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Computational Aspects of Cooperative Game Theory Comput CHALKIADAKIS • ELKIND • WOOLDRIDGE • • ELKIND CHALKIADAKIS THEORY GAME ASPECTS OF COOPERATIVE COMPUTATIONAL SeriesSeries ISSN: ISSN: 1939-4608 1939-4608 WOOLDRIDGE • • ELKIND WOOLDRIDGE • CHALKIADAKIS • ELKIND CHALKIADAKIS THEORY GAME THEORY ASPECTS OF COOPERATIVE GAME ASPECTS OF COOPERATIVE COMPUTATIONAL COMPUTATIONAL SSYNTHESISYNTHESIS L LLECTURESECTURES ON ON A AARTIFRTIF ICIAL ICIAL MM MorganMorgan & & ClaypoolClaypool PublishersPublishers IINTELLIGENCENTELLIGENCE AND AND M MMACHINEACHINE L LLEARNINGEARNING &&CC SeriesSeries Editors: Editors: RonaldRonald J. J. Brachman, Brachman, Yahoo! Yahoo!Yahoo! Research ResearchResearch and and Thomas Thomas G. G. Dietterich, Dietterich, Oregon Oregon State State University University ComputationalComputational AspectsAspects ofof ComputationalComputational Aspects Aspects of of CooperativeCooperative Game Game Theory Theory CooperativeCooperative GameGame Theory Theory GeorgiosGeorgios Chalkiadakis, Chalkiadakis, Technical Technical University University of of Crete, Crete, Greece Greece EdithEdith Elkind, Elkind, Nanyang Nanyang Technological Technological University, University, Singapore Singapore MichaelMichael Wooldridge, Wooldridge, University University of of Liverpool, Liverpool, United United Kingdom Kingdom CooperativeCooperative game game theory theory is is a abranch branch of of (micro-)economics (micro-)economics that that studies studies the the behavior behavior of of self-interested self-interested agentsagentsagents in inin strategic strategicstrategic settings settingssettings where wherewhere binding bindingbinding agreements agreementsagreements among amongamong agents agentsagents are areare possible. possible.possible. Our OurOur aim aimaim in inin this thisthis book bookbook isis isto toto present presentpresent a aasurvey surveysurvey of ofof work workwork on onon the thethe computational computationalcomputational aspects aspectsaspects of ofof cooperative cooperativecooperative game gamegame theory. theory.theory. We WeWe begin beginbegin by byby formallyformallyformally defining definingdefining tr trtransferableansferableansferable utility utilityutility games gamesgames in inin characteristic characteristiccharacteristic function functionfunction form, form,form, and andand introducing introducingintroducing key keykey solution solutionsolution conceptsconceptsconcepts such suchsuch as asas the thethe core corecore and andand the thethe Shapley ShapleyShapley value. value.value. We WeWe then thenthen discuss discussdiscuss two twotwo major majormajor issues issuesissues that thatthat arise arisearise when whenwhen consideringconsideringconsidering such suchsuch games gamesgames from fromfrom a aacomputational computationalcomputational perspective: perspective:perspective: identifying identifyingidentifying compact compactcompact representations representationsrepresentations for forfor games, games,games, andandand the thethe closely closelyclosely related relatedrelated problem problemproblem of ofof efficiently efficientlyefficiently computing computingcomputing solution solutionsolution concepts conceptsconcepts for forfor games. games.games. We WeWe survey surveysurvey several severalseveral formalismsformalismsformalisms for forfor cooperative cooperativecooperative games gamesgames that thatthat have havehave been beenbeen pr prproposedoposed in in the the literature, literature, including, including, for for example, example, GeorgiosGeorgios Chalkiadakis Chalkiadakis cooperativecooperativecooperative games gamesgames defined defineddefined on onon networks, networks,networks, as asas well wellwell as asas general generalgeneral compact compactcompact representation representationrepresentation schemes schemesschemes such suchsuch as asas MC- MC-MC- Edith Elkind netsnets and and skill skill games. games. As As a adetailed detailed case case study, study, we we consider consider weighted weighted voting voting games: games: a awidely-used widely-used and and Edith Elkind practicallypractically important important class class of of cooperative cooperative games games that that inherently inherently have have a anatural natural compact compact representation. representation. MichaelMichael Wooldridge Wooldridge WeWe investigate investigate the the complexity complexity of of solution solution concepts concepts f orfor such such games, games, and and generalizations generalizations of of them. them. We We brieflybriefly discuss discuss games games with with non-transferable non-transferable utility utility and and partition partition function function games. games. We We then then overview overview algorithmsalgorithmsalgorithms for forfor identifying identifyingidentifying welfare-maximizing welfare-maximizingwelfare-maximizing coalition coalitioncoalition structures structuresstructures and andand methods methodsmethods used usedused by byby rational rationalrational agents agentsagents tototo form formform coalitions coalitionscoalitions (even (even(even under underunder uncertainty), uncertainty),uncertainty), including includingincluding bargaining bargainingbargaining algorithms. algorithms.algorithms. We WeWe conclude concludeconclude by byby considering consideringconsidering somesomesome developing developingdeveloping topics, topics,topics, applications, applications,applications, and andand future futurefuture research researchresearch directions. directions.directions. AboutAbout SYNTHESIs SYNTHESIs ThisThis volume volume is is a aprinted printed version version of of a awork work that that appears appears in in the the Synthesis Synthesis MORGAN MORGANMORGAN DigitalDigital Library Library of of Engineering Engineering and and Computer Computer Science. Science. Synthesis Synthesis Lectures Lectures provideprovide concise, concise, original original presentations presentations of of important important research research and and development development topics,topics,topics, published publishedpublished quickly, quickly,quickly, in inin digital digitaldigital and andand print printprint formats. formats.formats. For ForFor more moremore information informationinformation & visitvisitvisit www.morganclaypool.com www.morganclaypool.com & & CLAYPOOL CLAYPOOLCLAYPOOL ISBN:ISBN:ISBN: 978-1-60845-652-9 978-1-60845-652-9978-1-60845-652-9 YNTHESISYNTHESIS ECTURESECTURESONON RTIFRTIF ICIAL ICIAL Morgan Claypool Publishers 9900000 SS L LL A AA Morgan& & Claypool Publishers IINTELLIGENCENTELLIGENCE AND AND M MMACHINEACHINE L LLEARNINGEARNING www.morganclaypool.comwww.morganclaypool.com 99787186106808454655625929 RonaldRonald J. J. Brachman Brachman and and Thomas Thomas G. G. Dietterich, Dietterich, Series Series Editors Editors Computational Aspects of Cooperative Game Theory Synthesis Lectures on Artificial Intelligence and Machine Learning Editors Ronald J. Brachman, Yahoo Research William W. Cohen, Carnegie Mellon University Thomas Dietterich, Oregon State University Computational Aspects of Cooperative Game Theory Georgios Chalkiadakis, Edith Elkind, and Michael Wooldridge 2012 Representations and Techniques for 3D Object Recognition and Scene Interpretation Derek Hoiem and Silvio Savarese 2011 A Short Introduction to Preferences: Between Artificial Intelligence and Social Choice Francesca Rossi, Kristen Brent Venable, and Toby Walsh 2011 Human Computation Edith Law and Luis von Ahn 2011 Trading Agents Michael P.Wellman 2011 Visual Object Recognition Kristen Grauman and Bastian Leibe 2011 Learning with Support Vector Machines Colin Campbell and Yiming Ying 2011 iii Algorithms for Reinforcement Learning Csaba Szepesvári 2010 Data Integration: The Relational Logic Approach Michael Genesereth 2010 Markov Logic: An Interface Layer for Artificial Intelligence Pedro Domingos and Daniel Lowd 2009 Introduction to Semi-Supervised Learning Xiaojin Zhu and Andrew B.Goldberg 2009 Action Programming Languages Michael Thielscher 2008 Representation Discovery using Harmonic Analysis Sridhar Mahadevan 2008 Essentials of Game Theory: A Concise Multidisciplinary Introduction Kevin Leyton-Brown and Yoav Shoham 2008 A Concise Introduction to Multiagent Systems and Distributed Artificial Intelligence Nikos Vlassis 2007 Intelligent Autonomous Robotics: A Robot Soccer Case Study Peter Stone 2007 Copyright © 2012 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Computational Aspects of Cooperative Game Theory Georgios Chalkiadakis, Edith Elkind, and Michael Wooldridge www.morganclaypool.com ISBN: 9781608456529 paperback ISBN: 9781608456536 ebook DOI 10.2200/S00355ED1V01Y201107AIM016 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING Lecture #16 Series Editors: Ronald J. Brachman, Yahoo! Research William W. Cohen, Carnegie Mellon University Thomas Dietterich, Oregon State University Series ISSN Synthesis Lectures on Artificial Intelligence and Machine Learning Print 1939-4608 Electronic 1939-4616 Computational Aspects of Cooperative Game Theory Georgios Chalkiadakis Technical University of Crete, Greece Edith Elkind Nanyang Technological University, Singapore Michael Wooldridge University of Liverpool, United Kingdom SYNTHESIS LECTURES ON ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING #16 M &C Morgan& cLaypool publishers ABSTRACT Cooperative
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