Jörg Rothe. Editor. Economics and Computation. An Introduction to Algorithmic Game. Theory, Computational Social Choice, and Fair Division

Transcription

1 Jörg Rothe Editor Economics and Computation An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division Illustrations by Irene Rothe 4^ Springer

2 Contents Foreword by Matthew O. Jackson and Yoav Shoham Preface by the Editor Contributors v vi xiii 1 Playing, Voting, and Dividing 1 J. Rothe 1.1 Playing Noncooperative Game Theory Cooperative Game Theory Voting Preference Aggregation by Voting Manipulative Actions in Single-Peaked Societies Judgment Aggregation Dividing Cake-cutting: Fair Division of Divisible Goods Fair Division of Indivisible Goods A Brief Digression to Single-Item Auctions Some Literature Pointers A Brief Digression to Computational Complexity Some Foundations of Complexity Theory The Satisfiability Problem of Propositional Logic A Brief Compendium of Complexity Classes 33 Part I Playing Successfully 2 Noncooperative Game Theory 41 P. Faliszewski, I. Rothe, and J. Rothe 2.1 Foundations Normal Form, Dominant Strategies, and Equilibria Further Two-Player Games Nash Equilibria in Mixed Strategies Definition and Application to Two-Player Games 60 ix

3 Contents Existence of Nash Equilibria in Mixcd Strategie* Checkmate: Trees for Games with Perfect Information Sequential Two-Player Games Equilibria in Game Trees Füll House: Games with Incomplete Information The Monty Hall Problem Analysis of a Simple Poker Variant How Hard Is It to Find a Nash Equilibrium? Nash Equilibria in Zero-Sum Games Nash Equilibria in General Normal Form Games Cooperative Game Theory 135 E. Elkind and J. Rothe 3.1 Foundations Cooperative Games with Transferable Utility Stability Concepts for Cooperative Games Convex Games Simple Garnes The Gore of a Simple Game Counting and Representing Simple Games Weighted Voting Games Dimensionality Power Indices The Shapley-Shubik Index and the Shapley Value The Banzhaf Indices Complexity of Problems for Succinctly Representable Games Games on Graphs Weighted Voting Games Hedonic Games 183 Part II Voting and Judging 4 Preference Aggregation by Voting 197 D. Baumeister and J. Rothe 4.1 Sorne Basic Voting Systems Scoring Protocols Voting Systems Based on Pairwise Comparisons Approval Voting and Range Voting Voting Systems Proceeding in Stages Hybrid Voting Systems Overview of Sorne Fundamental Voting Systems Properties of Voting Systems and Impossibility Theorems The Condorcet and the Majority Criterion Nondictatorship, Pareto Consistency, and Consistency Independence of Irrelevant Alternatives Resoluteness and Citizens' Sovereignty 237

4 Contents %i Strategy-Proofness and Independence of Clones Anonymity, Neutrality, and Monotonicity Homogeneity, Participation, and Twins Welcome Overview of Properties of Voting Systems Complexity of Voting Problems Winner Determination Possible and Necessary Winners Manipulation Control Bribery The Complexity of Manipulative Actione in Single-Peaked Societies 327 E. Hemaspaandra, LA. Hemaspaandra, and J. Rothe 5.1 Single-Peaked Electorates Control of Single-Peaked Electorates Manipulation of Single-Peaked Electorates Bribery of Single-Peaked Electorates Do Nearly Single-Peaked Electorates Restore Intractability? ff-Maverick-Single-Peakedness Swoon-Single-Peakedness Judgment Aggregation 361 D. Baumeister, G. Erdelyi, and J. Rothe 6.1 Foundations Judgment Aggregation Procedures and Their Properties Some Specific Judgment Aggregation Procedures Properties, Impossibility Results, and Characterizations Complexity of Judgment Aggregation Problems Winner Determination in Judgment Aggregation Safety of the Agenda Manipulation in Judgment Aggregation Bribery in Judgment Aggregation Control in Judgment Aggregat ion Concluding Remarks 391 Part III Fair Division 7 Cake-Cutting: Fair Division of Divisible Goods 395 C. Lindner and J. Rothe 7.1 How to Have a Great Party with only a Single Cake Basics Valuation Criteria Fairness Efficiency 410

5 xii Contents Manipulability Runtime ^ Cake-Cutting Protocols Two Erivy-Free Protocols for Two Players Proportional Protocols for n Players Super-Proportional Protocols for n Players A Royal Wedding: Dividing into Unequal Sliares Envy-Free Protocols for Three and Four Players Oversalted Cream Cake: Dirty-Work Protocols Avoiding Crumbs: Minimizing the Nuniber of Cuts Degree of Guaranteed Envy-Freeness Overview of Some Cake-Cutting Protocols Fair Division of Indivisible Goods 493 J. Lang and J. Rothe 8.1 Introduction Definition and Classification of Allocation Problems Allocation Problems Classification of Allocation Problems Preference Elicitation and Compact Representation Ordinal Preference Languagcs Cardinal Preference Languages Criteria for Allocations Ordinal Criteria Cardinal Criteria Computing Allocations: Centralized Mechanisins Centralized Fair Division with Ordinal PreferenceK Centralized Fair Division with Cardinal Prcferences without Money Centralized Fair Division with Cardinal Prcferences and Money Decentralized Allocation Protocols The Descending Demand Protocols The Picking Sequences Protocols Contested Pile-Based Protocols: Undercut Protocols Based on Local Exchanges Further Issues Strategy-Proofness Matching Private Endowments Randornized Fair Division 549 References 551 List of Figures 5gj List of Tables 535 Index sgy