{"id":5193,"date":"2025-03-21T23:16:27","date_gmt":"2025-03-21T14:16:27","guid":{"rendered":"https:\/\/saraheee.com\/?p=5193"},"modified":"2025-03-23T18:20:40","modified_gmt":"2025-03-23T09:20:40","slug":"gt-mechanism-2-vickrey-clarke-groves-mechanisms-definitions","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2025\/03\/gt-mechanism-2-vickrey-clarke-groves-mechanisms-definitions\/","title":{"rendered":"[GT Mechanism] #2. Vickrey-Clarke-Groves Mechanisms: Definitions"},"content":{"rendered":"<h3 class=\"wp-block-heading\">GTO2-3-02: Vickrey-Clarke-Groves Mechanisms: Definitions<\/h3>\n\n\n\n<p>Vickrey-Clarke-Groves(VGC) \uba54\ucee4\ub2c8\uc998\uc5d0 \ub300\ud574 \uc774\uc57c\uae30\ud560 \uac83\uc774\ub2e4.<br>\uc774 \uba54\ucee4\ub2c8\uc998\uc740 \uac8c\uc784 \uc774\ub860\uc5d0\uc11c \uac00\uc7a5 \ub9ce\uc774 \uc5f0\uad6c\ub41c \uba54\ucee4\ub2c8\uc998 \uc911 \ud558\ub098\uc774\ub2e4. \uba3c\uc800 \uc774 \uba54\ucee4\ub2c8\uc998\uc774 \uc81c\uacf5\ud558\ub294 \uae0d\uc815\uc801\uc778 \uacb0\uacfc\ub4e4\uc5d0 \ub300\ud574 \uac04\ub7b5\ud788 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">A positive result &#8211; \uae30\ubcf8 \uc124\uc815: \uc900\uc120\ud615 \ud658\uacbd<\/h4>\n\n\n\n<p>Recall that in the quasilinear utility setting, a direct mechanism consists of a choice rule and a payment rule.<\/p>\n\n\n\n<p>\uc6b0\ub9ac\ub294 \uc900\uc120\ud615(quasi-linear) \ud658\uacbd\uc5d0\uc11c \uc791\uc5c5\ud560 \uac83\uc774\ub2e4.<br>\uc774\ub294 \uc9c1\uc811 \uba54\ucee4\ub2c8\uc998(direct mechanism)\uc5d0\uc11c, \uc0ac\ud68c\uac00 \uc120\ud0dd \uaddc\uce59(choice rule)\uacfc \uc9c0\ubd88 \uaddc\uce59(payment rule)\uc744 \uac1c\uc778\ub4e4\uc774 \ubcf4\uace0\ud558\ub294 \uc120\ud638(preferences)\uc5d0 \ub530\ub77c \uacb0\uc815\ud558\ub294 \uad6c\uc870\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\n\n\n\n<p>VCG \uba54\ucee4\ub2c8\uc998\uc758 \uac00\uc7a5 \ud070 \uc7a5\uc810\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">\uc9c4\uc2e4\uc744 \ub9d0\ud558\ub294 \uac83\uc774 \uc9c0\ubc30 \uc804\ub7b5(dominant strategy)\uc774\ub2e4.<\/mark><br>(has truth as a dominant strategy (satisfies truthfulness, is strategy-proof))<br>\uc989, \ub2e4\ub978 \uc0ac\ub78c\ub4e4\uc774 \ubb34\uc5c7\uc744 \ud558\ub4e0 \uc0c1\uad00\uc5c6\uc774, \uac1c\uc778\uc740 \uc790\uc2e0\uc758 \ud6a8\uc6a9\uc744 \ucd5c\ub300\ud654\ud558\uae30 \uc704\ud574 \ud56d\uc0c1 \uc9c4\uc2e4\uc744 \ub9d0\ud558\ub294 \uac83\uc774 \ucd5c\uc120\uc774\ub2e4.<\/li>\n\n\n\n<li><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">\uc120\ud0dd\ub41c \uacb0\uacfc\ub294 \ud6a8\uc728\uc801(efficient)\uc774\ub2e4.<\/mark><br>(makes efficient choices (not including payments))<br>\uc0ac\ud68c \uc804\uccb4\uc758 \ud6a8\uc6a9\uc758 \ucd1d\ud569\uc744 \ucd5c\ub300\ud654\ud558\ub294 \uacb0\uacfc\ub97c \uc120\ud0dd\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4.<br>\ub2e4\ub9cc, \uc9c0\ubd88 \ucd1d\ud569\uc774 \ud56d\uc0c1 \uade0\ud615(balance)\uc744 \uc774\ub8e8\ub294 \uac83\uc740 \uc544\ub2d0 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>And, under additional assumptions about the setting, can satisfy: <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>weak budget balance<\/li>\n\n\n\n<li>interim individual rationality<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc5ed\uc0ac\uc801 \ubc30\uacbd<\/h4>\n\n\n\n<p>Vickrey\ub294 \uacbd\ub9e4 \uc0c1\ud669\uc5d0\uc11c \ucc98\uc74c\uc73c\ub85c \uc774 \uba54\ucee4\ub2c8\uc998\uc744 \uc815\uc758\ud558\uc600\uc73c\uba70, \uc774\ub294 2\ub4f1 \uac00\uaca9 \uacbd\ub9e4(second-price auction)\uc758 \uc77c\ubc18\ud654\ub77c\uace0 \ubcfc \uc218 \uc788\ub2e4.<br>Clarke\ub294 \uc774\ub97c \uc77c\ubc18 \ud658\uacbd\uc73c\ub85c \ud655\uc7a5\ud558\uace0, \ud53c\ubc97 \uba54\ucee4\ub2c8\uc998(pivotal mechanism)\uc774\ub77c\ub294 \ud2b9\uc218\ud55c \ud615\ud0dc\ub97c \uc815\uc758\ud558\uc600\ub2e4.<br>Groves\ub294 \uc774\ub4e4\uc758 \uc77c\ubc18\uc801\uc778 \ud615\ud0dc\ub97c \ud3ec\uad04\ud558\ub294 \uc774\ub860\uc801 \ud2c0\uc744 \uc815\ub9bd\ud558\uc600\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Groves \uba54\ucee4\ub2c8\uc998<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\"><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">Definition (Groves mechanisms)<\/mark><\/h5>\n\n\n\n<p>Direct mechanisms, \\((\\chi, p)\\), such that<\/p>\n\n\n\n<p>\\(\\chi(\\hat{v}) \\in \\arg \\max_x \\sum_i \\hat{v}_i(x)\\)<\/p>\n\n\n\n<p>\\(p_i(\\hat{v}) = h_i(\\hat{v}_{-i}) &#8211; \\sum_{j \\neq i} \\hat{v}_j (\\chi(\\hat{v}))\\)<\/p>\n\n\n\n<p>Some people refer to these as VCG mechanisms, although that name has more recently started to be used to refer to a specific mechanism within this class.<\/p>\n\n\n\n<p>Groves \uba54\ucee4\ub2c8\uc998\uc774\ub77c\ub294 \uc77c\ubc18\uc801\uc778 \uba54\ucee4\ub2c8\uc998 \ud074\ub798\uc2a4\ub97c \ubcf4\uba74, Groves \uba54\ucee4\ub2c8\uc998\uc774\ub780 \ub2e4\uc74c\uacfc \uac19\uc740 \uad6c\uc870\ub97c \uac00\uc9c4 \uba54\ucee4\ub2c8\uc998\uc744 \ub9d0\ud55c\ub2e4:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\uac01 \uac1c\uc778\uc740 \uc790\uc2e0\uc758 \ud6a8\uc6a9 \ud568\uc218(valuation function)\ub97c \uba54\ucee4\ub2c8\uc998\uc5d0 \ubcf4\uace0\ud55c\ub2e4.<br>\uc608: \\(\\hat{v}_1, \\hat{v}_2, \\dots, \\hat{v}_n\\)<\/li>\n\n\n\n<li>\uc0ac\ud68c\ub294 \ubcf4\uace0\ub41c \ud6a8\uc6a9 \ud568\uc218\ub4e4\uc758 \ud569\uc744 \ucd5c\ub300\ud654\ud558\ub294 \uc120\ud0dd\uc9c0\ub97c \uc120\ud0dd\ud55c\ub2e4.<\/li>\n\n\n\n<li>\uc9c0\ubd88 \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4:<br>\uac1c\uc778 i\uc758 \uc9c0\ubd88\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4: \\(p_i(\\hat{v})\\)<\/li>\n<\/ol>\n\n\n\n<p>\uc5ec\uae30\uc11c \\(h_i\\)\ub294 \uac1c\uc778 i\ub97c \uc81c\uc678\ud55c \ub098\uba38\uc9c0 \uc0ac\ub78c\ub4e4\uc758 \ud6a8\uc6a9 \ud568\uc218\uc5d0 \uae30\ubc18\ud55c \uc5b4\ub5a4 \ud568\uc218\uc774\uba70, x\ub294 \uc120\ud0dd\ub41c \uacb0\uacfc\uc774\ub2e4.<br>\uc774\ub7ec\ud55c \uad6c\uc870\ub97c \uac00\uc9c0\ub294 \uba54\ucee4\ub2c8\uc998\uc744 Groves \uba54\ucee4\ub2c8\uc998\uc774\ub77c \ud55c\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">VCG \uba54\ucee4\ub2c8\uc998 (The Vickrey-Clarke-Groves Mechanism)<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\"><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">Definition (A Vickrey-Clarke-Groves (VCG) mechanism, a.k.a. a Pivotal mechanism)<\/mark><\/h5>\n\n\n\n<p>A <strong>Vickrey-Clarke-Groves mechanism<\/strong> or a <strong>pivotal mechanism<\/strong> is a Groves mechanism \\((\\chi, p)\\), such that<\/p>\n\n\n\n<p>\\(\\chi(\\hat{v}) \\in \\arg \\max_x \\sum_i \\hat{v}_i(x)\\)<\/p>\n\n\n\n<p>\\(p_i(\\hat{v}) = max_x \\sum_{j \\neq i} \\hat{v}_j (x) &#8211; \\sum_{j \\neq i} \\hat{v}_j (\\chi(\\hat{v}))\\)<\/p>\n\n\n\n<p>You get paid everyone&#8217;s utility the allocation that is actually chosen<br>&#8211; except your own, but you get that directly as utility<br>Then you get charged everyone&#8217;s utility in the world where you don&#8217;t participate<br>Thus you pay your <strong>social cost<\/strong><\/p>\n\n\n\n<p>VCG \uba54\ucee4\ub2c8\uc998\uc740 Groves \uba54\ucee4\ub2c8\uc998\uc758 \ud2b9\uc218\ud55c \ud615\ud0dc\uc774\ub2e4.<br>\uc5ec\uae30\uc11c \ud568\uc218 \\(h_i\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uac1c\uc778 i\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc558\uc744 \ub54c \uc0ac\ud68c\uac00 \uc5bb\ub294 \ucd1d \ud6a8\uc6a9<\/li>\n\n\n\n<li>\uac1c\uc778 i\uac00 \uc874\uc7ac\ud560 \ub54c \uc0ac\ud68c\uac00 \uc5bb\ub294 \ucd1d \ud6a8\uc6a9<\/li>\n<\/ul>\n\n\n\n<p>\uc9c0\ubd88\uc740 \uc774 \ub458\uc758 \ucc28\uc774\ub85c \uacb0\uc815\ub41c\ub2e4.<br>\uc989, \uac1c\uc778\uc774 \uc0ac\ud68c\uc5d0 \ub07c\uce5c \uc601\ud5a5(\uc0ac\ud68c\uc801 \ube44\uc6a9)\uc744 \uc9c0\ubd88\ud558\uac8c \ub41c\ub2e4.<br>\ub9cc\uc57d \uac1c\uc778 i\uc758 \uc874\uc7ac\uac00 \ub2e4\ub978 \uc0ac\ub78c\ub4e4\uc5d0\uac8c \ud574\uac00 \ub41c\ub2e4\uba74, \uadf8\ub294 \ub354 \ub9ce\uc740 \uae08\uc561\uc744 \uc9c0\ubd88\ud574\uc57c \ud55c\ub2e4.<br>\ubc18\ub300\ub85c, \ub2e4\ub978 \uc0ac\ub78c\ub4e4\uc758 \ud6a8\uc6a9\uc744 \uc99d\uac00\uc2dc\ucf30\ub2e4\uba74 \ubcf4\uc0c1\uc744 \ubc1b\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">VCG discussion<\/h4>\n\n\n\n<p>Quertions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>who pays 0?<br>agents who don&#8217;t affect the outcome<\/li>\n\n\n\n<li>who pays more than 0?<br>(pivotal) agents who make things worse for others by existing<\/li>\n\n\n\n<li>who gets paid?<br>(pivotal) agents who make things better for others by existing<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc9c4\uc2e4\uc740 \uc9c0\ubc30 \uc804\ub7b5\uc774\ub2e4 (Truth is a Dominant Strategy) <br>&#8211; VCG and Groves Mechanisms: Truthrfulness<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\"><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">Theorem<\/mark><\/h5>\n\n\n\n<p>Truth telling is a dominant strategy under any Groves mechanism including the pivotal mechanism (a VCG mechanism).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"489\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-1024x489.png\" alt=\"\" class=\"wp-image-5292\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-1024x489.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-300x143.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-768x366.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-1536x733.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-8-2048x977.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\uc5d0\uc774\uc804\ud2b8 i\uac00 \uc120\ud0dd\ud55c \uc804\ub7b5\uc5d0 \ub530\ub77c \uc5bb\ub294 \ud6a8\uc6a9 \\(v_i\\)\uc5d0\uc11c \uc9c0\ubd88\ud574\uc57c \ud560 \uae08\uc561 \\(p\\)\ub97c \ube80 \uac83\uc744 \ucd5c\ub300\ud654\ud558\ub294 \ubb38\uc81c\uc774\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"641\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-1024x641.png\" alt=\"\" class=\"wp-image-5295\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-1024x641.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-300x188.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-768x481.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-1536x962.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-9-2048x1282.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Groves \uba54\ucee4\ub2c8\uc998\uc758 \ud575\uc2ec \uc774\ub860\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4:<\/p>\n\n\n\n<p>\uac1c\uc778\uc758 \uc9c0\ubd88\uc740 \uc790\uc2e0\uc774 \uc544\ub2cc \ub2e4\ub978 \uc0ac\ub78c\ub4e4\uc758 \ubcf4\uace0\uc5d0\ub9cc \uc758\uc874\ud558\ubbc0\ub85c, \uc790\uc2e0\uc758 \ud6a8\uc6a9\uc744 \uc9c4\uc2e4\ud558\uac8c \ubcf4\uace0\ud558\ub294 \uac83\uc774 \ud56d\uc0c1 \ucd5c\uc120\uc774\ub2e4.<br>Groves \uba54\ucee4\ub2c8\uc998\uc740 \uc0ac\ud68c \uc804\uccb4\uc758 \ud6a8\uc6a9\uc758 \ud569\uc744 \uadf9\ub300\ud654\ud558\ubbc0\ub85c, \uc790\uc2e0\uc758 \uc9c4\uc9dc \ud6a8\uc6a9\uc744 \ubcf4\uace0\ud558\ub294 \uac83\uc774 \ubc14\ub85c \uadf8 \uacb0\uacfc\ub97c \uc720\ub3c4\ud558\ub294 \uc720\uc77c\ud55c \ubc29\ubc95\uc774\ub2e4.<\/p>\n\n\n\n<p>\ub530\ub77c\uc11c, VCG \uba54\ucee4\ub2c8\uc998\uc740 \uc9c4\uc2e4 \ubcf4\uace0\ub97c \uc9c0\ubc30 \uc804\ub7b5\uc73c\ub85c \ub9cc\ub4dc\ub294 \uc720\uc77c\ud55c \ud6a8\uc728\uc801\uc778 \uba54\ucee4\ub2c8\uc998\uc774\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\ub300\uc6b0 \uc815\ub9ac (The Converse Theorem)<br>&#8211; Groves Uniqueness<\/h4>\n\n\n\n<p>Green &amp; Laffont (1970\ub144\ub300 \ud6c4\ubc18)\uc758 \uc815\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4:<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">Theorem (Green-Laffont)<\/mark><\/h5>\n\n\n\n<p>Suppose that for all agents any \\(v_i: X \\mapsto \\mathbb{R}\\) is a feasible preference.<br>Then an &#8220;<strong>efficient<\/strong>&#8221; mechanism \\((\\chi, p)\\) (such that \\(\\chi(\\hat{v}) \\in \\arg \\max _x \\sum_i \\hat{v}_i(x)\\)) has truthful reporting as a dominant strategy for all agents and preferences <strong>only if it is Groves mechanism: \\(p_i(v) = h(v_{-i}) &#8211; \\sum_{j \\neq i} v_j (\\chi(v))\\)<\/strong><\/p>\n\n\n\n<p>\uac1c\uc778\ub4e4\uc774 \uc784\uc758\uc758 \ud6a8\uc6a9 \ud568\uc218\ub97c \uac00\uc9c8 \uc218 \uc788\ub294 \ud658\uacbd\uc5d0\uc11c, \uba54\ucee4\ub2c8\uc998\uc774 \ud6a8\uc728\uc801\uc778 \uacb0\uacfc\ub97c \uc120\ud0dd\ud558\uace0, \uc9c4\uc2e4 \ubcf4\uace0\uac00 \uc9c0\ubc30 \uc804\ub7b5\uc774 \ub418\uae30\ub97c \uc6d0\ud55c\ub2e4\uba74, Groves \uba54\ucee4\ub2c8\uc998\ub9cc\uc774 \uc720\uc77c\ud55c \ud574\ub2f5\uc774\ub2e4.<\/p>\n\n\n\n<p>\uc989, \uc9c4\uc2e4 \uc720\ub3c4\uc131\uacfc \ud6a8\uc728\uc131\uc744 \ub3d9\uc2dc\uc5d0 \ub9cc\uc871\ud558\ub824\uba74, \uba54\ucee4\ub2c8\uc998\uc740 \ubc18\ub4dc\uc2dc Groves \ud615\uc2dd\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc694\uc57d (Summary)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Groves \uba54\ucee4\ub2c8\uc998\uc740 \ud6a8\uc728\uc801\uc778 \uc120\ud0dd\uc744 \ud558\uba74\uc11c \uc9c4\uc2e4 \ubcf4\uace0\ub97c \uc720\ub3c4\ud560 \uc218 \uc788\ub294 \uad6c\uc870\uc774\ub2e4.<\/li>\n\n\n\n<li>VCG \uba54\ucee4\ub2c8\uc998\uc740 \uadf8 \uc911\uc5d0\uc11c\ub3c4 \uac1c\uc778\uc774 \uc0ac\ud68c\uc5d0 \ubbf8\uce58\ub294 \uc601\ud5a5\uc744 \uae30\ubc18\uc73c\ub85c \uc9c0\ubd88\uc744 \uacc4\uc0b0\ud558\ub294 \ud2b9\uc218\ud55c \ud615\ud0dc\uc774\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>\uac1c\uc778\uc758 \uc778\uc13c\ud2f0\ube0c\uc640 \uc0ac\ud68c\uc758 \uc778\uc13c\ud2f0\ube0c\uac00 \uc815\ub82c\ub418\uba70, \uc678\ubd80\ud6a8\uacfc\ub97c \ub0b4\ubd80\ud654\ud558\uc5ec \ud6a8\uc728\uc801\uc778 \uacb0\uacfc\ub97c \ub3c4\ucd9c\ud55c\ub2e4.<\/p>\n\n\n\n<p>\ub2e4\ub9cc, \ub2e4\uc74c\uacfc \uac19\uc740 \uc8fc\uc758\uc810\ub3c4 \uc874\uc7ac\ud55c\ub2e4:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ucd1d \uc9c0\ubd88\uc774 \uc591\uc218\uc77c \uc218 \uc788\uc73c\ubbc0\ub85c, \uadf8 \uc789\uc5ec\uae08\uc744 \uc5b4\ub5bb\uac8c \ucc98\ub9ac\ud560\uc9c0 \uace0\ubbfc\uc774 \ud544\uc694\ud558\ub2e4.<\/li>\n\n\n\n<li>\uc774\ub97c \ub2e4\uc2dc \ubc30\ubd84\ud558\ub824 \ud558\uba74 \uc778\uc13c\ud2f0\ube0c \uad6c\uc870\uac00 \uae68\uc9c8 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>\uc774\ub7ec\ud55c \uc774\uc720\ub85c VCG \uba54\ucee4\ub2c8\uc998\uc740 \ub2e4\uc591\ud55c \ud658\uacbd\uc5d0\uc11c \ubca4\uce58\ub9c8\ud06c\ub85c \uc0ac\uc6a9\ub418\uba70, \uc77c\ubd80 \uc870\uac74\uc5d0\uc11c\ub294 \ud55c\uacc4\uac00 \uc788\uc9c0\ub9cc \ub9e4\uc6b0 \uac15\ub825\ud55c \uba54\ucee4\ub2c8\uc998\uc73c\ub85c \ub110\ub9ac \uc5f0\uad6c\ub418\uace0 \uc788\ub2e4.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">References<\/h4>\n\n\n\n<p>Game Theory Online, (2\/6) GTO2-3-02: Vickrey-Clarke-Groves Mechanisms: Definitions, Dec 3, 2013, <a href=\"https:\/\/www.youtube.com\/watch?v=kEjvysDPyUQ\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=kEjvysDPyUQ<\/a><\/p>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>This post from Game Theory Online (http:\/\/www.game-theory-class.org) formally defines the VCG mechanism, and proves some of its desirable properties.  It features Matt Jackson (Stanford).<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[4,215,198,214],"class_list":["post-5193","post","type-post","status-publish","format-standard","hentry","category-game-theory-and-applications","tag-game-theory","tag-mar-21-2025","tag-mechanism","tag-vcg"],"_links":{"self":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5193"}],"collection":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/comments?post=5193"}],"version-history":[{"count":54,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5193\/revisions"}],"predecessor-version":[{"id":5313,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5193\/revisions\/5313"}],"wp:attachment":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/media?parent=5193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/categories?post=5193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/tags?post=5193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}