Introduction. What Is a Game? Two Approaches to Game Analysis. Some Classical Games. The Underlying Biology. Matrix Games. Nonlinear Games. Asymmetric Games. Multi-Player Games. Extensive Form Games and Other Concepts in Game Theory. State-Based Games. Games in Finite and Structured Populations. Adaptive Dynamics. The Evolution of Cooperation. Group Living. Mating Games. Food Competition. Predator-Prey and Host-Parasite Interactions. Epidemic Models. Conclusions. Appendix. Bibliography. Index.
Mark Broom is a professor of mathematics at City University London. For 20 years, he has carried out mathematical research in game theory applied to biology. His major research themes include multi-player games, patterns of evolutionarily stable strategies, models of parasitic behavior (especially kleptoparasitism), the evolution of defense and signaling, and evolutionary processes on graphs. He received his PhD in mathematics from the University of Sheffield.
Jan Rychtář is an associate professor of mathematics at the University of North Carolina at Greensboro, where he helped start a math-biology research group involving faculty and students from the biology and mathematics departments. He works on game theoretical models and mathematical models of kleptoparasitism. His recent research themes focus on models of brood parasitism in dung beetles, models of mate selection in honey bees, and evolutionary processes on graphs. He received his PhD in mathematics from the University of Alberta.
"… a comprehensive, up-to-date introduction that uniquely blends
mathematical clarity and biological intuition.
The first half explores the many ways that the concepts ‘game’ and
‘evolution’ can be realized. … [The authors] discuss not only
evolution in terms of competition among existing strategies but
also long-term evolution through successive trait substitutions.
The authors also examine the effects of population size and
structure, providing an entry point into one of the most active and
exciting new directions in the field.
The second half brings to life the mathematical frameworks
introduced earlier … the authors illuminate not only the behaviors
that emerge in these particular contexts but also the process of
matching mathematical framework to biological reality, a critical
skill for aspiring evolutionary theorists. …
Broom and Rychtář offer a refreshingly clear exposition of kin
selection, using a simple model with direct biological
interpretation. They present this alongside other, distinct
mechanisms for cooperation, such as direct and indirect
reciprocity, avoiding the confusion that muddles much of the
literature on this topic. …
Students of evolutionary game theory … would do well to read
Game-Theoretical Models in Biology all the way to the finish line.
This engaging primer demonstrates that there is no tension between
mathematical elegance and biological fidelity: both are needed to
further our understanding of evolution."
—Benjamin Allen, Emmanuel College, and Martin A. Nowak, Harvard
University, Science, Vol. 341, August 2013"In the biological
sciences, there is probably no better time to become a game
theorist, and anyone who so aspires will value this text as a
guide. Assuming only a modicum of mathematics, Broom and Rychtář
lead their readers all the way from the rudiments of evolutionary
game theory to the research frontier. They are appealingly candid
on how their scope reflects their taste. Nonetheless, their
coverage is remarkably wide-ranging, from old standards like the
Hawk-Dove game to newer applications such as epidemiology. The
authors strike an excellent compromise between breadth and depth by
limiting the generality of some theoretical treatments, choosing
good examples, and using up-to-date references to round out their
coverage. By focusing on evolutionary stable strategy as a "static
concept," Broom and Rychtář convincingly demonstrate the power of
game-theoretic models to describe real animal behaviour, in ways
that mathematicians who specialize on evolutionary dynamics are apt
to overlook. Thus the book brings a timely sense of balance to the
range of texts now available. At the research frontier, the trail
has many forks; but whichever fork readers decide to explore, this
book will leave them admirably well prepared for the way
ahead."
—Mike Mesterton-Gibbons, Florida State University"This book should
prove to be a valuable addition to the bookshelf of anyone working
in, or wishing to work in, the area of application of game
theoretical approaches to modelling biological phenomena. The last
39 years, since the seminal paper of Maynard Smith and Price, have
seen an explosion of research in this area. The early work
concentrated on fairly simple models such as Hawk-Dove and the War
of Attrition, but this rapidly expanded to encompass matrix games
and multi-player games. Recently, additional complexities through
population structure and adaptive dynamics have greatly enhanced
the applicability of these models. Here, the authors, who have
themselves made several contributions to these more complex models,
in particular with respect to kleptoparisitism, have set out to
provide both a solid underpinning of the mathematical aspects of
the subject, but also to anchor it solidly in its biological
context. They have succeeded admirably in both aims, and this book
should become the standard reference for this area. I shall
certainly find it an invaluable resource, and recommend it
highly."
—Chris Cannings, Professor Emeritus, University of Sheffield"Many
books on evolutionary game dynamics are on my shelf — why would I
put another one there? The first thing that caught my attention in
the new book of Mark Broom and Jan Rychtář are the exercises.
Reading a book on mathematics is a fruitless exercise for me
without a pencil and paper and maybe a computer. The wonderful
exercises in this book are sufficiently deep to provoke some
serious thinking, but not so difficult that the reader turns them
down in despair. Broom and Rychtář cover a multitude of subjects,
from the very basics of game theory to concrete biological
applications. Some of them have not found their place into the
minds of many young scientists, such as food competition and the
ideal free distribution, but it pays to learn about these classical
applications. The book focuses on static aspects. However, with
complex dynamical considerations, theoreticians are often going too
far and it is absolutely fascinating to see how far you can get
from such a focus on static properties of games. I highly recommend
this book—not for your shelf, but for your desk!"
—Arne Traulsen, Max Planck Gesellschaft "Evolutionary game theory
originally flourished some thirty years ago as a means to predict
individual behavior in biological systems through its static
game-theoretic solution concept of an evolutionarily stable
strategy (ESS). Since then, the advancement of the theory has
increasingly occurred in other disciplines. In their timely book,
Broom and Rychtář have returned the theory to its biological roots
and illustrated the relevance of these recent developments to
biology. Their careful mathematical analysis of diverse biological
models based on such current topics as nonlinear and multi-player
games, structured population effects and the stochastic effects of
finite populations provides a comprehensive set of applications.
The book will serve both as an important resource for researchers
in the field and as a valuable text for students at a graduate or
senior undergraduate level. Students will especially appreciate the
extensive set of exercises for each chapter and that the book is
exceptionally well-written and self-contained."
—Ross Cressman, Wilfrid Laurier University
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