Game-Theoretical Models in Biology (Chapman & Hall/CRC Mathematical and Computational Biology)

516 Pages·2013·7.398 MB·English

by  Mark Broom, Jan Rychtar

Game-Theoretical
Models in Biology
CHAPMAN & HALL/CRC
Mathematical and Computational Biology Series
Aims and scope:
This series aims to capture new developments and summarize what is known
over the entire spectrum of mathematical and computational biology and
medicine. It seeks to encourage the integration of mathematical, statistical,
and computational methods into biology by publishing a broad range of
textbooks, reference works, and handbooks. The titles included in the
series are meant to appeal to students, researchers, and professionals in the
mathematical, statistical and computational sciences, fundamental biology
and bioengineering, as well as interdisciplinary researchers involved in the
field. The inclusion of concrete examples and applications, and programming
techniques and examples, is highly encouraged.
Series Editors
N. F. Britton
Department of Mathematical Sciences
University of Bath
Xihong Lin
Department of Biostatistics
Harvard University
Hershel M. Safer
School of Computer Science
Tel Aviv University
Maria Victoria Schneider
European Bioinformatics Institute
Mona Singh
Department of Computer Science
Princeton University
Anna Tramontano
Department of Biochemical Sciences
University of Rome La Sapienza
Proposals for the series should be submitted to one of the series editors above or directly to:
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Published Titles
Algorithms in Bioinformatics: A Practical Differential Equations and Mathematical
Introduction Biology, Second Edition
Wing-Kin Sung D.S. Jones, M.J. Plank, and B.D. Sleeman
Bioinformatics: A Practical Approach Dynamics of Biological Systems
Shui Qing Ye Michael Small
Biological Computation Engineering Genetic Circuits
Ehud Lamm and Ron Unger Chris J. Myers
Biological Sequence Analysis Using Exactly Solvable Models of Biological
the SeqAn C++ Library Invasion
Andreas Gogol-Döring and Knut Reinert Sergei V. Petrovskii and Bai-Lian Li
Cancer Modelling and Simulation Game-Theoretical Models in Biology
Luigi Preziosi Mark Broom and Jan Rychtáˇr
Cancer Systems Biology Gene Expression Studies Using
Edwin Wang Affymetrix Microarrays
Hinrich Göhlmann and Willem Talloen
Cell Mechanics: From Single Scale-
Based Models to Multiscale Modeling Genome Annotation
Arnaud Chauvière, Luigi Preziosi, Jung Soh, Paul M.K. Gordon, and
and Claude Verdier Christoph W. Sensen
Clustering in Bioinformatics and Drug Glycome Informatics: Methods and
Discovery Applications
John D. MacCuish and Norah E. MacCuish Kiyoko F. Aoki-Kinoshita
Combinatorial Pattern Matching Handbook of Hidden Markov Models
Algorithms in Computational Biology in Bioinformatics
Using Perl and R Martin Gollery
Gabriel Valiente
Introduction to Bioinformatics
Computational Biology: A Statistical Anna Tramontano
Mechanics Perspective
Introduction to Bio-Ontologies
Ralf Blossey
Peter N. Robinson and Sebastian Bauer
Computational Hydrodynamics of
Introduction to Computational
Capsules and Biological Cells
Proteomics
C. Pozrikidis
Golan Yona
Computational Neuroscience:
Introduction to Proteins: Structure,
A Comprehensive Approach
Function, and Motion
Jianfeng Feng
Amit Kessel and Nir Ben-Tal
Computational Systems Biology of
An Introduction to Systems Biology:
Cancer
Design Principles of Biological Circuits
Emmanuel Barillot, Laurence Calzone,
Uri Alon
Philippe Hupé, Jean-Philippe Vert, and
Kinetic Modelling in Systems Biology
Andrei Zinovyev
Oleg Demin and Igor Goryanin
Data Analysis Tools for DNA Microarrays
Knowledge Discovery in Proteomics
Sorin Draghici
Igor Jurisica and Dennis Wigle
Published Titles (continued)
Meta-analysis and Combining Quantitative Biology: From Molecular to
Information in Genetics and Genomics Cellular Systems
Rudy Guerra and Darlene R. Goldstein Sebastian Bassi
Methods in Medical Informatics: Spatial Ecology
Fundamentals of Healthcare Stephen Cantrell, Chris Cosner, and
Programming in Perl, Python, and Ruby Shigui Ruan
Jules J. Berman
Spatiotemporal Patterns in Ecology
Modeling and Simulation of Capsules and Epidemiology: Theory, Models,
and Biological Cells and Simulation
C. Pozrikidis Horst Malchow, Sergei V. Petrovskii, and
Ezio Venturino
Niche Modeling: Predictions from
Statistical Distributions Statistics and Data Analysis for
David Stockwell Microarrays Using R and Bioconductor,
Second Edition
Normal Mode Analysis: Theory and
Applications to Biological and Chemical Sorin Dra˘ghici
Systems Stochastic Modelling for Systems
Qiang Cui and Ivet Bahar Biology, Second Edition
Darren J. Wilkinson
Optimal Control Applied to Biological
Models Structural Bioinformatics: An Algorithmic
Suzanne Lenhart and John T. Workman Approach
Forbes J. Burkowski
Pattern Discovery in Bioinformatics:
Theory & Algorithms The Ten Most Wanted Solutions in
Laxmi Parida Protein Bioinformatics
Anna Tramontano
Python for Bioinformatics
Sebastian Bassi
Game-Theoretical
Models in Biology
Mark Broom
Jan Rychtář
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To Monica and Denisa
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Contents
Preface xxi
Authors xxv
1 Introduction 1
1.1 The history of evolutionary games . . . . . . . . . . . . . . 1
1.1.1 Early game playing and strategic decisions . . . . . . 3
1.1.2 The birth of modern game theory . . . . . . . . . . . 4
1.1.3 The beginnings of evolutionary games. . . . . . . . . 5
1.2 The key mathematical developments . . . . . . . . . . . . . 7
1.2.1 Static games . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 Dynamic games . . . . . . . . . . . . . . . . . . . . . 8
1.3 The range of applications . . . . . . . . . . . . . . . . . . . 10
1.4 Reading this book . . . . . . . . . . . . . . . . . . . . . . . 11
2 What is a game? 13
2.1 Key game elements . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Players . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Strategies . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2.1 Pure strategies . . . . . . . . . . . . . . . . 15
2.1.2.2 Mixed strategies . . . . . . . . . . . . . . . 16
2.1.2.3 Pure or mixed strategies? . . . . . . . . . . 18
2.1.3 Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3.1 Representation of payoffs by matrices . . . 19
2.1.3.2 Payoffs from contests between mixed
strategists . . . . . . . . . . . . . . . . . . . 20
2.1.3.3 Generic payoffs . . . . . . . . . . . . . . . . 21
2.1.4 Games in normal form . . . . . . . . . . . . . . . . . 23
2.2 Games in biological settings . . . . . . . . . . . . . . . . . . 24
2.2.1 Representing the population . . . . . . . . . . . . . . 25
2.2.2 Payoffs in matrix games . . . . . . . . . . . . . . . . 26
2.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
ix