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In this book we study systematically the main solutions of cooperative games:
the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games,
and the core, the Shapley value, and the ordinal bargaining set of NTU games.
To each solution we devote a separate chapter wherein we study its properties
in full detail. Moreover, important variants are defined or even intensively
analyzed. We also investigate in separate chapters continuity, dynamics, and
geometric properties of solutions of TU games. Our study culminates in uniform
and coherent axiomatizations of all the foregoing solutions (excluding
the bargaining set).
It is our pleasure to acknowledge the help of the following persons and institutions.
We express our gratitude to Michael Maschler for his detailed comments
on an early version, due to the first author, of Chapters 2 – 8. We
thank Michael Borns for the linguistic edition of the manuscript of this book.
We are indebted to Claus-Jochen Haake, Sven Klauke, and Christian Weiß
for reading large parts of the manuscript and suggesting many improvements.
Peter Sudh¨olter is grateful to the Center for Rationality and Interactive Decision
Theory of the Hebrew University of Jerusalem and to the Edmund
Landau Center for Research in Mathematical Analysis and Related Areas,
the Institute of Mathematics of the Hebrew University of Jerusalem, for their
hospitality during the academic year 2000-01 and during the summer of 2002.
These institutions made the typing of the manuscript possible. He is also
grateful to the Institute of Mathematical Economics, University of Bielefeld,
for its support during several visits in the years 2001 and 2002.
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