Evolutionary games and population dynamics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | Transferred to digital printing |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXVII, 323 S. graph. Darst. |
| ISBN: | 0521623650 052162570X |
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MARC
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| 100 | 1 | |a Hofbauer, Josef |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Evolutionary games and population dynamics |c Josef Hofbauer ; Karl Sigmund |
| 250 | |a Transferred to digital printing | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XXVII, 323 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804136482008465408 |
|---|---|
| adam_text | Contents
ťreji
ace
tage xi
Introduction for game theorists
xiv
Introduction for biologists
XX
About this book
xxvi
Part one: Dynamical Systems and Lotka-Volterra Equations
1
1
Logistic growth
3
1.1
Population dynamics and density dependence
3
1.2
Exponential growth
4
1.3
Logistic growth
5
1.4
The recurrence relation x
—
Rx(l
—
x)
5
1.5
Stable and unstable fixed points
6
1.6
Bifurcations
7
1.7
Chaotic motion
9
1.8
Notes
10
2
Lotka-Volterra equations for predator-prey systems
11
2.1
A predator-prey equation
11
2.2
Solutions of differential equations
12
2.3
Analysis of the Lotka-Volterra predator-prey equation
13
2.4
Volterra s principle
15
2.5
The predator-prey equation with intraspecific competition
16
2.6
On
ω
-limits and Lyapunov functions
18
2.7
Coexistence of predators and prey
19
2.8
Notes
21
3
The Lotka-Volterra equations for two competing species
22
3.1
Linear differential equations
22
3.2
Linearization
24
vi
Contents
3.3
A competition equation
26
3.4
Cooperative systems
28
3.5
Notes
30
4
Ecological equations for two species
31
4.1
The
Poincaré-Bendixson
theorem
31
4.2
Periodic orbits for two-dimensional Lotka-Volterra equations
33
4.3
Limit cycles and the predator-prey model of Gause
34
4.4
Saturated response
37
4.5
Hopf
bifurcations
38
4.6
Notes
40
5
Lotka-Volterra equations for more than two populations
42
5.1
The general Lotka-Volterra equation
42
5.2
Interior rest points
43
5.3
The Lotka-Volterra equations for food chains
45
5.4
The exclusion principle
47
5.5
A model for cyclic competition
48
5.6
Notes
53
Part two: Game Dynamics and Replicator Equations
55
6
Evolutionarily stable strategies
57
6.1
Hawks and doves
57
6.2
Evolutionary stability
59
6.3
Normal form games
61
6.4
Evolutionarily stable strategies
62
6.5
Population games
65
6.6
Notes
66
7
Replicator dynamics
67
7.1
The replicator equation
67
7.2
Nash equilibria and evolutionarily stable states
69
7.3
Strong stability
72
7.4
Examples of replicator dynamics
74
7.5
Replicator dynamics and the Lotka-Volterra equation
77
7.6
Time averages and an exclusion principle
78
7.7
The rock-scissors-paper game
79
7.8
Partnership games and gradients
82
7.9
Notes
85
8
Other game dynamics
86
8.1
Imitation dynamics
86
Contents
vii
8.2
Monotone
selection dynamics
88
8.3
Selection against iteratively dominated strategies
90
8.4
Best-response dynamics
93
8.5
Adjustment dynamics
97
8.6
A universally cycling game
98
8.7
Notes
100
9
Adaptive dynamics
101
9.1
The repeated Prisoner s Dilemma
101
9.2
Stochastic strategies for the Prisoner s Dilemma
103
9.3
Adaptive Dynamics for the Prisoner s Dilemma
104
9.4
An ESS may be unattainable
107
9.5
A closer look at adaptive dynamics
108
9.6
Adaptive dynamics and gradients
109
9.7
Notes
112
10
Asymmetric games
113
10.1
Bimatrix games
113
10.2
The Battle of the Sexes
114
10.3
A differential equation for asymmetric games
116
10.4
The case of two players and two strategies
119
10.5
Role games
122
10.6
Notes
125
И
More on bimatrix games
126
11.1
Dynamics for bimatrix games
126
11.2
Partnership games and zero-sum games
127
11.3
Conservation of volume
132
11.4
Nash-Pareto pairs
135
11.5
Game dynamics and Nash-Pareto pairs
137
11.6
Notes
139
Part three: Permanence and Stability
141
12
Catalytic bypercycles
143
12.1
The hypercycle equation
143
12.2
Permanence
145
12.3
The permanence of the hypercycle
149
12.4
The competition of disjoint hypercycles
151
12.5
Notes
152
13
Criteria for permanence
153
13.1
Permanence and persistence for replicator equations
153
viii Contents
13.2
Brouwer s degree and
Poincaré s
index
155
13.3
An index theorem for permanent systems
158
13.4
Saturated rest points and a general index theorem
159
13.5
Necessary conditions for permanence
162
13.6
Sufficient conditions for permanence
166
13.7
Notes
170
14
Replicator networks
171
14.1
A periodic attractor for
η
= 4 171
14.2
Cyclic symmetry
173
14.3
Permanence and irreducibility
175
14.4
Permanence of catalytic networks
176
14.5
Essentially hypercyclic networks
177
14.6
Notes
180
15
Stability of n-species communities
181
15.1
Mutualism and M-matrices
181
15.2
Boundedness and B-matrices
185
15.3
VL-stability and global stability
191
15.4
Ρ
-matrices
193
15.5
Communities with a special structure
196
15.6
D-stability and total stability
199
15.7
Notes
201
16
Some low-dimensional ecological systems
203
16.1
Heteroclinic cycles
203
16.2
Permanence for three-dimensional Lotka-Volterra systems
206
16.3
General three-species systems
211
16.4
A two-prey two-predator system
213
16.5
An epidemiological model
216
16.6
Notes
219
17
Heteroclinic cycles:
Poincaré
maps and characteristic matrices
220
17.1
Cross-sections and
Poincaré
maps for periodic orbits
220
17.2
Poincaré
maps for heteroclinic cycles
221
17.3
Heteroclinic cycles on the boundary of
S„
224
17.4
The characteristic matrix of a heteroclinic cycle
227
17.5
Stability conditions for heteroclinic cycles
230
17.6
Notes
232
Contents ix
Part four: Population Genetics and Game Dynamics
233
18
Discrete dynamical systems in population genetics
235
18.1
Genotypes
235
18.2
The Hardy-Weinberg law
236
18.3
The selection model
237
18.4
The increase in average fitness
238
18.5
The case of two
alíeles
240
18.6
The mutation-selection equation
241
18.7
The selection-recombination equation
243
18.8
Linkage
245
18.9
Fitness under recombination
247
18.10
Notes
248
19
Continuous selection dynamics
249
19.1
The selection equation
249
19.2
Convergence to a rest point
251
19.3
The location of stable rest points
254
19.4
Density dependent fitness
256
19.5
The Shahshahani gradient
257
19.6
Mixed strategists and gradient systems
261
19.7
Notes
264
20
Mutation and recombination
265
20.1
The selection-mutation model
265
20.2
Mutation and additive selection
266
20.3
Special mutation rates
268
20.4
Limit cycles for the selection-mutation equation
270
20.5
Selection at two loci
273
20.6
Notes
277
21
Fertility selection
278
21.1
The fertility equation
278
21.2
Two
alíeles
280
21.3
Multiplicative fertility
282
21.4
Additive fertility
285
21.5
The fertility-mortality equation
286
21.6
Notes
288
22
Game dynamics for Mendelian populations
289
22.1
Strategy and genetics
289
22.2
The discrete model for two strategies
292
22.3
Genetics and ESS
295
χ
Contents
22.4
ESS and long-term evolution
298
22.5
Notes
300
References
301
Index
321
Every form of behaviour is shaped by trial and error. Such stepwise
adaptation can occur through individual learning or through natural
selection, the basis of evolution. Since the work of May
nard
Smith and
others, it has been realised how game theory can model this process.
Evolutionary game theory replaces the static solutions of classical game
theory by a dynamical approach centered not on the concept of rational
players but on the population dynamics of behavioural programs.
In this book the authors investigate the nonlinear dynamics of the self-
regulation of social and economic behaviour, and of the closely related
interactions between species in ecological communities. Replicator
equations describe how successful strategies spread and thereby create
new conditions which can alter the basis of their success, i.e. to enable us
to understand the strategic and genetic foundations of the endless
chronicle of invasions and extinctions which punctuate evolution.
In short, evolutionary game theory describes when to
how to elicit cooperation, why to expect a balance of tl
understand natural selection in mathematical terms.
and how to
|
| adam_txt |
Contents
ťreji
ace
tage xi
Introduction for game theorists
xiv
Introduction for biologists
XX
About this book
xxvi
Part one: Dynamical Systems and Lotka-Volterra Equations
1
1
Logistic growth
3
1.1
Population dynamics and density dependence
3
1.2
Exponential growth
4
1.3
Logistic growth
5
1.4
The recurrence relation x'
—
Rx(l
—
x)
5
1.5
Stable and unstable fixed points
6
1.6
Bifurcations
7
1.7
Chaotic motion
9
1.8
Notes
10
2
Lotka-Volterra equations for predator-prey systems
11
2.1
A predator-prey equation
11
2.2
Solutions of differential equations
12
2.3
Analysis of the Lotka-Volterra predator-prey equation
13
2.4
Volterra's principle
15
2.5
The predator-prey equation with intraspecific competition
16
2.6
On
ω
-limits and Lyapunov functions
18
2.7
Coexistence of predators and prey
19
2.8
Notes
21
3
The Lotka-Volterra equations for two competing species
22
3.1
Linear differential equations
22
3.2
Linearization
24
vi
Contents
3.3
A competition equation
26
3.4
Cooperative systems
28
3.5
Notes
30
4
Ecological equations for two species
31
4.1
The
Poincaré-Bendixson
theorem
31
4.2
Periodic orbits for two-dimensional Lotka-Volterra equations
33
4.3
Limit cycles and the predator-prey model of Gause
34
4.4
Saturated response
37
4.5
Hopf
bifurcations
38
4.6
Notes
40
5
Lotka-Volterra equations for more than two populations
42
5.1
The general Lotka-Volterra equation
42
5.2
Interior rest points
43
5.3
The Lotka-Volterra equations for food chains
45
5.4
The exclusion principle
47
5.5
A model for cyclic competition
48
5.6
Notes
53
Part two: Game Dynamics and Replicator Equations
55
6
Evolutionarily stable strategies
57
6.1
Hawks and doves
57
6.2
Evolutionary stability
59
6.3
Normal form games
61
6.4
Evolutionarily stable strategies
62
6.5
Population games
65
6.6
Notes
66
7
Replicator dynamics
67
7.1
The replicator equation
67
7.2
Nash equilibria and evolutionarily stable states
69
7.3
Strong stability
72
7.4
Examples of replicator dynamics
74
7.5
Replicator dynamics and the Lotka-Volterra equation
77
7.6
Time averages and an exclusion principle
78
7.7
The rock-scissors-paper game
79
7.8
Partnership games and gradients
82
7.9
Notes
85
8
Other game dynamics
86
8.1
Imitation dynamics
86
Contents
vii
8.2
Monotone
selection dynamics
88
8.3
Selection against iteratively dominated strategies
90
8.4
Best-response dynamics
93
8.5
Adjustment dynamics
97
8.6
A universally cycling game
98
8.7
Notes
100
9
Adaptive dynamics
101
9.1
The repeated Prisoner's Dilemma
101
9.2
Stochastic strategies for the Prisoner's Dilemma
103
9.3
Adaptive Dynamics for the Prisoner's Dilemma
104
9.4
An ESS may be unattainable
107
9.5
A closer look at adaptive dynamics
108
9.6
Adaptive dynamics and gradients
109
9.7
Notes
112
10
Asymmetric games
113
10.1
Bimatrix games
113
10.2
The Battle of the Sexes
114
10.3
A differential equation for asymmetric games
116
10.4
The case of two players and two strategies
119
10.5
Role games
122
10.6
Notes
125
И
More on bimatrix games
126
11.1
Dynamics for bimatrix games
126
11.2
Partnership games and zero-sum games
127
11.3
Conservation of volume
132
11.4
Nash-Pareto pairs
135
11.5
Game dynamics and Nash-Pareto pairs
137
11.6
Notes
139
Part three: Permanence and Stability
141
12
Catalytic bypercycles
143
12.1
The hypercycle equation
143
12.2
Permanence
145
12.3
The permanence of the hypercycle
149
12.4
The competition of disjoint hypercycles
151
12.5
Notes
152
13
Criteria for permanence
153
13.1
Permanence and persistence for replicator equations
153
viii Contents
13.2
Brouwer's degree and
Poincaré's
index
155
13.3
An index theorem for permanent systems
158
13.4
Saturated rest points and a general index theorem
159
13.5
Necessary conditions for permanence
162
13.6
Sufficient conditions for permanence
166
13.7
Notes
170
14
Replicator networks
171
14.1
A periodic attractor for
η
= 4 171
14.2
Cyclic symmetry
173
14.3
Permanence and irreducibility
175
14.4
Permanence of catalytic networks
176
14.5
Essentially hypercyclic networks
177
14.6
Notes
180
15
Stability of n-species communities
181
15.1
Mutualism and M-matrices
181
15.2
Boundedness and B-matrices
185
15.3
VL-stability and global stability
191
15.4
Ρ
-matrices
193
15.5
Communities with a special structure
196
15.6
D-stability and total stability
199
15.7
Notes
201
16
Some low-dimensional ecological systems
203
16.1
Heteroclinic cycles
203
16.2
Permanence for three-dimensional Lotka-Volterra systems
206
16.3
General three-species systems
211
16.4
A two-prey two-predator system
213
16.5
An epidemiological model
216
16.6
Notes
219
17
Heteroclinic cycles:
Poincaré
maps and characteristic matrices
220
17.1
Cross-sections and
Poincaré
maps for periodic orbits
220
17.2
Poincaré
maps for heteroclinic cycles
221
17.3
Heteroclinic cycles on the boundary of
S„
224
17.4
The characteristic matrix of a heteroclinic cycle
227
17.5
Stability conditions for heteroclinic cycles
230
17.6
Notes
232
Contents ix
Part four: Population Genetics and Game Dynamics
233
18
Discrete dynamical systems in population genetics
235
18.1
Genotypes
235
18.2
The Hardy-Weinberg law
236
18.3
The selection model
237
18.4
The increase in average fitness
238
18.5
The case of two
alíeles
240
18.6
The mutation-selection equation
241
18.7
The selection-recombination equation
243
18.8
Linkage
245
18.9
Fitness under recombination
247
18.10
Notes
248
19
Continuous selection dynamics
249
19.1
The selection equation
249
19.2
Convergence to a rest point
251
19.3
The location of stable rest points
254
19.4
Density dependent fitness
256
19.5
The Shahshahani gradient
257
19.6
Mixed strategists and gradient systems
261
19.7
Notes
264
20
Mutation and recombination
265
20.1
The selection-mutation model
265
20.2
Mutation and additive selection
266
20.3
Special mutation rates
268
20.4
Limit cycles for the selection-mutation equation
270
20.5
Selection at two loci
273
20.6
Notes
277
21
Fertility selection
278
21.1
The fertility equation
278
21.2
Two
alíeles
280
21.3
Multiplicative fertility
282
21.4
Additive fertility
285
21.5
The fertility-mortality equation
286
21.6
Notes
288
22
Game dynamics for Mendelian populations
289
22.1
Strategy and genetics
289
22.2
The discrete model for two strategies
292
22.3
Genetics and ESS
295
χ
Contents
22.4
ESS and long-term evolution
298
22.5
Notes
300
References
301
Index
321
Every form of behaviour is shaped by trial and error. Such stepwise
adaptation can occur through individual learning' or through natural
selection, the basis of evolution. Since the work of May
nard
Smith and
others, it has been realised how game theory can model this process.
Evolutionary game theory replaces the static solutions of classical game
theory by a dynamical approach centered not on the concept of rational
players but on the population dynamics of behavioural programs.
In this book the authors investigate the nonlinear dynamics of the self-
regulation of social and economic behaviour, and of the closely related
interactions between species in ecological communities. Replicator
equations describe how successful strategies spread and thereby create
new conditions which can alter the basis of their success, i.e. to enable us
to understand the strategic and genetic foundations of the endless
chronicle of invasions and extinctions which punctuate evolution.
In short, evolutionary game theory describes when to
how to elicit cooperation, why to expect a balance of tl
understand natural selection in mathematical terms.
and how to |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hofbauer, Josef Sigmund, Karl 1945- |
| author_GND | (DE-588)115427368 |
| author_facet | Hofbauer, Josef Sigmund, Karl 1945- |
| author_role | aut aut |
| author_sort | Hofbauer, Josef |
| author_variant | j h jh k s ks |
| building | Verbundindex |
| bvnumber | BV022415209 |
| classification_rvk | QH 430 QU 000 SK 860 WC 7000 |
| classification_tum | MAT 926f |
| ctrlnum | (OCoLC)699110874 (DE-599)BVBBV012037433 |
| discipline | Biologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Biologie Mathematik Wirtschaftswissenschaften |
| edition | Transferred to digital printing |
| format | Book |
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| id | DE-604.BV022415209 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:23:37Z |
| indexdate | 2024-07-09T20:57:06Z |
| institution | BVB |
| isbn | 0521623650 052162570X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015623608 |
| oclc_num | 699110874 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-523 DE-859 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-523 DE-859 |
| physical | XXVII, 323 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Hofbauer, Josef Verfasser aut Evolutionary games and population dynamics Josef Hofbauer ; Karl Sigmund Transferred to digital printing Cambridge [u.a.] Cambridge Univ. Press 2003 XXVII, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Populationsdynamik (DE-588)4046803-3 gnd rswk-swf Evolution (DE-588)4071050-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Evolutionäre Spieltheorie (DE-588)4732282-2 gnd rswk-swf Populationsdynamik (DE-588)4046803-3 s Evolution (DE-588)4071050-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Evolutionäre Spieltheorie (DE-588)4732282-2 s Sigmund, Karl 1945- Verfasser (DE-588)115427368 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015623608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015623608&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hofbauer, Josef Sigmund, Karl 1945- Evolutionary games and population dynamics Populationsdynamik (DE-588)4046803-3 gnd Evolution (DE-588)4071050-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Evolutionäre Spieltheorie (DE-588)4732282-2 gnd |
| subject_GND | (DE-588)4046803-3 (DE-588)4071050-6 (DE-588)4114528-8 (DE-588)4732282-2 |
| title | Evolutionary games and population dynamics |
| title_auth | Evolutionary games and population dynamics |
| title_exact_search | Evolutionary games and population dynamics |
| title_exact_search_txtP | Evolutionary games and population dynamics |
| title_full | Evolutionary games and population dynamics Josef Hofbauer ; Karl Sigmund |
| title_fullStr | Evolutionary games and population dynamics Josef Hofbauer ; Karl Sigmund |
| title_full_unstemmed | Evolutionary games and population dynamics Josef Hofbauer ; Karl Sigmund |
| title_short | Evolutionary games and population dynamics |
| title_sort | evolutionary games and population dynamics |
| topic | Populationsdynamik (DE-588)4046803-3 gnd Evolution (DE-588)4071050-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Evolutionäre Spieltheorie (DE-588)4732282-2 gnd |
| topic_facet | Populationsdynamik Evolution Mathematisches Modell Evolutionäre Spieltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015623608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015623608&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hofbauerjosef evolutionarygamesandpopulationdynamics AT sigmundkarl evolutionarygamesandpopulationdynamics |