Table Of ContentEvolutionary Games in Natural, Social,
and Virtual Worlds
Evolutionary Games in Natural,
Social, and Virtual Worlds
DANIEL FRIEDMAN AND BARRY SINERVO
1
1
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LibraryofCongressCataloging-in-PublicationData
Names:Friedman,Daniel,1947–author.|Sinervo,Barry,author.
Title:Evolutionarygamesinnatural,social,andvirtualworlds/Daniel
FriedmanandBarrySinervo.
Description:Oxford;NewYork:OxfordUniversityPress,[2016]|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2015034942|ISBN9780199981151(alk.paper)
Subjects:LCSH:Gametheory.|Evolution.
Classification:LCCHB144.F7462016|DDC519.3–dc23LCrecordavailable
athttp://lccn.loc.gov/2015034942
ISBN978–0–19–998115–1
9 8 7 6 5 4 3 2 1
TypesetinArno
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PrintedintheUnitedStatesofAmerica
CONTENTS
Preface xi
PART ONE Basics
1. PopulationDynamics 3
1.1. Fitness 4
1.2. Tradeoffsandfitnessdependence 5
1.3. Dependenceonenvironment,density,andfrequency 8
1.4. Statespacegeometry 9
1.5. Memesandgenes 12
1.6. Finitepopulationsandrandomness 13
1.7. Replicatordynamicsindiscretetime 13
1.8. Replicatordynamicsincontinuoustime 15
1.9. Steadystatesandstability 16
1.10. Sexualdynamics 18
1.11. Discussion 25
AppendixA:DerivationoftheFisherequation 25
AppendixB:Replicatordynamics,meanfitness,andentropy 26
Exercises 29
Notes 30
Bibliography 32
2. SimpleFrequencyDependence 33
2.1. TheHawk-Dovegame 34
2.2. H-Dparametersanddynamics 36
2.3. Thethreekindsof2×2games 40
2.4. DilemmasplayedbyvirusesandeBaysellers 45
2.5. Nonlinearfrequencydependence 49
2.6. RPSandthesimplex 51
2.7. ReplicatordynamicsforRPS 53
vi CONTENTS
2.8. Discussion 58
Appendix:Payoffdifferencesin3×3games 59
Exercises 60
Notes 62
Bibliography 63
3. Dynamicsinn-DimensionalGames 64
3.1. Sectoringthe2-dsimplex 64
3.2. Estimating3×3payoffmatrices 69
3.3. Morestrategies 73
3.4. Nonlinearfrequencydependence 77
3.5. Two-populationgames:Thesquare 78
3.6. Hawk-Dovewithtwopopulations 81
3.7. Own-populationeffects 83
3.8. Higher-dimensionalgames 87
3.9. Alternativedynamics 87
3.10. Discussion 90
Appendix:Estimating3×3payoffmatrices 91
Exercises 98
Notes 99
Bibliography 100
4. Equilibrium 102
4.1. Equilibriumin1dimension 103
4.2. Nashequilibriumwithnstrategies 106
4.3. ESSwithnstrategies 107
4.4. Equilibriuminmulti-populationgames 114
4.5. Fisherianrunawayequilibrium 115
4.6. Discussion 117
Appendix:TechniquestoAssessStability 118
Exercises 124
Notes 125
Bibliography 125
5. SocialGames 127
5.1. Assortativematching 128
5.2. Socialtwists 131
5.3. Inheritancefromtwoparents 135
5.4. ThestandardPriceequation 141
Contents vii
5.5. Group-structuredPriceequationandcooperation 143
5.6. Groupstructureandassortativityinlizards 145
5.7. Priceequationincontinuoustime 147
5.8. Discussion 149
Appendix:EquilibriumintheKirkpatrick(1982)model 149
Exercises 152
Notes 152
Bibliography 153
6. CellularAutomatonGames 155
6.1. SpecifyingaCA 155
6.2. Prisoner’sdilemma 158
6.3. Snowdrift 159
6.4. Publicgoodsgameswithtwostrategies 160
6.5. Spatialrock-paper-scissorsdynamic 163
6.6. Applicationtobacterialstrains 166
6.7. Buyer-Sellergameasatwo-populationCA 168
Exercises 170
Notes 171
Bibliography 172
PART TWO APPLICATIONS
7. Rock-Paper-ScissorsEverywhere 177
7.1. SomeRPStheory 178
7.2. HumansplayRPSinthelab 183
7.3. RPSmatingsystems 187
7.4. Predatorslearn 194
7.5. Aco-evolutionarymodelofpredatorsandprey 196
7.6. Discussion 203
Appendix 204
Exercises 206
Notes 208
Bibliography 209
8. LearninginGames 212
8.1. Perspectivesonlearningandevolution 213
8.2. Anempiricalexample 214
8.3. Learningrules 215
viii CONTENTS
8.4. Decisionrules 217
8.5. Estimatingamodel 219
8.6. Results 221
8.7. Learningincontinuoustime 223
8.8. Othermodelsoflearning 226
8.9. Openfrontiers 229
Appendix:Towardsmodelsoflearningincontinuoustime 231
Exercises 232
Notes 233
Bibliography 234
9. ContingentLife-CycleStrategies 236
9.1. Hawks,doves,andplasticity 238
9.2. Costlyplasticity 242
9.3. Classiclife-cycleanalysis 244
9.4. Strategiclife-cycleanalysis:Twoperiods 245
9.5. Strategiclife-cycleanalysis:Moregeneralcases 248
9.6. Application:Maleelephantseals 250
9.7. Discussion 257
Appendix:Formalizingaperfectlifetimeequilibrium 259
Exercises 261
Notes 262
Bibliography 263
10. TheBlessingandtheCurseoftheMultiplicativeUpdates 265
ManfredK.Warmuth
10.1. Demonstratingtheblessingandthecurse 266
10.2.Dispellingthecurse 270
10.3.Discussion 284
Notes 286
Bibliography 287
11. TrafficGames 290
JohnMusacchio
11.1. Simplenon-atomictrafficgames 291
11.2. Braess’sparadox 294
11.3. Thepriceofanarchywithnonlinearlatencyfunctions 296
11.4. Pigoviantaxes 298
11.5. Selfishpricing 299
Description:Over the last 25 years, evolutionary game theory has grown with theoretical contributions from the disciplines of mathematics, economics, computer science and biology. It is now ripe for applications. In this book, Daniel Friedman---an economist trained in mathematics---and Barry Sinervo---a biologi
