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".

Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

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 book is an introductory graduate-level text on game theory that grew out of courses in mathematics and economics and operations research. Game theory deals with mathematical models of conflict and cooperation. In the first nine chapters, the author covers noncooperative games in extensive and strategic form and some economic applications. Relations with the theory of linear programing and the theory of linear complementarity are indicated. The last chapter treats different types of cooperative games and solution concepts. Discussed are economic applications and applications in OR-situations with multiple agents. The book includes a rich collection of exercises, partly with solutions.