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"Chapter 61 Implementation Theory.”" Handbook of Game Theory with Economic Applications, 2002. https://{{doi.org/|10.1016/S1574-0005(02)03024-2}}.</ref>

{{unreferenced|date=January 2014}}

'''Implementation theory''' is an area of research in [[game theory]] concerned with whether a class of mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of normative goals or welfare criteria.<ref name = "palfrey">Palfrey, Thomas R. “Chapter 61 Implementation Theory.” Handbook of Game Theory with Economic Applications, 2002. https://doi.org/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 [[private goodsgood]]s and choosing over a finite set of alternativealternatives.<ref name = "maskin">Maskin, Eric and Sjöström, Tomas. “Implementation"Implementation Theory.”" Handbook of Social Choice and ScienceWelfare, 2002. https://{{doi.org/|10.11111016/j.1477S1574-0110(02)80009-9552.2010.00281.x1}}.</ref> In the case of producing and allocating public/private goods, [[solution conceptsconcept]]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"Counterspeculation, AUCTIONSAuctions, ANDand COMPETITIVECompetitive SEALEDSealed TENDERSTenders.”" The Journal of Finance 16, no. 1 (1961): 8–37. https://{{doi.org/|10.1111/j.1540-6261.1961.tb02789.x}}. {{JSTOR|2977633}}.

</ref> “A"A [[social choice]] rule is dominant strategy [[incentive compatible]], or [[Strategy proof|strategy-proof]], if the associated [[revelation mechanism]] has the property that honestly reporting the truth is always a dominant strategy for each agent.”"<ref name="maskin" /> However, the payments to agents become large, sacrificing budget neutrality to incentive compatibility.

In a game where multiple agents are to report their preferences (or their type), it may be in the best interest of some agents to lie about their preferences. This may improve their [[outcome (game theory)|payoff]], but it may not be seen as a fair outcome to other agents.<ref>Jackson, Matthew InO. order"A toCrash implementCourse ain moreImplementation "fairTheory." outcome,Social inChoice aand repeatedWelfare game18, theno. other4 players(2001): may655–708. choose to punish{{doi|10.1007/s003550100152}}. any "cheaters"{{JSTOR|41106420}}.</ref>

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" />

The conditions of a repeated game where an arbitrary outcome may be enforced are set out in theorems often known as [[folk theorem (game theory)|folk theorems]]. If a game is not repeated, it may only be possible to implement outcomes which are [[Nash equilibrium|Nash equilibria]] or satisfy some other [[equilibrium selection|equilibrium]] concept.

== 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]]