Game-theoretical models in biology. (English) Zbl 1264.92002

Broom, Mark; Rychtář, Jan

Chapman & Hall/CRC Mathematical and Computational Biology Series. Boca Raton, FL: CRC Press (ISBN 978-1-4398-5321-4/hbk). xxv, 494 p. (2013).

Game theory studies competition which is a basic aspect of life. The payoff of each player depends on the behavior of other players. Thus it is different from optimization. It has been a long time since the classic book [J. Hofbauer and K. Sigmund, Evolutionary games and population dynamics. Cambridge: Cambridge University Press (1998; Zbl 0914.90287)] has appeared. Hence this book is both important and appeared in the appropriate time. This book strikes a good balance between mathematics and biology. The exercise part is important for students although this reviewer proposes a solution hint section to be added. Due to the extraordinary depth and variety of topics of this book, its size is large (494) pages but this reviewer proposes that some references are given for games that are studied using fractional order calculus. Such games may have different outcomes from those using integer order calculus. Also surprisingly missing from the reference list is the excellent introductory book of J. N. Webb [Game theory. Decisions, interaction and evolution. London: Springer (2007; Zbl 1107.91001)]. Finally this reviewer believes that this book will be a basic reference for almost anyone studying game theory in biology. I thank the authors for this outstanding book.

Reviewer: E. Ahmed (Mansoura)

MSC:

92B05	General biology and biomathematics
91A22	Evolutionary games
91A80	Applications of game theory
92-02	Research exposition (monographs, survey articles) pertaining to biology
91A40	Other game-theoretic models

Software:

Matlab