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> |
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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. |
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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 |
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 good|private goods]] and choosing over a finite set of alternatives.<ref name = "maskin">Maskin, Eric. "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, [[Solution concept|solution concepts]] are focused on finding [[Dominant Strategy|dominant strategies]]. |
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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. |
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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</ref> |
</ref> "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. |
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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. |
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 Crash Course in Implementation Theory." Social Choice and Welfare 18, no. 4 (2001): 655–708. {{doi|10.1007/s003550100152}}. {{JSTOR|41106420}}.</ref> |
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</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" /> |
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" /> |
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== Implementability == |
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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: |
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<references /> |
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* A function is '''dominant-strategy implementable''' if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called [[strategyproof]]). |
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* A function is '''Bayesian-Nash implementable''' if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible. |
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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> |
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== See also == |
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* [[Implementability (mechanism design)]] |
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{{reflist}} |
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{{game theory}} |
{{game theory}} |
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[[Category:Game theory]] |
[[Category:Game theory]] |
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Latest revision as of 19:19, 1 July 2024
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.[1]
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 alternatives.[2] 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.[3] "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."[2] 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 payoff, but it may not be seen as a fair outcome to other agents.[4]
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.[1]
Implementability
[edit]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.[5]
See also
[edit]References
[edit]- ^ a b Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. doi:10.1016/S1574-0005(02)03024-2.
- ^ a b Maskin, Eric. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. doi:10.1016/S1574-0110(02)80009-1.
- ^ 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.
- ^ Jackson, Matthew O. "A Crash Course in Implementation Theory." Social Choice and Welfare 18, no. 4 (2001): 655–708. doi:10.1007/s003550100152. JSTOR 41106420.
- ^ Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).
