Networks, crowds and markets. Reasoning about a highly connected world.

*(English)*Zbl 1205.91007
Cambridge: Cambridge University Press (ISBN 978-0-521-19533-1/hbk; 978-0-511-77157-6/ebook). xv, 727 p. (2010).

This book, split into 24 chapters, studies information networks in a social context. The first five chapters present the necessary foundations examining relevant areas of graph theory, network properties, partitioning and balanced networks where several useful theorems are outlined. The next four chapters move on the study of networks in game theory. This includes Nash equilibria, mixed strategies and Pareto-optimality, and interaction between games and evolutionary graph theory. This part of the book concludes with a study of network traffic and the Braess paradox and a study of game theory in auctions.

The third part of this book looks at markets and strategic interactions such as price setting, equilibria in trading networks and bargaining power. The fourth part consisting of three chapters studies information networks and the world wide web using a directed network model. This includes models used in searching the web as well as algorithms for sponsored search advertising.

The book then turns to population problems: in particular the study of crowds and crowd behavior, markets and the economy, and rich-get-richer models and their unpredictable effects. This section is followed by three chapters looking at dynamic structural models, which includes cascading behavior, network diffusion, and the study, from a network angle, of epidemiology and the spread of diseases and genealogy. The last part of this book looks at institutions and aggregate behavior, and develops network theoretical models for betting, voting and property rights.

This very interesting and detailed book manages to expose the wide-ranging applications of graph and network theory in a variety of areas such as game theory, auctions, web searches, horse-betting, voting, crowd behavior, trade markets and the spread of diseases. Throughout the book all necessary mathematical background is outlined in an easy to understand way, including the most interesting and curious aspects of the theory such as the Braess paradox, prisoner’s dilemma and Arrow’s impossibility theorem. The book concludes with a useful index and a detailed bibliography.

The third part of this book looks at markets and strategic interactions such as price setting, equilibria in trading networks and bargaining power. The fourth part consisting of three chapters studies information networks and the world wide web using a directed network model. This includes models used in searching the web as well as algorithms for sponsored search advertising.

The book then turns to population problems: in particular the study of crowds and crowd behavior, markets and the economy, and rich-get-richer models and their unpredictable effects. This section is followed by three chapters looking at dynamic structural models, which includes cascading behavior, network diffusion, and the study, from a network angle, of epidemiology and the spread of diseases and genealogy. The last part of this book looks at institutions and aggregate behavior, and develops network theoretical models for betting, voting and property rights.

This very interesting and detailed book manages to expose the wide-ranging applications of graph and network theory in a variety of areas such as game theory, auctions, web searches, horse-betting, voting, crowd behavior, trade markets and the spread of diseases. Throughout the book all necessary mathematical background is outlined in an easy to understand way, including the most interesting and curious aspects of the theory such as the Braess paradox, prisoner’s dilemma and Arrow’s impossibility theorem. The book concludes with a useful index and a detailed bibliography.

Reviewer: Efstratios Rappos (Athens)

##### MSC:

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

05C90 | Applications of graph theory |

91B74 | Economic models of real-world systems (e.g., electricity markets, etc.) |

91A80 | Applications of game theory |

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91D30 | Social networks; opinion dynamics |

92C60 | Medical epidemiology |

97K10 | Comprehensive works on combinatorics, graph theory, and probability (educational aspects) |