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Evolutionary Games in Natural, Social, and Virtual Worlds

Daniel Friedman and Barry Sinervo
Oxford University Press
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Megan Sawyer
, on

The reader looking for a simple, non-mathematical introduction to evolutionary game theory should look elsewhere. For those comfortable with mathematical notation liberally used within the text, however, Evolutionary Games is an excellent resource for understanding and applying game theory to a variety of topics, including life-cycle strategies, traffic flow, and cooperation. Written by a professor of economics (Friedman) and an evolutionary biologist (Sinervo), this text combines information from both fields in a cohesive manner.

Evolutionary Games begins with six chapters of mathematical background behind evolutionary game theory. Core concepts (utilized in application chapters later in the text) are presented sequentially with thorough explanation and diagrams. The mathematical notation is clearly presented, with a discussion of significant terms in the immediate surrounding text. This clarity becomes quite helpful for reference when reading subsequent eight application chapters.

Rather than focusing solely on economic and/or biological topics, Evolutionary Games seems to operate on a continuum between and transcending the two fields with the choice of applications explored. Each chapter is complete with an appendix further detailing the mathematics behind the material presented, but also with exercises for the reader. Within the exercises in the application chapters, many problems refer back to a specific “Basics” chapter, helping point the reader in a helpful direction. Various sections contain code (R, Mathematica, Excel, and/or MATLAB) to help explain concepts; the DOI for this downloadable material is buried in the Preface (page xii). Finally, a glossary of terms and mathematical notation is conveniently included for the occasional head-scratching moment.

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.

Megan Sawyer is an assistant professor of mathematics at Southern New Hampshire University in Manchester, NH.


1. Population Dynamics
1.1 Fitness
1.2 Tradeoffs and Fitness Dependence
1.3 Dependence on environment, density and frequency
1.4 State space geometry
1.5 Memes and Genes
1.6 Finite populations and randomness
1.7 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 equation
1.13 Appendix B. Replicator dynamics, mean fitness, and entropy
1.14 Exercises
1.15 Endnotes
1.16 Bibliography

2. Simple Frequency Dependence
2.1 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 simplex
2.7 Replicator dynamics for RPS
2.8 Discussion
2.9 Appendix A. Payoff differences in 3x3 games
2.10 Exercises
2.11 Endnotes
2.12 Bibliography

3. Dynamics in n-dimensional Games
3.1 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 Discussion
3.11 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 equilibrium
4.6 Discussion
4.7 Appendix A: Techniques to Assess Stability
4.8 Exercises
4.9 Notes
4.10 Bibilography

5. 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 Lizards
5.7 Price Equation in Continuous Time
5.8 Discussion
5.9 Appendix: Equilibrium in the Kirkpatrick (1982) model
5.10 Exercises
5.11 Notes
5.12 Bibliography

6. Cellular Automaton Games
6.1 Specifying a CA
6.2 Prisoner's Dilemma
6.3 Snowdrift
6.4 Public goods games with two strategies
6.5 Spatial rock-paper-scissors dynamic
6.6 Application to bacterial strains
6.7 Buyer-seller game as a two population CA
6.8 Exercises
6.9 Notes
6.10 Bibliography


7. 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 Learn
7.5 A coevolutionary model of Predators and Prey
7.6 Discussion
7.7 Appendix
7.8 Exercises
7.9 Notes
7.10 Bibliography

8. 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 model
8.6 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 Bibliography

9. Contingent Life Cycle Strategies
9.1 Hawks, Doves and Plasticity
9.2 Costly Plasticity
9.3 Classic Life Cycle Analysis
9.4 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 Appendix
9.9 Exercises
9.10 Notes
9.11 Bibliography

10. 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 Notes
10.5 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 Pricing
11.6 Circuit Analogy
11.7 Discussion
11.8 Exercises
11.9 Endnotes
11.10 Bibliography

12. 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 Exercises
12.8 Notes
12.9 Bibliography

13. Evolution of Cooperation
13.1 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 Exercises
13.11 Notes
13.12 Bibliography

14. Speciation
14.1 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 Bibliography