Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Implementation Theory

  • Luis C. CorchónEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_283-2


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.


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

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.

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I am grateful to Pablo Amorós, Claude d’Aspremont, Carmen Beviá, Luis Cabral, Eric Maskin, Bernardo Moreno, Carlos Pimienta, Socorro Puy, Tömas Sjöstrom, William Thomson, Matteo Triossi, Galina Zudenkova, and an anonymous referee for helpful suggestions and to the Spanish Ministry 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 the first draft of this survey. This survey was dedicated to Leo Hurwicz to celebrate 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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Authors and Affiliations

  1. 1.Departamento de EconomíaUniversidad Carlos IIIMadridSpain