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Implementation theory
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<h2 id="implementability">Implementability</h2> <p>In <a href="/facts/Mechanism_design/l3Uj6wfe">mechanism design</a>, implementability is a property of a <a href="/facts/Social_choice_function/l3Uj6wfe">social choice function</a>. It means that there is an <a href="/facts/Incentive-compatible/pE8NEGNx">incentive-compatible</a> mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, including: </p> <ul><li>A function is dominant-strategy implementable if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called <a href="/facts/Strategyproof/mQfERF7h">strategyproof</a>).</li> <li>A function is Bayesian-Nash implementable if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible.</li></ul> <p>See for a recent reference. In some textbooks, the entire field of mechanism design is called implementation theory.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p> <h2 id="see-also">See also</h2> <p><a href="/facts/Incentive_Compatibility/pE8NEGNx">Incentive Compatibility</a> </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. doi:10.1016/S1574-0005(02)03024-2. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. doi:10.1016/S1574-0110(02)80009-1. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. doi:10.1016/S1574-0110(02)80009-1. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. doi:10.1016/S1574-0005(02)03024-2. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994). <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> </ol>