This collection of papers is an outgrowth of the "Game Practice I" th th conference held in Genoa from 28 to 30 June 1998. More precisely, it is the result of the call for papers that was issued in association with that conference: actually, nearly half of the contributions to this book are papers that were presented in Genoa. The name chosen for the conference and for this book is in evident and provocative contrast with "Game Theory" this choice needs some explanation, and to that we shall devote a few words of this Preface. Let us say at the outset that "Game Practice" would not exist without Game Theory. As one can see, the overall content of this book is firmly rooted in the existing Game Theory. It could be hardly otherwise, given the success and influence of Game Theory (just think of the basic issues in Economic Theory), and the tremendous development that has taken place within Game Theory. This success, however, makes even more evident the existence of problems with respect to the verification of the theory. This is patent from the point of view of the predictive value of Game Theory (the "positive" side): a lot of experimental and observational evidence demon strates that there is a large gap between theory and "practice.""

This collection of papers is an outgrowth of the "Game Practice I" th th conference held in Genoa from 28 to 30 June 1998. More precisely, it is the result of the call for papers that was issued in association with that conference: actually, nearly half of the contributions to this book are papers that were presented in Genoa. The name chosen for the conference and for this book is in evident and provocative contrast with "Game Theory": this choice needs some explanation, and to that we shall devote a few words of this Preface. Let us say at the outset that "Game Practice" would not exist without Game Theory. As one can see, the overall content of this book is firmly rooted in the existing Game Theory. It could be hardly otherwise, given the success and influence of Game Theory (just think of the basic issues in Economic Theory), and the tremendous development that has taken place within Game Theory. This success, however, makes even more evident the existence of problems with respect to the verification of the theory. This is patent from the point of view of the predictive value of Game Theory (the "positive" side): a lot of experimental and observational evidence demon strates that there is a large gap between theory and "practice".

Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory. This book is published in cooperation with Real Sociedad Matematica Espanola.