{"id":5230,"date":"2025-03-22T00:06:25","date_gmt":"2025-03-21T15:06:25","guid":{"rendered":"https:\/\/saraheee.com\/?p=5230"},"modified":"2025-03-24T00:24:35","modified_gmt":"2025-03-23T15:24:35","slug":"gt-mechanism-5-individual-rationality-and-budget-balance-in-vcg","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2025\/03\/gt-mechanism-5-individual-rationality-and-budget-balance-in-vcg\/","title":{"rendered":"[GT Mechanism] #5. Individual Rationality and Budget Balance in VCG"},"content":{"rendered":"<p>\uc774 \uc7a5\uc5d0\uc11c\ub294 VCG \uba54\ucee4\ub2c8\uc998\uc774 \uac1c\ubcc4 \ud569\ub9ac\uc131(individual rationality)\uacfc \uc608\uc0b0 \uade0\ud615(budget balance)\uc744 \ub2ec\uc131\ud560 \uc218 \uc788\ub294 \uc870\uac74\uacfc \uc774\uc640 \uad00\ub828\ub41c \uc774\ub860\uc801 \uacb0\uacfc\ub4e4\uc744 \ub2e4\ub8e8\uace0 \uc788\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\uc758 \uae30\ubcf8 \uc131\uc9c8 \ub2e4\uc2dc \ubcf4\uae30 (Two definitions)<\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"589\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-1024x589.png\" alt=\"\" class=\"wp-image-5394\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-1024x589.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-300x173.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-768x442.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-1536x884.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-17-2048x1179.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>VCG \uba54\ucee4\ub2c8\uc998\uc740 <strong>\uc9c0\ubc30 \uc804\ub7b5(dominant strategy)<\/strong>\uc744 \uc720\ub3c4\ud558\uace0 <strong>\uc0ac\ud68c\uc801 \ud6a8\uc728\uc131(efficient allocation)<\/strong>\uc744 \ub2ec\uc131\ud558\ub294 \uac83\uc73c\ub85c \uc54c\ub824\uc838 \uc788\ub2e4.<br>\ud558\uc9c0\ub9cc \uc77c\ubc18\uc801\uc73c\ub85c\ub294 <strong>\uac1c\ubcc4 \ud569\ub9ac\uc131(individual rationality)<\/strong>\uacfc <strong>\uc608\uc0b0 \uade0\ud615(budget balance)<\/strong>\uc744 \ud56d\uc0c1 \ubcf4\uc7a5\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4.<\/p>\n\n\n\n<p>(\uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131) \uc5b4\ub5a4 \uc5d0\uc774\uc804\ud2b8 i\ub97c \uc81c\uac70\ud558\uba74, \uac00\ub2a5\ud55c \uc120\ud0dd\uc758 \uc9d1\ud569 X\ub294 \uc57d\ud558\uac8c \uac10\uc18c\ud55c\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \ub2e4\uc2dc \ub9d0\ud574, \uc120\ud0dd\uc9c0\ub294 \uc904\uc5b4\ub4e4 \uc218\ub294 \uc788\uc5b4\ub3c4 \ub298\uc5b4\ub098\uc9c0\ub294 \uc54a\ub294\ub2e4.<br>(\ubd80\uc815\uc801 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c) \uc5d0\uc774\uc804\ud2b8 i\ub294 \uc790\uc2e0\uc774 \ube60\uc9c4 \uc0c1\ud0dc\uc5d0\uc11c \uc774\ub8e8\uc5b4\uc9c8 \uc218 \uc788\ub294 \uc5b4\ub5a4 \uc120\ud0dd x\uc5d0 \ub300\ud574\uc11c\ub3c4 \ud6a8\uc6a9\uc774 0 \uc774\uc0c1\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc989, \ucc38\uc5ec\ud558\uc9c0 \uc54a\uc544\ub3c4 \uc790\uc2e0\uc5d0\uac8c \ud574\ub85c\uc6b4 \uacb0\uacfc\ub294 \uc77c\uc5b4\ub098\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n\n\n\n<p>\uc774\ubc88 \uc601\uc0c1\uc5d0\uc11c\ub294 \uc77c\uc815\ud55c \uc870\uac74 \ud558\uc5d0 \uc774 \ub450 \uac00\uc9c0\ub97c \ub3d9\uc2dc\uc5d0 \ub2ec\uc131\ud560 \uc218 \uc788\uc74c\uc744 \ubcf4\uc778\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uac1c\ubcc4 \ud569\ub9ac\uc131: \uc815\uc758\uc640 \ud544\uc694 \uc870\uac74<\/h4>\n\n\n\n<p>\uac1c\ubcc4 \ud569\ub9ac\uc131\uc774\ub780, \uc5d0\uc774\uc804\ud2b8\uac00 \uba54\ucee4\ub2c8\uc998\uc5d0 \ucc38\uc5ec\ud558\ub294 \uac83\uc774 \uc790\ubc1c\uc801\uc73c\ub85c \uc774\ub4dd\uc774 \ub418\ub294 \uc0c1\ud0dc\ub97c \ub9d0\ud55c\ub2e4.<br>\uc989, \ucc38\uc5ec\ud558\uc9c0 \uc54a\ub294 \uac83\ubcf4\ub2e4 \ucc38\uc5ec\ud558\ub294 \uac83\uc774 \uc720\ub9ac\ud574\uc57c \ud55c\ub2e4.<\/p>\n\n\n\n<p>VCG \uba54\ucee4\ub2c8\uc998\uc5d0\uc11c \uac1c\ubcc4 \ud569\ub9ac\uc131\uc744 \uc5bb\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c \ub450 \uac00\uc9c0 \uc870\uac74\uc774 \ud544\uc694\ud558\ub2e4:<\/p>\n\n\n\n<p>1. \uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131 (Choice Set Monotonicity)<\/p>\n\n\n\n<p>\uc5b4\ub5a4 \uc5d0\uc774\uc804\ud2b8\ub97c \uc81c\uc678\ud574\ub3c4 \uba54\ucee4\ub2c8\uc998\uc774 \uc120\ud0dd\ud560 \uc218 \uc788\ub294 \uc120\ud0dd\uc9c0\uc758 \uc9d1\ud569\uc740 \uc57d\ud55c \uc758\ubbf8\uc5d0\uc11c \uc904\uc5b4\ub4e0\ub2e4\ub294 \uc870\uac74\uc774\ub2e4.<br>\uc989, \uc5d0\uc774\uc804\ud2b8\ub97c \uc81c\uac70\ud588\uc744 \ub54c \uc0c8\ub85c\uc6b4 \uc120\ud0dd\uc9c0\uac00 \ucd94\uac00\ub418\uc5b4\uc11c\ub294 \uc548 \ub41c\ub2e4.<\/p>\n\n\n\n<p>2. \uc74c\uc758 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c (No Negative Externalities)<\/p>\n\n\n\n<p>\uc5b4\ub5a4 \uc5d0\uc774\uc804\ud2b8\ub97c \uc81c\uc678\ud55c \ud6c4\uc758 \uc120\ud0dd\uc9c0\uac00, \ud574\ub2f9 \uc5d0\uc774\uc804\ud2b8\uc5d0\uac8c \uc74c\uc758 \ud6a8\uc6a9(negative utility)\uc744 \uc8fc\uc9c0 \uc54a\uc544\uc57c \ud55c\ub2e4.<br>\uc989, \ud574\ub2f9 \uc5d0\uc774\uc804\ud2b8\uac00 \ube60\uc84c\uc744 \ub54c\ub3c4 \uc801\uc5b4\ub3c4 0 \uc774\uc0c1\uc758 \ud6a8\uc6a9\uc744 \uac00\uc838\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\">\uc608\uc2dc 1: \ub3c4\ub85c \uac74\uc124 \uc8fc\ubbfc \ud22c\ud45c<br>&#8211; Example: road referendum<\/h4>\n\n\n\n<p>Example<br>Consider the problem of holding a referendum to decide whether or not to build a road.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The set of choices is independent of the number of agents, satisfying choice-set monotonicity.<\/li>\n\n\n\n<li>No agent negatively values the project, though some might value the situation in which the project is not undertaken more highly than the situation in which it is.<\/li>\n<\/ul>\n\n\n\n<p>\uc120\ud0dd\uc9c0\ub294 \u201c\ub3c4\ub85c \uac74\uc124\u201d \ub610\ub294 \u201c\uac74\uc124\ud558\uc9c0 \uc54a\uc74c\u201d \ub450 \uac00\uc9c0\ubfd0\uc774\ub2e4.<\/p>\n\n\n\n<p>\uc120\ud0dd\uc9c0\ub294 \uc5d0\uc774\uc804\ud2b8 \uc218\uc640 \ubb34\uad00\ud558\ubbc0\ub85c, \uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131 \ub9cc\uc871. (\uc0ac\ub78c \uc218\uac00 \uba87 \uba85\uc774\ub4e0 \uc120\ud0dd\uc9c0 \uc790\uccb4\uac00 \ubcc0\ud558\uc9c0 \uc54a\uc74c.)<br>\uc5d0\uc774\uc804\ud2b8\ub4e4\uc774 \ub3c4\ub85c \uac74\uc124\uc744 \uc120\ud638\ud558\uc9c0 \uc54a\ub354\ub77c\ub3c4, \uc74c\uc758 \ud6a8\uc6a9\uc744 \uac16\ub294 \uc0c1\ud669\uc740 \uc5c6\ub2e4\uace0 \uac00\uc815\ud558\uba74 \uc74c\uc758 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c \uc870\uac74\ub3c4 \ub9cc\uc871\ud55c\ub2e4. (\ub204\uad6c\ub294 \ub3c4\ub85c \uac74\uc124 \uc790\uccb4\ub97c \uc88b\uc544\ud558\uace0, \ub204\uad6c\ub294 \ub3c4\ub85c\uac00 \uc5c6\uae38 \ubc14\ub784 \uc218\ub3c4 \uc788\uc9c0\ub9cc, \uac74\uc124\uc774 \ub418\ub354\ub77c\ub3c4 \uadf8\uac83\uc774 \u2018\uace0\ud1b5\u2019\uc774 \ub418\ub294 \uc0ac\ub78c\uc740 \uc5c6\ub2e4.)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\uc608\uc2dc 2: \ub2e8\uc21c \uac70\ub798 \uc2dc\uc7a5<\/h4>\n\n\n\n<p>Example<br>Consider a market setting consisting of agents interested in buying a single unit of a good such as a share of stock, and another set of agents interested in selling a single unit of this good. The choices in this environment are sets of buyer-seller pairings (prices are imposed through the payment function).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a new agent is introduced into the market, no previously-existing pairings become infeasible, but new ones become possible; thus choice-set monotonicity is satisfied.<\/li>\n\n\n\n<li>Because agents have zero utility both for choices that involve trades between other agents and no trades at all, there are no negative externalities.<\/li>\n<\/ul>\n\n\n\n<p>\uc8fc\uc2dd \ud558\ub098\ub97c \ud314\ub824\ub294 \uc0ac\ub78c\uacfc \ud558\ub098\ub97c \uc0ac\ub824\ub294 \uc0ac\ub78c\ub4e4\ub85c \uad6c\uc131\ub41c \uc2dc\uc7a5.<\/p>\n\n\n\n<p>\ub9e4\uce6d \ubc29\uc2dd\uc740 \ub2e4\uc591\ud558\uc9c0\ub9cc, \uc5b4\ub5a4 \uc5d0\uc774\uc804\ud2b8\ub97c \ucd94\uac00\ud574\ub3c4 \uae30\uc874\uc758 \ub9e4\uce6d \ubc29\uc2dd\uc740 \uc720\uc9c0\ub420 \uc218 \uc788\ub2e4.<br>\u2192 \uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131 \ub9cc\uc871<\/p>\n\n\n\n<p>\uc608\ub97c \ub4e4\uc5b4 A, B\ub77c\ub294 \uae30\uc874 \uad6c\ub9e4\uc790-\ud310\ub9e4\uc790 \uc30d\uc774 \uc788\uc5c8\ub294\ub370, \uc0c8\ub85c\uc6b4 \uc0ac\ub78c C\uac00 \uc640\ub3c4 A\uc640 B\uac00 \uac70\ub798 \ubabb \ud558\uac8c \ub418\uc9c4 \uc54a\uc74c.<br>\uc624\ud788\ub824 A-C, B-C \uac19\uc740 \uc0c8\ub85c\uc6b4 \uac70\ub798 \uac00\ub2a5\uc131(pairing)\ub9cc \ucd94\uac00\ub428.<br>\uc774\uac74 \uc120\ud0dd \uc9d1\ud569\uc774 \uc57d\ud558\uac8c \uc99d\uac00\ud558\uac70\ub098 \uadf8\ub300\ub85c \uc720\uc9c0\ub41c\ub2e4\ub294 \uc758\ubbf8\uc774\ubbc0\ub85c,<br>\\(X_{-i} \\subseteq X\\) \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba70, choice-set monotonicity\uac00 \ucda9\uc871\ub428.<\/p>\n\n\n\n<p>\ub2e4\ub978 \uc0ac\ub78c\ub4e4\uc758 \uac70\ub798 \uc5ec\ubd80\uc5d0 \ub300\ud574 \uc544\ubb34\ub7f0 \ud6a8\uc6a9\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4\uace0 \uac00\uc815\ud55c\ub2e4\uba74<br>\u2192 \uc74c\uc758 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c \uc870\uac74\ub3c4 \ub9cc\uc871<\/p>\n\n\n\n<p>\ub098 \uc5c6\uc774 \uc774\ub8e8\uc5b4\uc9c4 \uac70\ub798\ub4e4\uc774 \ub098\uc5d0\uac8c \uc190\ud574\ub97c \uc8fc\uc9c0\ub294 \uc54a\uc74c.<br>\uc608\ub97c \ub4e4\uc5b4 \ub0b4\uac00 \ud310\ub9e4\uc790\uc600\ub294\ub370, \ub0b4\uac00 \ube60\uc84c\ub2e4\uace0 \ud574\uc11c \ub204\uad70\uac00 \ub098 \ub300\uc2e0 \ub354 \uc720\ub9ac\ud558\uac8c \uac70\ub798\ud55c \uac83\uc774 \ub098\uc5d0\uac8c \ud574\uac00 \ub418\uc9c0\ub294 \uc54a\uc74c.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc815\ub9ac: VCG\uc758 \uac1c\ubcc4 \ud569\ub9ac\uc131 \uc815\ub9ac (VCG Individual Rationality)<\/h4>\n\n\n\n<p>The VCG mechanism is ex-post individual rational when the choice set monotonicity and no negative externalities properties hold.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"669\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-1024x669.png\" alt=\"\" class=\"wp-image-5415\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-1024x669.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-300x196.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-768x502.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-1536x1004.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2025\/03\/image-18-2048x1338.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131 + \uc74c\uc758 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c<br><strong>\u2192<\/strong> VCG\ub294 ex post \uac1c\ubcc4 \ud569\ub9ac\uc131\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\n\n\n\n<p>\uc5ec\uae30\uc11c ex post\ub780, \uc5b4\ub5a4 \uac00\uce58 \uc120\uc5b8\uc774 \uc8fc\uc5b4\uc9c0\ub354\ub77c\ub3c4 \uc774 \uc18d\uc131\uc774 \ud56d\uc0c1 \uc131\ub9bd\ud568\uc744 \uc758\ubbf8\ud55c\ub2e4.<br>\uc989, \uc774\ub294 \uac00\uc7a5 \uac15\ud55c \ud615\ud0dc\uc758 \uac1c\ubcc4 \ud569\ub9ac\uc131\uc774\ub2e4.<\/p>\n\n\n\n<p>VCG\uc5d0\uc11c\uc758 \uc720\ud2f8\ub9ac\ud2f0\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ub41c\ub2e4:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc790\uc2e0\uc758 \uac00\uce58 \\(v_i(x)\\)<\/li>\n\n\n\n<li>\uc790\uc2e0\uc758 \uc9c0\ubd88\uc561 \\(p_i\\)<\/li>\n<\/ul>\n\n\n\n<p>\ub458\uc758 \ucc28\uc774\uac00 0 \uc774\uc0c1\uc784\uc744 \uc704 \uc99d\uba85 \uacfc\uc815\uc744 \ud1b5\ud574 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc608\uc0b0 \uade0\ud615 (Budget Balance)<\/h4>\n\n\n\n<p>\ub2e4\uc74c\uc73c\ub85c, \uc608\uc0b0 \uade0\ud615\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uc790.<br>VCG\ub294 \uc77c\ubc18\uc801\uc73c\ub85c\ub294 \uc608\uc0b0 \uade0\ud615\uc744 \ubcf4\uc7a5\ud558\uc9c0 \uc54a\ub294\ub2e4. \ud558\uc9c0\ub9cc \ub2e4\uc74c \uc870\uac74\uc774 \ub9cc\uc871\ub418\uba74, \ucd5c\uc18c\ud55c \uc57d\ud55c \uc758\ubbf8\uc758 \uade0\ud615(weak budget balance)\uc740 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\n\n\n\n<p><strong>\ub2e8\uc77c \uc5d0\uc774\uc804\ud2b8 \ud6a8\uacfc \uc5c6\uc74c (No Single Agent Effect)<\/strong><\/p>\n\n\n\n<p>\uc5b4\ub5a4 \uc5d0\uc774\uc804\ud2b8 i\ub97c \uc81c\uac70\ud574\ub3c4, \ub098\uba38\uc9c0 \uc5d0\uc774\uc804\ud2b8\ub4e4\uc758 \ud6c4\uc0dd\uc774 \uc904\uc9c0 \uc54a\ub294 \uc870\uac74\uc774\ub2e4.<br>\uc989, i\uac00 \ube60\uc9d0\uc73c\ub85c\uc368 \ub098\uba38\uc9c0 \ubaa8\ub450\uc5d0\uac8c \ub354 \ub098\uc740 \uacb0\uacfc\ub97c \uac00\uc838\uc624\ub294 \ub300\uccb4 \uc120\ud0dd\uc9c0\uac00 \uc874\uc7ac\ud574\uc57c \ud55c\ub2e4.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\uc608\uc2dc: \ub2e8\uba74 \uacbd\ub9e4 (Single-sided auction)<\/h5>\n\n\n\n<p>\ub9cc\uc57d \uc5d0\uc774\uc804\ud2b8 i\uac00 \ub099\ucc30\uc790\uac00 \uc544\ub2c8\uc5c8\ub2e4\uba74, \uc81c\uac70\ud558\ub354\ub77c\ub3c4 \uacb0\uacfc\uc5d0 \ubcc0\ud654\uac00 \uc5c6\ub2e4.<br>\ubc18\ub300\ub85c \ub099\ucc30\uc790\uc600\ub2e4\uba74, \uc81c\uac70 \ud6c4 \ub098\uba38\uc9c0 \uc911 \ud558\ub098\uac00 \ub099\ucc30\ub418\uc5b4 \ub098\uba38\uc9c0 \uc5d0\uc774\uc804\ud2b8\ub4e4\uc5d0\uac8c\ub294 \ud6c4\uc0dd \uc99d\uac00\uac00 \ub41c\ub2e4.<br>\u2192 \uc774\ub7ec\ud55c \uad6c\uc870\uc5d0\uc11c\ub294 \ub2e8\uc77c \uc5d0\uc774\uc804\ud2b8 \ud6a8\uacfc \uc5c6\uc74c \uc870\uac74\uc774 \uc790\uc5f0\uc2a4\ub7fd\uac8c \ub9cc\uc871\ub41c\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\uc99d\uba85 \uc694\uc9c0<\/h4>\n\n\n\n<p>VCG \uc9c0\ubd88 \uad6c\uc870\ub97c \ubaa8\ub450 \ub354\ud588\uc744 \ub54c, \ucd1d\ud569\uc774 0 \uc774\uc0c1\uc784\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<br>\uc774\ub294 \uace7 \uc57d\ud55c \uc758\ubbf8\uc758 \uc608\uc0b0 \uade0\ud615(weak budget balance)\uc774 \ubcf4\uc7a5\ub428\uc744 \uc758\ubbf8\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\">\ucd94\uac00 \uc815\ub9ac: Krishna &amp; Perry\uc758 \uc815\ub9ac<\/h4>\n\n\n\n<p>VCG\uac00 ex post \uac1c\ubcc4 \ud569\ub9ac\uc131\uc744 \ub9cc\uc871\ud558\ub294 \uacbd\uc6b0, VCG\ub294 \uc5b4\ub5a4 \ub2e4\ub978 \ud6a8\uc728\uc801\uc778 \uba54\ucee4\ub2c8\uc998\ubcf4\ub2e4\ub3c4 \ub354 \ub9ce\uc740 \uc218\uc775\uc744 \uac70\ub458 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p>\ube44\uad50 \ub300\uc0c1 \uba54\ucee4\ub2c8\uc998\uc740 <strong>Bayes-Nash \uade0\ud615 \uae30\ubc18<\/strong>\uc774\uace0 <strong>interim \uac1c\ubcc4 \ud569\ub9ac\uc131<\/strong>\ub9cc \uc694\uad6c\ub41c\ub2e4.<br>\ubc18\uba74, VCG\ub294 <strong>dominant strategy<\/strong>\uc5d0 <strong>ex post \uac1c\ubcc4 \ud569\ub9ac\uc131<\/strong>\uae4c\uc9c0 \uc694\uad6c\ub41c\ub2e4.<br>\u2192 \uc989, VCG\ub294 \ud6e8\uc52c \ub354 \uac15\ub825\ud55c \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba74\uc11c\ub3c4 \uc218\uc775 \uba74\uc5d0\uc11c\ub3c4 \ucd5c\uc801\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\">\uacb0\ub860<\/h4>\n\n\n\n<p>\uc774\ubc88 \uc601\uc0c1\uc5d0\uc11c \uc54c \uc218 \uc788\ub294 \ud575\uc2ec \ub0b4\uc6a9\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\uc120\ud0dd \uc9d1\ud569 \ub2e8\uc870\uc131<\/strong>\uacfc <strong>\uc74c\uc758 \uc678\ubd80\ud6a8\uacfc \uc5c6\uc74c<\/strong> \uc870\uac74\uc774 \ucda9\uc871\ub418\uba74, VCG\ub294 <strong>\ud56d\uc0c1 \uac1c\ubcc4 \ud569\ub9ac\uc131<\/strong>\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/li>\n\n\n\n<li><strong>\ub2e8\uc77c \uc5d0\uc774\uc804\ud2b8 \ud6a8\uacfc \uc5c6\uc74c<\/strong> \uc870\uac74\uc774 \ucda9\uc871\ub418\uba74, VCG\ub294 <strong>\uc57d\ud55c \uc608\uc0b0 \uade0\ud615<\/strong>\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/li>\n\n\n\n<li><strong>Krishna &amp; Perry\uc758 \uc815\ub9ac<\/strong>\uc5d0 \ub530\ub974\uba74, <strong>VCG\ub294 \ud6a8\uc728\uc131\uacfc \uc218\uc775 \uce21\uba74 \ubaa8\ub450\uc5d0\uc11c \ucd5c\uc801\uc758 \uba54\ucee4\ub2c8\uc998<\/strong>\uc774\ub2e4.<\/li>\n<\/ol>\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, (5\/6) GTO2-3-05: Individual Rationality and Budget Balance in VCG, Dec 3, 2013, <a href=\"https:\/\/www.youtube.com\/watch?v=dLs-s3PgSIg\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=dLs-s3PgSIg<\/a><\/p>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>In general, VCG is neither budget balanced nor individually rational.  This post from Game Theory Online (http:\/\/www.game-theory-class.org) introduces some additional assumptions under which it is possible to get individual rationality and budget balance in VCG.  It features Kevin Leyton-Brown (UBC).<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[4,217,215,198,214,216],"class_list":["post-5230","post","type-post","status-publish","format-standard","hentry","category-game-theory-and-applications","tag-game-theory","tag-mar-21","tag-mar-21-2025","tag-mechanism","tag-vcg","tag-vickrey"],"_links":{"self":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5230"}],"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=5230"}],"version-history":[{"count":16,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5230\/revisions"}],"predecessor-version":[{"id":5417,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/5230\/revisions\/5417"}],"wp:attachment":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/media?parent=5230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/categories?post=5230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/tags?post=5230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}