A Toolbox for Economic Design

Contents Introduction 1 A Story from Ancient Athens Institutions and Economics The Big Picture Auction Example A Taste of Social Choice Theory Arrow's Impossibility Theorem Social Choice Functions Economic Domain Exchange Economies Social Choice Correspondences on the Exchange Economy Domain The Pareto Social Choice Correspondence The Individually Rational Social Choice Correspondence The Core Social Choice Correspondence The No-Envy Social Choice Correspondence Combinations of the previous Social Choice Correspondences The Walrasian Social Choice Correspondence Quasilinear Preferences and Their Uses Appendix: Proofs Arrow's Impossibility Theorem Gibbard-Satterthwaite Theorem Exercises Dominant Strategy Implementation Definitions Revelation Principle Restricting Domains: Single-Peaked Preferences Restricted Domains: Quasilinear Domains and Groves Mechanisms Balance Problem Voluntary Participation Problem The Vickrey Auction Exercises Implementation in Nash Equilibria: A Lot of Information Assumed A Quick Lesson on Nash Equilibrium Nash Equilibrium in Mixed Strategies Nash Equilibrium in Implementation Strategy Space Reduction Two Person Cases Exercises 4 Bayesian Equilibrium and Mechanisms Preliminary: How to Represent Information Bayesian Equilibrium The Bayesian Revelation Principle The Mechanism of d'Aspremont and Gérard-Varet and of Arrow Voluntary Participation Optimal Auctions Bilateral Trading Exercises Refined Nash Implementation Implementation in Subgame Perfect Equilibrium Subgame Perfect Implementation in Quasilinear Environments Implementation using Undominated Strategies Double Implementation Definitions Ratio Correspondence Virtual Nash Implementation Applications Manipulation-Resistant Online Reputation Systems Walrasian Implementation via Market Games Implementing the Lindahl Social Choice Correspondence Implementing Fair Allocations Application to Negative Externality Problems: Pollution Abatement A Nearly Efficient Mutual Insurance Mechanism Financing the Athenian Fleet Bayesian Implementation Example of Multiple Bayesian Equilibria Bayesian Implementation and Bayesian Monotonicity Resrictiveness of Bayesian Monotonicity Virtual Bayesian Implementation Further Topics in Mechanism Design Endogenous Mechanisms Notation and Definitions An Application: Public Goods Positive Results for Endogenous Games with 3 or More Players Overcoming Incentive Constraints by Linking Decisions Notation and Definitions Results Robust Mechanism Design Notation and Definitions Results The Limits of Ex Post Implementation Notation and a Result An Illustration of the Geometric Condition Exercises Matching Models: Theory and Applications 203 What is Matching? Definitions and Notation Two-Sided Matching One-to-One Matching Many-to-One Matching One-Sided Matching The Shapley and Scarf House Market House Allocation Problems The Kidney Exchange Problem Exercises Empirical Evidence on Mechanisms Introduction Voluntary Contribution Mechanisms for Public Goods Tests of Incentive Compatibility Research on Mechanism Dynamics Tests of Implementation Concepts Applied Economic Design: Notes from the Field Conclusion A Mathematics Review and More on Economic Domains A.1 Sets, Correspondences, Functions, Intervals A.2 Derivatives and Related Notation Elements of Mathematical Optimization Envelope Theorem The Edgeworth Box Public Good Economies The Simplest Public Project Model Public Goods Models Social Choice Correspondences on Public Good Economy Domains Pareto Social Choice Correspondence Lindahl and Constrained Lindahl Social Choice Correspondences Ratio Social Choice Correspondence Exercises Notation Bibliography Index