442 The mathematical model 64
443 Mathematical analysis 65
4 5 MATLAB program 65
4 6 Further reading 67
4 7 Exercises 68
5 The underlying biology 71
5 1 Darwin and natural select ion 71
5 2 Genetics 73
521 Hardy-Weinberg equilibrium 7-5
522 Genotypes with different fitnesses 77
5 3 Games involving genetics 80
531 Genetic version of the Hawk-Dove game 80
532A rationale for symmetric games 81
533 Restricted repertoire and the streetcar theory 82
5 4 Fitness, strategies and players 82
541 Fitness 1 83
542 Fitness 2 83
543 Fitness 3 83
544 Fitness 4 84
545 Fitness 5 84
546 Further considerations 84
5 5 Selfish genes: How can non-benefical genes propagate? 85
551 Genetic hitchhiking 85
552 Selfish genes 87
553 Merries and cultural evolution 88
554 Selection at the level of the cell 88
5 6 The role of simple mathematical models 89
5 7 MATLAB program 90
5 8 Further reading 91
5 9 Exercises 91
6 Matrix games 93
6 1 Properties of ESSs 93
611 An equivalent definition of an ESS 93
612A uniform invasion barrier 94
613 Local superiority of an ESS 96
614 ESS supports and the Bishop-Cannings theorem 97
6 2 ESSs in a2x2 matrix game 99
6 3 Haiglrs procedure to locate all ESSs 101
6 4 ESSs in a3x3 matrix game 103
6 4,1 Pure strategies 103
xii Contents
642A mixture of two strategies 104
643 Internal ESSs 104
644 No ESS 105
6 5 Patterns of ESSs 106
651 Attainable patterns 107
652 Exclusion results 108
653 Construction methods 109
654 How many ESSs can there be? 110
6 6 Extensions to the Hawk-Dove game Ill
661 The extended Hawk-Dove game with generic payoffs 112
662 ESSs on restricted strategy sets 113
663 Sequential introduction of strategies 113
6 7 MATLAB program 114
6 8 Further reading 117
6 9 Exercises 118
7 Nonlinear games 121
7 1 Overview and general theory 121
7 2 Linearity in the focal player strategy and playing the field 124
721A generalisation of results for linear games 124
722 Playing the field 127
7221 Parker s matching principle 127
7 3 Nonlinearity due to non-constant interaction rates 129
731 Nonlinearity in pairwise games 129
732 Other games with nonlinear interaction rates 131
7 4 Nonlinearity in the strategy of the focal player 131
741A sperm allocation game 132
742A tree height competition game 133
7 5 Some differences between linear and nonlinear
theory 134
7 6 MATLAB program 135
7 7 Further reading 137
7 8 Exercises 137
8 Asymmetric games 141
8 1 Selten s theorem for games with two roles 142
8 2 Bimatrix games 144
821 Dynamics in bimatrix games 146
8 3 Uncorrelated asymmetry—The Owner-Intruder game 148
8 4 Correlated asymmetry 150
841 Asymmetry in the probability of victory 151
842A game of brood care and desertion 152
8421 Linear version 152
8422 Nonlinear version 153
Contents xiii
843 Asymmetries in rewards and costs: the asymmetric war
of attrition 155
8 5 MATLAB program 157
8 6 Further reading 158
8 7 Exercises 158
9 Multi-player games 161
9 1 Multi-player matrix games 162
911 Two-strategy games 163
912 ESSs for multi-plaver games 165
913 Patterns of ESSs 167
914 More on two-strategy, m-player matrix games 167
915 Dynamics of multi-player matrix games 170
9 2 The multi-player war of attrition 172
921 The multi-player war of attrition without strategy
adjustments 172
922 The multi-player war of attrition with strategy
adjustments 174
923 Multi-player war of attrition with several rewards 175
9 3 Structures of dependent pairwise games 176
931 Knockout contests 176
9 4 MATLAB program 179
9 5 Further reading 181
9 6 Exercises 181
10 Extensive form games and other concepts in game theory 185
10 1 Games in extensive form 185
10 1 1 Key components 186
10 111 The game tree 186
10 112 The player partition 186
10 113 Choices 186
10 114 Strategy 187
10 115 The payoff function 187
10 1 2 Backwards induct ion and sequential equilibria 187
10 1 3 Games in extensive form and games in normal
form 191
10 2 Perfect, imperfect and incomplete information 193
10 2 1 Disturbed games 194
10 2 2 Games in extensive form with imperfect information—
The information partition 196
10 3 Repeated games 199
10 4 MATLAB program 201
10 5 Further reading 202
10 6 Exercises 203
xiv Contents
11 State-based games 207
11 1 State-based games 208
11 1 1 Optimal foraging 208
11 1 2 The general theory of state-based games 210
11 13A simple foraging game 211
11 1 4 Evolutionary games based upon state 212
11 2 A question of size 215
11 2 1 Setting up the model 216
11 2 2 ESS analysis 217
11 23A numerical example 217
11 3 Life history theory 218
11 4 MATLAB program 220
11 5 Further reading 221
11 6 Exercises 222
12 Games in finite and structured populations 225
12 1 Finite populations and stochastic games 225
12 1 1 The Moran process 225
12 1 2 The fixation probability 227
12 1 3 General Birth-Death processes 229
12 1 4 The Moran process and discrete replicator
dynamics 230
12 1 5 Fixation and absorption times 231
12 151 Exact formulae 231
12 152 The diffusion approximation 232
12 1 6 Games in finite populations 233
12 2 Evolution on graphs 236
12 2 1 The fixed fitness case 239
12 211 Regular graphs 240
12 212 Selection suppressors and amplifiers 241
12 2 2 Games on graphs 242
12 2 3 Dynamics and fitness 243
12 3 Spatial games and cellular automata 245
12 4 MATLAB program 247
12 5 Further reading 248
12 6 Exercises _ 249
13 Adaptive dynamics 251
13 1 Introduction and philosophy 2-51
13 2 Fitness functions and the fitness landscape 2-52
13 2 1 Taylor expansion of s(y , 254
13 2 2 Adaptive dynamics for matrix games 255
13 3 Pairwise invasibility and Evolutionarily Singular
Strategies 2-56
Contents xv
13 3 1 Four key properties of Evolutionarily Singular
Strategies 256
13 311 Non-invnsible strategies 256
13 312 When an ess can invade nearby
strategies 257
13 313 Convergence stability 257
13 314 Protected polymorphism 257
13 3 2 Classification of Evolutionarily Singular
Strategies 257
13 321 Case 5 258
13 322 Case 7 260
13 323 Case 3™ Branching points 260
13 4 Adaptive dynamics with multiple traits 262
13 5 The assumptions of adaptive dynamics 264
13 6 MATLAB program 265
13 7 Further reading 266
13 8 Exercises 267
14 The evolution of cooperation 271
14 1 Kin selection and inclusive fitness 272
14 2 Greenbeard genes 274
14 3 Direct reciprocity: developments of the Prisoner s
Dilemma 277
14 3 1 An error-free environment 277
14 3 2 An error-prone environment 279
14 3 3 ESSs in the IPD game 280
14 34A simple rule for the evolution of cooperation by
direct reciprocity 281
14 4 Punishment 281
14 5 Indirect reciprocity and reputation dynamics 283
14 6 The evolution of cooperation on graphs 286
14 7 Multi-level selection 288
14 8 MATLAB program 289
14 9 Further reading 290
14 10 Exercises 291
15 Group living 293
15 1 The costs and benefits of group living 293
15 2 Dominance hierarchies: formation and maintenance 294
15 2 1 Stability and maintenance of dominance
hierarchies 294
15 2 2 Dominance hierarchy formation 297
15 221 Winner and loser models 298
15 2 3 Swiss tournaments 299
15 3 The enemy without: responses to predators 301
xvi Contents
15 3 1 Setting up the game 302
15 311 Modelling scanning for predators 302
15 312 Payoffs 303
15 3 2 Analysis of the game 304
15 4 The enemy within: infanticide and other anti-social
behaviour 305
15 4 1 Infanticide 305
15 4 2 Other behaviour which negatively affects groups 307
15 5 MATLAB program 308
15 6 Further reading 309
15 7 Exercises 310
16 Mating games 313
16 1 Introduction and overview 313
16 2 Direct conflict 314
16 2 1 Setting up the model 314
16 211 Analysis of a single contest 315
16 212 The case of a limited number of contests pet-
season 315
16 2 2 An unlimited number of contests 318
16 2 3 Determining rewards and costs 319
16 3 Indirect conflict and sperm competition 320
16 3 1 Setting up the model 320
16 311 Modelling sperm production 320
16 312 Model parameters 321
16 313 Modelling fertilization and payoffs 321
16 3 2 The ESS if males have no knowledge 322
16 3 3 The ESS if males have partial knowledge 323
16 3 4 Summary 324
16 4 The Battle of the Sexes 324
16 4 1 Analysis as a bimatrix game 325
16 4 2 The coyness game 325
16 421 The model 326
16 422 Fitness 327
16 423 Determining the ESS 329
16 5 Selecting mates: signalling and the handicap
principle 330
16 5 1 Setting up the model 332
16 5 2 Assumptions about the game parameters 332
16 5 3 ESSs 334
16 54A numerical example 335
16 5 5 Properties of the ESS—honest signalling 336
16 6 Other signalling scenarios 337
16 6 1 Limited options 337
16 6 2 Signalling without cost 338
Contents xvii
16 7 MATLAB program 340
16 8 Further Reading 341
16 9 Exercises 342
17 Food competition 345
17 1 Introduction 345
17 2 Ideal Free Distribution for a single species 345
17 2 1 The model 345
17 3 Ideal Free Distribution for multiple species 349
17 3 1 The model 349
17 3 2 Both patches occupied by both species 350
17 3 3 One patch occupied by one species, another
by both 350
17 3 4 Species on different patches 351
17 3 5 Species on the same patch 351
17 4 Distributions at and deviations from the Ideal Free
Distribution 351
17 5 Compartmental models of kleptoparasitism 353
17 5 1 The model 354
17 5 2 Analysis 355
17 5 3 Extensions of the model 359
17 6 Compartmental models of interference 362
17 7 Producer-scrounger models 363
17 7 1 The Finder-Joiner game—the sequential version with
complete information 364
17 711 The model 364
17 712 Analysis 364
17 713 Discussion 365
17 7 2 The Finder-Joiner game—the sequential version with
partial information 367
17 8 MATLAB program 368
17 9 Further reading 370
17 10 Exercises 370
18 Predator-prey and host-parasite interactions 373
18 1 Game-theoretical predator-prey models 373
18 1 1 The model 374
18 1 2 Analysis 375
18 1 3 Results 376
18 2 The evolution of defence and signalling 376
18 2 1 The model 377
18 211 Interaction of prey with a predator 377
18 212 Payoff to an individual prey 378
18 2 2 Analysis and results 379
18 2 3 An alternative model 379
xviii Contents
18 2 4 Cheating 381
18 3 Brood parasitism 382
18 3 1 The model 382
18 3 2 Results 384
18 4 Parasitic wasps and the asymmetric war of attrition 385
18 4 1 The model 386
18 4 2 Analysis—evaluating the payoffs 388
18 4 3 Discussion 389
18 5 Complex parasite lifecycles 390
18 51A model of upwards incorporation 390
18 5 2 Analysis and results 392
18 6 MATLAB program 392
18 7 Further reading 395
18 8 Exercises 395
19 Epidemic models 399
19 1 SIS and SIR models 399
19 1 1 The SIS epidemic 400
19 111 The model 400
19 112 Analysis 401
19 113 Summary of results 402
19 1 2 The SIR epidemic 402
19 121 The model 403
19 122 Analysis and results 404
19 123 Some other models 404
19 1 3 Epidemics on graphs 406
19 2 The evolution of virulence 407
19 2 1 An SI model for single epidemics with immigration and
death 407
19 211 Model and results 408
19 2 2 An SI model for two epidemics with immigration and
death and no superinfection 408
19 221 Model and results 409
19 2 3 Superinfection 409
19 231 Model and results 410
19 3 Viruses and the Prisoner s Dilemma 411
19 3 1 The model 411
19 3 2 Results 411
19 33A real example 412
19 4 MATLAB program 413
19 5 Further reading 414
19 6 Exercises 414
Co i dents xix
20 Conclusions 417
20 1 Types of evolutionary games used in biology 417
20 1 1 Classical games, linearity on the left and replicator
dynamics 417
20 1 2 Strategies as a com inuous trait and nonlinearity on the
left 419
20 1 3 Departures from infinite, well-mixed populations of
identical individuals 419
20 1 4 More complex interactions and other mathematical
complications 421
20 1 5 Some biological issues 422
20 1 6 Models of specific behaviours 423
20 2 What makes a good mathematical model? 424
20 3 Future developments 426
20 3 1 Agent-based modelling 426
20 3 2 Multi-level selection 426
20 3 3 Unifying timescales 427
20 3 4 Games in structured populations 427
20 3 5 Nonlinear games 427
20 3 6 Asymmetries in populations 428
20 3 7 What is a payoff? 428
20 38A more unified approach to model applications 428
A Intro to MATLAB 429
Bibliography 445
Index 489
i
|
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| author | Broom, Mark Rychtář, Jan |
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| dewey-full | 570.1/5195 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570.1/5195 |
| dewey-search | 570.1/5195 |
| dewey-sort | 3570.1 45195 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV041351732 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:54:42Z |
| institution | BVB |
| isbn | 1439853215 9781439853214 |
| language | English |
| lccn | 2012048740 |
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| open_access_boolean | |
| owner | DE-83 DE-91G DE-BY-TUM |
| owner_facet | DE-83 DE-91G DE-BY-TUM |
| physical | XXV, 494 Seiten Diagramme 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall/CRC mathematical and computational biology series |
| spelling | Broom, Mark (DE-588)1018666788 aut Game-theoretical models in biology Mark Broom ; Jan Rychtář Boca Raton, Fla. CRC Press 2013 XXV, 494 Seiten Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematical and computational biology series Literaturverz. S. 445 - 488 Evolution (DE-588)4071050-6 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Evolution (DE-588)4071050-6 s Spieltheorie (DE-588)4056243-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Rychtář, Jan (DE-588)1042646422 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026800287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Broom, Mark Rychtář, Jan Game-theoretical models in biology Evolution (DE-588)4071050-6 gnd Spieltheorie (DE-588)4056243-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4071050-6 (DE-588)4056243-8 (DE-588)4114528-8 |
| title | Game-theoretical models in biology |
| title_auth | Game-theoretical models in biology |
| title_exact_search | Game-theoretical models in biology |
| title_full | Game-theoretical models in biology Mark Broom ; Jan Rychtář |
| title_fullStr | Game-theoretical models in biology Mark Broom ; Jan Rychtář |
| title_full_unstemmed | Game-theoretical models in biology Mark Broom ; Jan Rychtář |
| title_short | Game-theoretical models in biology |
| title_sort | game theoretical models in biology |
| topic | Evolution (DE-588)4071050-6 gnd Spieltheorie (DE-588)4056243-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Evolution Spieltheorie Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026800287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT broommark gametheoreticalmodelsinbiology AT rychtarjan gametheoreticalmodelsinbiology |