Evolutionary Games in Natural, Social, and Virtual Worlds

Daniel Friedman is Distinguished Professor of Economics at the University of California, Santa Cruz. The author of over 100 articles and 5 previous books, his work has appeared in leading academic journals in economics, finance, and psychology. He is founder and director of LEEPS lab which conducts human subject experiments in market and strategic interaction, supported by 14 National Science Foundation grants along with grants from IBM, HP labs, Google, and Environmental Defense.Barry Sinervo, Full Professor, University of California, Santa Cruz, is an evolutionary biologist who conducts research on Behavioral Ecology, Game Theory and the Biotic Impacts of Climate Change. He has authored over 100 peer-reviewed publications. In addition to his research in game theory, he is currently researching contemporary extinctions of reptiles and amphibians and changes in plant communities driven by climate change, at sites distributed on five continents, leading a multinational research team of scientists developing physiological models of the biotic impacts of climate change on diverse biological systems, and measuring the biotic impacts of climate from equatorial sites to polar regions. He is also Director of the UC-wide Institute for the Study of the Ecological and Evolutionary Climate Impacts, a research consortium funded by a UC Presidential Research Catalyst Award.

Evolutionary Games is an excellent resource for self-study on applications of evolutionary game theory. The underlying mathematics is thoroughly and clearly presented, and the coding resources to help the reader further understand the material are helpful. Exercises and detailed appendices for most chapters round out this well-written and engaging text.

• PART I: BASICS1. Population Dynamics 1.1 Fitness 1.2 Tradeoffs and Fitness Dependence 1.3 Dependence on environment, density and frequency1.4 State space geometry 1.5 Memes and Genes 1.6 Finite populations and randomness1.7 Replicator dynamics in discrete time 1.8 Replicator dynamics in continuous time 1.9 Steady states and stability 1.10 Sexual dynamics 1.11 Discussion 1.12 Appendix A: Derivation of the Fisher equation1.13 Appendix B. Replicator dynamics, mean fitness, and entropy 1.14 Exercises 1.15 Endnotes 1.16 Bibliography 2. Simple Frequency Dependence2.1 The Hawk-Dove game 2.2 H-D parameters and dynamics 2.3 The three kinds of 2x2 games . 2.4 Dilemmas played by viruses and eBay sellers 2.5 Nonlinear frequency dependence 2.6 RPS and the simplex2.7 Replicator dynamics for RPS 2.8 Discussion 2.9 Appendix A. Payoff differences in 3x3 games 2.10 Exercises2.11 Endnotes 2.12 Bibliography3. Dynamics in n-dimensional Games3.1 Sectoring the 2-d simplex 3.2 Estimating 3x3 payoff matrices 3.3 More strategies 3.4 Nonlinear frequency dependence 3.5 Two population games: the square 3.6 Hawk-Dove with two populations 3.7 Own population effects 3.8 Higher dimensional games 3.9 Alternative dynamics 3.10 Discussion3.11 Appendix: Estimating 3x3 payoff matrices 3.12 Exercises 3.13 Notes 3.14 Bibliography 4. Equilibrium 4.1 Equilibrium in 1 dimension 4.2 Nash equilibrium with n strategies 4.3 ESS with n strategies 4.4 Equilibrium in multi-population games 4.5 Fisherian runaway equilibrium4.6 Discussion 4.7 Appendix A: Techniques to Assess Stability4.8 Exercises4.9 Notes4.10 Bibilography5. Social games 5.1 Assortative matching 5.2 Social Twists 5.3 Inheritance from two parents 5.4 The standard Price equation 5.5 Group-structured Price equation and cooperation 5.6 Group Structure and Assortativity in Lizards5.7 Price Equation in Continuous Time 5.8 Discussion5.9 Appendix: Equilibrium in the Kirkpatrick (1982) model 5.10 Exercises 5.11 Notes 5.12 Bibliography6. Cellular Automaton Games 6.1 Specifying a CA 6.2 Prisoner's Dilemma6.3 Snowdrift6.4 Public goods games with two strategies 6.5 Spatial rock-paper-scissors dynamic 6.6 Application to bacterial strains6.7 Buyer-seller game as a two population CA 6.8 Exercises 6.9 Notes 6.10 BibliographyPART II: APPLICATIONS7. Rock-Paper-Scissors Everywhere 7.1 Some RPS Theory 7.2 Humans Play RPS in the Lab 7.3 RPS Mating Systems 7.4 Predators Learn7.5 A coevolutionary model of Predators and Prey 7.6 Discussion 7.7 Appendix7.8 Exercises 7.9 Notes 7.10 Bibliography8. Learning in Games 8.1 Perspectives on learning and evolution 8.2 An empirical example 8.3 Learning rules 8.4 Decision rules 8.5 Estimating a model8.6 Results 8.7 Learning in Continuous Time .8.8 Other Models of Learning 8.9 Open Frontiers 8.10 Appendix: Towards Models of Learning in Continuous Time 8.11 Exercises 8.12 Notes 8.13 Bibliography9. Contingent Life Cycle Strategies9.1 Hawks, Doves and Plasticity 9.2 Costly Plasticity 9.3 Classic Life Cycle Analysis9.4 Strategic Life Cycle Analysis: Two Periods 9.5 Strategic Life Cycle Analysis: More general cases 9.6 Application: male elephant seals 9.7 Discussion 9.8 Appendix9.9 Exercises9.10 Notes 9.11 Bibliography10. The Blessing and the Curse of the Multiplicative Updates (Contributed by Manfred K. Warmuth)10.1 Demonstrating the blessing and the curse 10.2 Dispelling the curse 10.3 Discussion 10.4 Notes10.5 Bibliography 11. Traffic Games (contributed by John Musacchio)11.1 Simple Non-Atomic Traffic Games 11.2 Braess's Paradox 11.3 The Price of Anarchy with Nonlinear Latency Functions 11.4 Pigovian Taxes 11.5 Selfish Pricing11.6 Circuit Analogy 11.7 Discussion 11.8 Exercises11.9 Endnotes 11.10 Bibliography12. International Trade and the Environment (contributed by Matthew McGinty)12.1 Economics and evolutionary game theory 12.2 Static Cournot model 12.3 Green technology diffusion 12.4 International trade 12.5 International Trade and Pollution Taxation 12.6 Other Economic Applications 12.7 Exercises12.8 Notes12.9 Bibliography13. Evolution of Cooperation13.1 Coordination, cooperation and social dilemmas 13.2 Solution K: Kin Selection 13.3 Solution R: Bilateral reciprocity 13.4 Social preferences: a problematic solution 13.5 Early Human Niches 13.6 Solution M: Moral memes 13.7 Illustrative models 13.8 Prehistoric and historic moral codes 13.9 Discussion 13.10 Exercises13.11 Notes 13.12 Bibliography 14. Speciation14.1 Long run evolution 14.2 Adaptive Dynamics 14.3 Morph loss in RPS 14.4 Emergent Boundary Layers in Cellular Automata 14.5 Speciation in Social and Virtual Worlds 14.6 Discussion 14.7 Exercises 14.8 Endnotes 14.9 BibliographyGlossaries