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Implementation Theory

  • Reference work entry
Computational Complexity

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Article Outline

Glossary

Definition of the Subject

Introduction

Brief History of Implementation Theory

The Main Concepts

The Main Insights

Unsolved Issues and Further Research

Answers to the Questions

Acknowledgments

Bibliography

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Abbreviations

Type of an agent :

All the information possessed by this agent. It may refer to the preferences of this agent and/or to the knowledge of this agent of the preferences of other agents.

State of the world :

Description of all information possessed by all agents.

Social choice rule :

A correspondence mapping the set of states of the world in the set of allocations. It represents the social objectives that the society or its representatives want to achieve.

Mechanism :

A list of message spaces and an outcome function mapping messages into allocations. It represents the communication and decision aspects of the organization.

Equilibrium concept:

A mapping (or a collection of them) from the set of states of the world into allocations yielded by equilibrium messages. This equilibrium is a game‐theoretical notion of how agents behave, e. g. Nash Equilibrium, Bayesian Equilibrium, Dominant Strategies, etc.

Implementable social choice rule in an equilibrium concept (e.g. Nash equilibrium):

A Social Choice Rule is implementable in an equilibrium concept (e. g. Nash Equilibrium) if there is a mechanism such that for each state of the world the allocations prescribed by the Social Choice Rule and those yielded by the equilibrium concept coincide.

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Acknowledgments

I am grateful to Pablo Amorós, Claude d'Aspremont, Carmen Beviá, Luis Cabral, Eric Maskin, Carlos Pimienta, Socorro Puy, Tömas Sjöstrom, William Thomson, Matteo Triossi, Galina Zudenkova and an anonymous referee for helpful suggestions and to the Spanish Ministery of Education for financial support under grant SEJ2005‐06167. I also thank the Department of Economics, Stern School of Business, NYU, for their hospitality while writing this survey. This survey is dedicated to Leo Hurwicz to celebrate his 90th birthday and his Nobel Prize and to the memory of those who contributed to the area and are no longer with us: Louis-André Gerard‐Varet, Jean‐Jacques Laffont, Richard McKelvey and Murat Sertel.

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  1. Departamento de Economía, Universidad Carlos III, Madrid, Spain

    Luis C. Corchón

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Corchón, L.C. (2012). Implementation Theory. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_102

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