{"id":4005,"date":"2024-03-20T21:33:25","date_gmt":"2024-03-20T12:33:25","guid":{"rendered":"https:\/\/saraheee.com\/?p=4005"},"modified":"2024-03-22T11:26:29","modified_gmt":"2024-03-22T02:26:29","slug":"differentially-private-properties-in-game-theory","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2024\/03\/differentially-private-properties-in-game-theory\/","title":{"rendered":"Differentially Private Properties in Game Theory"},"content":{"rendered":"<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"120\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-1024x120.png\" alt=\"\" class=\"wp-image-4010\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-1024x120.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-300x35.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-768x90.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-1536x179.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-8-2048x239.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc\uac00 \uc81c\uacf5\ud558\ub294 \uba54\ucee4\ub2c8\uc998\uc774 \ubaa8\ub4e0 \uc5d0\uc774\uc804\ud2b8\uc5d0 \ub300\ud574, \uadf8\ub4e4\uc774 \uc5b4\ub5a0\ud55c \uc720\ud2f8\ub9ac\ud2f0 \ud568\uc218\ub97c \uac00\uc9c0\uace0 \uc788\ub4e0<br>\ub2e8\uc77c \ubcc0\ud654\uc5d0 \uc758\ud574 \uadf8\ub4e4\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0\uac00 exp(\u03b5) \uc774\uc0c1\uc73c\ub85c \uc99d\uac00\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc7a5\ud55c\ub2e4.<br>\ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc\ub294 \ub2e8\uc77c \ud589\uc704\uc790\uac00 \uc790\uc2e0\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0\ub97c \ub2e8\ub3c5\uc73c\ub85c \uc870\uc791\ud558\uc5ec \ud06c\uac8c \uc99d\uac00\uc2dc\ud0ac \uac00\ub2a5\uc131\uc744 \uc81c\ud55c\ud55c\ub2e4.<\/p>\n\n\n\n<p>\\(\\mathbb{E}_{o \\sim M(t)}[u_i(o)]\\): \uc6d0\ub798 \uc804\ub7b5 t\ub97c \uc0ac\uc6a9\ud588\uc744 \ub54c \uc5d0\uc774\uc804\ud2b8 i\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0<br>\\(\\mathbb{E}_{o \\sim M(t_{-i}, t&#8217;_i)}[u_i(o)]\\): \uc5d0\uc774\uc804\ud2b8 i\uac00 \uc790\uc2e0\uc758 \uc804\ub7b5\uc744 \\(t&#8217;_i\\)\ub85c \ubcc0\uacbd\ud588\uc744 \ub54c\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0<br>exp(\u03b5): \ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc \ud30c\ub77c\ubbf8\ud130 \u03b5\uc5d0 \uc758\ud574 \uc815\uc758\ub41c \uc0c1\uc218 \ubc30\uc728, \u03b5\uac00 \uc791\uc744\uc218\ub85d \ud504\ub77c\uc774\ubc84\uc2dc \ubcf4\ud638\uac00 \uac15\ud654\ub428<\/p>\n\n\n\n<p>\\(t_{-i}\\): \uc5d0\uc774\uc804\ud2b8 i\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \ub2e4\ub978 \uc5d0\uc774\uc804\ud2b8\ub4e4\uc758 \uc804\ub7b5 \uc9d1\ud569<br>\\(t&#8217;_i\\): \uc5d0\uc774\uc804\ud2b8 i\uac00 \uc0c8\ub86d\uac8c \uc120\ud0dd\ud55c \uc804\ub7b5<br>\\(M(t_{-i}, t&#8217;_i)\\): \uc5d0\uc774\uc804\ud2b8 i\uac00 \uc804\ub7b5\uc744 \\(t&#8217;_i\\)\ub85c \ubcc0\uacbd\ud588\uc744 \ub54c, \uadf8\ub9ac\uace0 \ub098\uba38\uc9c0 \uc5d0\uc774\uc804\ud2b8\ub4e4\uc774 \uadf8\ub300\ub85c \\(t_{-i}\\) \uc804\ub7b5\uc744 \uc720\uc9c0\ud588\uc744 \ub54c \uba54\ucee4\ub2c8\uc998\uc758 \uacb0\uacfc<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"76\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-1024x76.png\" alt=\"\" class=\"wp-image-4011\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-1024x76.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-300x22.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-768x57.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-1536x114.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-9-2048x152.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u03b5\uc774 1 \uc774\ud558\uc77c \ub54c, \u03b5-differentially privacy \uba54\ucee4\ub2c8\uc998\uc774 \u03b5-\uadfc\uc0ac\uc801\uc73c\ub85c \uc9c0\ubc30 \uc804\ub7b5\uc801 \uc9c4\uc2e4\uc131(approximately dominant strategy truthful)\uc744 \ubcf4\uc7a5\ud55c\ub2e4.<br>\uc9c4\uc2e4\ub41c \uc720\ud615(type)\uc744 \ubcf4\uace0\ud558\ub294 \uac83\uc774 \uac00\uc7a5 \uc774\uc775\uc774 \ub418\uba70, \uac70\uc9d3\ub9d0\uc744 \ud568\uc73c\ub85c\uc368 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc774\uc775\uc774 \u03b5\uc73c\ub85c \uc81c\ud55c\ub41c\ub2e4.<\/p>\n\n\n\n<p>\\(u_i(t_i, M(t_{-i}, t_i)) \\geq u_i(t&#8217;_i, M(t_{-i}, t_i))-\\epsilon\\)<\/p>\n\n\n\n<p>\\(u_i(t_i, M(t_{-i}, t_i))\\): \uc5d0\uc774\uc804\ud2b8 i\uac00 \uc790\uc2e0\uc758 \uc9c4\uc2e4\ub41c \uc720\ud615 \\(t_i\\)\ub97c \ubcf4\uace0\ud588\uc744 \ub54c \uc5bb\ub294 \uc720\ud2f8\ub9ac\ud2f0<br>\\(u_i(t&#8217;_i, M(t_{-i}, t_i))\\): \uc5d0\uc774\uc804\ud2b8 i\uac00 \ub2e4\ub978 \uc720\ud615 \\(t&#8217;_i\\)\ub97c \ubcf4\uace0\ud588\uc744 \ub54c \uc5bb\ub294 \uc720\ud2f8\ub9ac\ud2f0<br>\\(M(t_{-i}, t_i)\\): \uc5d0\uc774\uc804\ud2b8 i\ub97c \uc81c\uc678\ud55c \ub2e4\ub978 \ubaa8\ub4e0 \uc5d0\uc774\uc804\ud2b8\uc758 \uc720\ud615 \\(t_{-i}\\)\uacfc \uc5d0\uc774\uc804\ud2b8 i\uc758 \uc720\ud615 \\(t_i\\)\ub97c \uc785\ub825\uc73c\ub85c \ubc1b\ub294 \uba54\ucee4\ub2c8\uc998 M\uc758 \ucd9c\ub825<br>\u03b5: \ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc \ud30c\ub77c\ubbf8\ud130, \uba54\ucee4\ub2c8\uc998\uc774 \uc5bc\ub9c8\ub098 \uac15\ud55c \ud504\ub77c\uc774\ubc84\uc2dc \ubcf4\ud638\ub97c \uc81c\uacf5\ud558\ub294\uc9c0 \ub098\ud0c0\ub0c4<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"138\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-1024x138.png\" alt=\"\" class=\"wp-image-4012\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-1024x138.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-300x40.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-768x104.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-1536x207.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2024\/03\/image-10-2048x276.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u03b5-\ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc\ub97c \ub9cc\uc871\ud560 \ub54c, \uc5b4\ub5a4 \uc720\ud2f8\ub9ac\ud2f0 \ud568\uc218\uc5d0 \ub300\ud574\uc11c\ub3c4 \ucd5c\ub300 k\uac1c\uc758 \uc694\uc18c\uac00 \ub2e4\ub978 \ub450 \uc785\ub825 \uc9d1\ud569\uc5d0 \ub300\ud574 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0\uac00 exp(\u03b5k) \uc774\uc0c1 \ucc28\uc774\ub098\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc7a5\ud55c\ub2e4.<br>\uc5d0\uc774\uc804\ud2b8\ub4e4\uc774 \uacb0\ud0c1\ud558\uc5ec \uba54\ucee4\ub2c8\uc998\uc5d0 \uc601\ud5a5\uc744 \ubbf8\uce58\ub824 \ud574\ub3c4, \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0\uc758 \uc99d\uac00\ub294 \uc81c\ud55c\uc801\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4.(\uac8c\uc784 \uc774\ub860\uc801 \uc0c1\ud669\uc5d0\uc11c\ub3c4 \uc720\uc6a9\ud558\uac8c \uc801\uc6a9\ub41c\ub2e4.)<\/p>\n\n\n\n<p>\\(\\mathbb{E}_{o \\sim M(t)}[u_i(o)]\\): \uba54\ucee4\ub2c8\uc998 M\uc774 \ub370\uc774\ud130 \uc9d1\ud569 t\uc5d0 \uc801\uc6a9\ub418\uc5c8\uc744 \ub54c \uc5d0\uc774\uc804\ud2b8 i\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0<br>\\(\\mathbb{E}_{o \\sim M(t&#8217;)}[u_i(o)]\\): \uba54\ucee4\ub2c8\uc998 M\uc774 \ucd5c\ub300 k\uac1c\uc758 \uc694\uc18c\uac00 \ub2e4\ub978 \ub370\uc774\ud130 \uc9d1\ud569 t&#8217;\uc5d0 \uc801\uc6a9\ub418\uc5c8\uc744 \ub54c \uc5d0\uc774\uc804\ud2b8 i\uc758 \uae30\ub300 \uc720\ud2f8\ub9ac\ud2f0<br>k: \ubcc0\uacbd\ub41c \uc694\uc18c\uc758 \uc218<br>\u03b5: \ucc28\ub4f1 \ud504\ub77c\uc774\ubc84\uc2dc \ud30c\ub77c\ubbf8\ud130<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">References<\/h4>\n\n\n\n<p>More than privacy: Adopting Differential Privacy in Game-theoretic Mechanism Design, 2.5 Differentially Private Properties in Game Theory<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>I present mathematical guarantees for how differential privacy provides truthfulness, limited incentives to lie, and collusion resistance in a game-theoretic context. These properties provide mechanism designers with powerful tools to control the strategic behaviour of agents while preserving privacy.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[154],"tags":[155,4,179],"class_list":["post-4005","post","type-post","status-publish","format-standard","hentry","category-dp","tag-differential-privacy","tag-game-theory","tag-mar-20-2024"],"_links":{"self":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4005"}],"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=4005"}],"version-history":[{"count":14,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4005\/revisions"}],"predecessor-version":[{"id":4033,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4005\/revisions\/4033"}],"wp:attachment":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/media?parent=4005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/categories?post=4005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/tags?post=4005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}