New branches of scientific disciplines often have a few paradigmatic models that serve as a testing ground for theories and a starting point for new inquiries. In the late 1990s, one of these models found fertile ground in the growing field of econophysics: the Minority Game (MG), a model for speculative markets that combined conceptual simplicity with interesting emergent behaviour and challenging mathematics. The two basic ingredients were the minority mechanism (a large number of players have to choose one of two alternatives in each round, and the minority wins) and limited rationality (each player has a small set of decision rules, and chooses the more successful ones). Combining these, one observes a phase transition between a crowded and an inefficient market phase, fat-tailed price distributions at the transition, and many other nontrivial effects.

Now, seven years after the first paper, three of the key players—Damien Challet, Matteo Marsili and Yi-Cheng Zhang—have published a monograph that summarizes the current state of the science. The book consists of two parts: a 100-page overview of the various aspects of the MG, and reprints of many essential papers.

The first chapters of Part I give a well-written description of the motivation and the history behind the MG, and then go into the phenomenology and the mathematical treatment of the model. The authors emphasize the `physics' underlying the behaviour and give coherent, intuitive explanations that are difficult to extract from the original papers. The mathematics is outlined, but calculations are not carried out in great detail (maybe they could have been included in an appendix).

Chapter 4 then discusses how and why the MG is a model for speculative markets, how it can be modified to give a closer fit to observed market statistics (in particular, reproducing the `stylized facts' of fat-tailed distributions and volatility clustering), and what conclusions one can draw from the behaviour of the MG when different kinds of agents are added. It is this chapter that really justifies the MG as a toy model, and the authors succeed in stating, but not overstating, the case for the MG.

The final chapter is devoted to extensions and alternative interpretations of the MG that take the `minority wins' mechanism as a starting point, but consider different approaches to inductive learning. Topics include evolutionary learning schemes, neural networks, and experiments with human players. The diversity of contributions demonstrates that the minority mechanism has a wider applicability and may inspire many more papers.

Part II, as mentioned, contains reprints of 27 articles on the MG and econophysics in general that are organized along the same lines as the chapters in Part I. The selection is good; the authors resisted the temptation to place too much emphasis on their own prolific output and represent a well-rounded picture of the literature.

The book thus serves several purposes, and it serves them well: it is a well-organized, concise and comprehensive introduction to the MG and the questions econophysics is concerned with, and thus of interest to researchers and graduate students who want to get involved in the field; it is a thorough summary and literature review of the MG and therefore mandatory for those who are already active on the topic; and it serves as a case study for how a toy model can be interpreted and modified to yield insight into complex phenomena, and what answers one can and cannot expect from such models. Whether the MG will serve as a foundation for econophysics in years to come (and investment firms will indeed use the MG score of applicants as a hiring criterion, as the authors jokingly speculate) or as a stepping stone to other models, only time can tell. But in the meantime, there is much to learn from it, and this book is a good place to start.