This book has as motivation the limits of standard decision theory, which has as underlying assumptions categorical preferences, the fact that each stakeholder has a predefined preference order over outcomes, and the doctrine of individual rationality, according to which each individual will restrict interest to its own benefit without regards to the interests of others or the interests of the group. The author reasonably claims that this is a simplification that, even if successful in competitive and market-driven decision making, does not model more sophisticated social relationships.

The author claims that there are two ways to address the limitations: retrofit the existing model or create a new framework to deal explicitly with complex social relationships. Stirling chose the latter, and this book is his proposed framework. This is a brave act on the part of the author, who dares to construct a new theory where a working one already exists.

However, the current presentation is not a reworking of a theory from square one. Rather, after presenting the crucial step in which the notion of preference from standard game theory is replaced with the notion of conditional utility, the book revisits the usual topics of game theory developed in the past decade under the new light of conditional game theory, thus covering the notions of conditional equilibria, coordination, uncertainty, and satisficing, basically dedicating one chapter to each topic.

The presentation of the conditioning of games is done by presenting several principles that the modeling of social interactions must follow (here, a strange point of the book must be noted, for these principles are presented as corollaries, never mentioning what main result is the source from which these corollaries are derived; I have come to the conclusion that this peculiarity should be understood as an editorial glitch rather than an important part of the presentation of the theory). Five principles are presented, and what these amount to is the following: conditional preferences cannot be represented as a set of preference orders, but rather a conditional utility measure that must respect the same laws as conditional probabilities. However, instead of events on which a probability measure is applied, these conditional utilities deal with a set of actions.

The book fails to properly address, or at least emphasize, an important combinatorial and computational consequence of that choice of solution. While an order on n actions over m stakeholders can be represented by a sequence of n × m positions, a conditional distribution has to deal with conditioning over all sets of actions, thus requiring that the utility be specified over an exponential number, in terms of the number of possible individual actions, of sets of actions. So the price of dealing with more sophisticated social interactions is the need to deal with a potentially explosive number of interactions.

This leads to another feature of the book, namely that it is basically a theoretical exposition. More examples would help readers better understand this new theory. The few examples that exist mostly deal with only two stakeholders, in variations of the classical prisoner’s dilemma. An example with a larger number of stakeholders would certainly bring to the forefront the problems of combinatorial explosion, which have been dealt with in probabilistic reasoning literature [1,2].

The failure to address combinatorial explosion is an important shortcoming of this new approach to game theory, and it is unsurprising that a theory that proposes an alternative to such a successfully developed area such as classical game theory would have to pay a price for its daring. Possible ways of addressing it would deal with a computational conditional game theory, an area with a lot of potential for future development.

One last word to potential readers: this is not an introductory course on game theory. Good knowledge of a mathematical approach to game theory (for example, Ferguson [3]) is a requirement.