Implementation theory: Difference between revisions

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'''Implementation theory''' is an area of research in [[game theory]] concerned with whether a class of [[Mechanism design|mechanisms (or institutions) can be designed]] whose equilibrium outcomes implement a given set of [[normative]] goals or [[Welfare economics|welfare]] criteria.<ref name = "palfrey">Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. {{doi|10.1016/S1574-0005(02)03024-2}}.</ref>

There are two general types of implementation problems: the economic problem of [[Production (economics)|producing]] and [[Resource allocation|allocating]] [[Public good (economics)|public]] and [[Privateprivate good|private goods]]s and choosing over a finite set of alternatives.<ref name = "maskin">Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. {{doi|10.1016/S1574-0110(02)80009-1}}.</ref> In the case of producing and allocating public/private goods, [[Solutionsolution concept|solution concepts]]s are focused on finding [[Dominant Strategy|dominant strategies]].

In his paper "Counterspeculation, Auctions, and Competitive Sealed Tenders", [[William Vickrey]] showed that if preferences are restricted to the case of quasi-linear utility functions then the mechanism dominant strategy is dominant-strategy implementable.<ref>Vickrey, William. "Counterspeculation, Auctions, and Competitive Sealed Tenders." The Journal of Finance 16, no. 1 (1961): 8–37. {{doi|10.1111/j.1540-6261.1961.tb02789.x}}. {{JSTOR|2977633}}.

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Although largely theoretical, implementation theory may have profound implications on policy creation because some [[Social choice theory|social choice]] rules may be impossible to implement under specific game conditions.<ref name="palfrey" />

== Implementability ==

In [[mechanism design]], implementability is a property of a [[social choice function]]. It means that there is an [[incentive-compatible]] mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, including:

* A function is '''dominant-strategy implementable''' if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called [[strategyproof]]).

* A function is '''Bayesian-Nash implementable''' if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible.

See for a recent reference. In some textbooks, the entire field of mechanism design is called '''implementation theory'''.<ref>Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).</ref>

== See also ==

[[Incentive Compatibility]]

==References==

{{reflist}}

{{game theory}}

[[Category:Game theory]]