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 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"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 producing and allocating public and private goods and choosing over a finite set of alternative.<ref name = "maskin">Maskin, Eric. “Implementation"Implementation Theory.”" Science, 2002. https://{{doi.org/|10.1111/j.1477-9552.2010.00281.x}}.</ref> In the case of producing and allocating public/private goods, solution concepts are focused on finding 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, 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 O. “A"A Crash Course in Implementation Theory.”" Social Choice and Welfare 18, no. 4 (2001): 655–708. https://{{doi.org/|10.1007/s003550100152}}. {{JSTOR|41106420}}.</ref>

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