{"id":5225,"date":"2025-03-21T23:55:54","date_gmt":"2025-03-21T14:55:54","guid":{"rendered":"https:\/\/saraheee.com\/?p=5225"},"modified":"2025-03-23T21:42:37","modified_gmt":"2025-03-23T12:42:37","slug":"gto2-3-04-limitations-of-vcg","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2025\/03\/gto2-3-04-limitations-of-vcg\/","title":{"rendered":"[GT Mechanism] #4. Limitations of VCG"},"content":{"rendered":"

GTO2-3-04: Limitations of VCG<\/h3>\n\n\n\n

VCG \uba54\ucee4\ub2c8\uc998\uc758 \ud55c\uacc4<\/h4>\n\n\n\n

\uc9c0\uae08\uae4c\uc9c0 VCG \uba54\ucee4\ub2c8\uc998\uc758 \uc7a5\uc810\uc5d0 \ub300\ud574 \ub9ce\uc774 \ub2e4\ub8e8\uc5c8\uc73c\uba70, \uadf8\ub7f4 \ub9cc\ud55c \uc774\uc720\uac00 \uc788\ub2e4.
\uadf8\ub7ec\ub098 VCG\ub294 \uba87 \uac00\uc9c0 \uc911\uc694\ud55c \uc81c\uc57d \uc0ac\ud56d\uc744 \uac00\uc9c0\uace0 \uc788\uc73c\uba70, \uc774 \uc601\uc0c1\uc5d0\uc11c\ub294 \uadf8 \ud55c\uacc4\ub4e4\uc744 \uc18c\uac1c\ud560 \uac83\uc774\ub2e4.<\/p>\n\n\n\n

\n\n\n\n

1. \ud504\ub77c\uc774\ubc84\uc2dc \ubb38\uc81c (Privacy)<\/h4>\n\n\n\n

VCG requires agents to fully reveal their private information<\/p>\n\n\n\n

This private information may have value to agents that extends beyond the current interaction
– for example, the agents may know that they will compete with each other again in the future<\/p>\n\n\n\n

It is often preferable to elicit only as much information from agents as is required to determine the social welfare maximizing choice and compute the VCG payments.<\/p>\n\n\n\n

VCG\ub294 \uc5d0\uc774\uc804\ud2b8\uac00 \uc790\uc2e0\uc758 \uac1c\uc778 \uc815\ubcf4\ub97c \ubaa8\ub450 \uba54\ucee4\ub2c8\uc998\uc5d0 \uacf5\uac1c\ud574\uc57c \ud558\ub294 \uad6c\uc870\uc774\ub2e4.
\uc774 \uc124\uc815\uc740 \uba54\ucee4\ub2c8\uc998\uc774 \uacb0\uc815\ud55c \uc120\ud0dd\uacfc \uc9c0\ubd88\ub9cc\uc774 \uc5d0\uc774\uc804\ud2b8\uc758 \ud6a8\uc6a9\uc5d0 \uc601\ud5a5\uc744 \ubbf8\uce5c\ub2e4\ub294 \ubaa8\ub378\uc744 \uc804\uc801\uc73c\ub85c \uc2e0\ub8b0\ud560 \uacbd\uc6b0\uc5d0\ub294 \ubb38\uc81c\uac00 \uc5c6\ub2e4.<\/p>\n\n\n\n

\ud558\uc9c0\ub9cc \ud604\uc2e4\uc5d0\uc11c\ub294 \uc5d0\uc774\uc804\ud2b8\ub4e4\uc774 \ubc18\ubcf5\uc801\uc73c\ub85c \uc0c1\ud638\uc791\uc6a9\ud560 \uc218 \uc788\uc73c\uba70, \uadf8 \uacfc\uc815\uc5d0\uc11c \uac1c\uc778 \uc815\ubcf4\ub97c \uacf5\uac1c\ud558\uba74 \ud5a5\ud6c4 \uacbd\uc7c1\uc5d0\uc11c \ubd88\ub9ac\ud574\uc9c8 \uac00\ub2a5\uc131\uc774 \uc874\uc7ac\ud55c\ub2e4.
\ub530\ub77c\uc11c \uc774\ub7ec\ud55c \ud658\uacbd\uc5d0\uc11c\ub294, \ucd5c\uc18c\ud55c\uc758 \uc815\ubcf4\ub9cc \uacf5\uac1c\ud558\uace0\ub3c4 \uc0ac\ud68c\uc801 \ud6c4\uc0dd \uadf9\ub300\ud654\uc640 VCG \uc9c0\ubd88\uc744 \uacc4\uc0b0\ud560 \uc218 \uc788\ub294 \uba54\ucee4\ub2c8\uc998\uc774 \uc120\ud638\ub420 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

VCG\ub294 \uc774\ub7ec\ud55c \ucd5c\uc18c \uc815\ubcf4 \uacf5\uac1c \uc694\uac74\uc744 \ucd08\uacfc\ud558\ub294 \uc815\ubcf4\ub97c \uc694\uad6c\ud558\ubbc0\ub85c, \uc774\ub7f0 \uacbd\uc6b0 VCG\ub294 \uc801\ud569\ud558\uc9c0 \uc54a\ub2e4.<\/p>\n\n\n\n

2. \ub2f4\ud569\uc5d0 \ucde8\uc57d\ud568 (Susceptibility to Collusion)<\/h4>\n\n\n\n

VCG\ub294 \ub2f4\ud569(collusion)\uc5d0\ub3c4 \ucde8\uc57d\ud558\ub2e4.<\/p>\n\n\n\n

\uc608\ub97c \ub4e4\uc5b4 \ub3c4\ub85c \uac74\uc124 \uac8c\uc784\uc5d0\uc11c, \uc138 \uba85\uc758 \uc5d0\uc774\uc804\ud2b8\uac00 \uc788\ub2e4\uace0 \ud558\uc790.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

– \ub3c4\ub85c\ub97c \uac74\uc124\ud558\uba74 \ucd1d \ud6a8\uc6a9\uc740 300\uc774\ub2e4.
– \uac74\uc124\ud558\uc9c0 \uc54a\uc73c\uba74 \ucd1d \ud6a8\uc6a9\uc740 250\uc774\ub2e4.<\/p>\n\n\n\n

\ub530\ub77c\uc11c \ub3c4\ub85c\ub294 \uac74\uc124\ub41c\ub2e4.<\/p>\n\n\n\n

\uc774\ub54c Agent 1\uc740 VCG \uc9c0\ubd88 \uaddc\uce59\uc5d0 \ub530\ub77c 100\uc744 \ubc1b\uc9c0\ub9cc, \uacb0\uad6d 250\uc744 \uc9c0\ubd88\ud558\uac8c \ub418\uc5b4 \uc21c\uc9c0\ubd88 150\uc744 \ud558\uac8c \ub41c\ub2e4.
VCG\ub294 \uac1c\ubcc4\uc801\uc73c\ub85c\ub294 \uc9c4\uc2e4\uc744 \ub9d0\ud558\ub294 \uac83\uc774 \uc9c0\ubc30 \uc804\ub7b5\uc774\ub77c\ub294 \ud2b9\uc131\uc744 \ubcf4\uc7a5\ud55c\ub2e4.<\/p>\n\n\n\n

Agent 1\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc73c\uba74, \ub3c4\ub85c\uac00 \ub9cc\ub4e4\uc5b4\uc9c0\uc9c0 \uc54a\uace0 \ud6a8\uc6a9\uc740 $250
Agent 1\uc774 \uc788\uc73c\uba74 \ub3c4\ub85c\uac00 \uc9c0\uc5b4\uc9c0\uace0, \ub2e4\ub978 \uc5d0\uc774\uc804\ud2b8(2, 3)\uc758 \ud6a8\uc6a9 \ud569\uc740 $100
\u2192 \\(p_1\\) = 250 – 100 = 150
\uc989, Agent 1\uc740 $150\uc744 \uc9c0\ubd88\ud568.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\ud558\uc9c0\ub9cc \ub9cc\uc57d Agent 1\uacfc Agent 2\uac00 \uc11c\ub85c \ud611\uc758\ud558\uc5ec \uc790\uc2e0\ub4e4\uc758 \uac00\uce58\ub97c \uac01\uac01 $50\uc529 \ub192\uc5ec \ubcf4\uace0\ud55c\ub2e4\uba74, \uc774\ub4e4\uc740 \uac01\uc790\uc758 \uc9c0\ubd88\uc561\uc744 $50\uc529 \uc904\uc77c \uc218 \uc788\ub2e4.
\uc989, \uc11c\ub85c\uc758 \ubcf4\uace0\uac00 \uc0c1\ub300\ubc29\uc758 \uc9c0\ubd88\uc744 \uc904\uc774\ub294 \ud6a8\uacfc\ub97c \uc77c\uc73c\ud0a8\ub2e4.<\/p>\n\n\n\n

Agent 1\uc758 \uc120\uc5b8\ub41c value\uac00 \ucee4\uc9c0\uba74,
Agent 1\uc740 \u201c\ub354 \uc911\uc694\ud55c \uc874\uc7ac\u201d\uac00 \ub3fc\uc11c \uc2dc\uc2a4\ud15c\uc5d0\uc11c \ube60\uc84c\uc744 \ub54c \ub354 \ud070 \uc190\ud574\uac00 \ubc1c\uc0dd\ud558\ub294 \uac83\ucc98\ub7fc \ubcf4\uc784<\/p>\n\n\n\n

\uadf8\ub7ec\uba74 \uc2e4\uc81c\ub85c\ub294 \uc774\ub807\uac8c \ub428:<\/p>\n\n\n\n

    \n
  1. Agent 2\uc758 \uc9c0\ubd88\uc561 \uacc4\uc0b0\uc2dc, Agent 1\uc774 \ub9e4\uc6b0 \uc911\uc694\ud55c \uc0ac\ub78c\uc774 \ub410\uae30 \ub54c\ubb38\uc5d0 Agent 2\uac00 \ube60\uc84c\uc744 \ub54c \uc2dc\uc2a4\ud15c\uc774 \uc720\uc9c0\ub420 \uc218 \uc788\uc74c.<\/li>\n\n\n\n
  2. \uc774\ub85c \uc778\ud574 Agent 2\uac00 less pivotal(\ub35c \uc911\uc2ec\uc801 \uc5ed\ud560\uc744 \ud55c \uc0ac\ub78c)\ucc98\ub7fc \ubcf4\uc774\uac8c \ub428.<\/li>\n\n\n\n
  3. \ub530\ub77c\uc11c Agent 2\uc758 \uc9c0\ubd88\uc561\uc774 \uc904\uc5b4\ub4ec.<\/li>\n<\/ol>\n\n\n\n

    \uadf8\ub9ac\uace0 \ub9c8\ucc2c\uac00\uc9c0\ub85c:
    Agent 2\uac00 \uc790\uc2e0\uc758 \uac12\uc744 \uc62c\ub838\uae30 \ub54c\ubb38\uc5d0 Agent 1\ub3c4 \ub35c \uc911\uc694\ud55c \uc0ac\ub78c\ucc98\ub7fc \ubcf4\uc774\uace0, Agent 1\uc758 \uc9c0\ubd88\uc561\ub3c4 \uc904\uc5b4\ub4ec.<\/p>\n\n\n\n

    What happens if agents 1 and 2 both increase their declared valuations by $50?
    The choice is unchanged, but both of their payments are reduced.
    Thus, while no agent can gain by changing his declaration, group can.<\/p>\n\n\n\n

    \uc774\ub7ec\ud55c \ud604\uc0c1\uc740 VCG\uac00 \uac1c\ubcc4 \uc804\ub7b5\uc801 \uc9c4\uc2e4\uc131\uc740 \uc720\uc9c0\ud558\ub354\ub77c\ub3c4, \uc9d1\ub2e8\uc801 \ub2f4\ud569\uc5d0\ub294 \ucde8\uc57d\ud558\ub2e4\ub294 \uc810\uc744 \ubcf4\uc5ec\uc900\ub2e4.<\/p>\n\n\n\n

    \u2192 VCG\ub294 \u201c\uc5bc\ub9c8\ub098 pivotal(\uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud588\ub294\uac00)\u201c\uc5d0 \ub530\ub77c \uc9c0\ubd88\uc561\uc774 \uacb0\uc815\ub428.<\/p>\n\n\n\n

    \n\n\n\n

    3. \uac80\uc57d\uc131 \ubd80\uc871 (VCG is not Frugal)<\/h4>\n\n\n\n

    VCG\ub294 \ub54c\ub54c\ub85c \uacfc\ub3c4\ud55c \uc9c0\ubd88\uc744 \ubc1c\uc0dd\uc2dc\ucf1c \ube44\uac80\uc57d\uc801(frugal\ud558\uc9c0 \uc54a\ub2e4)\uc774\ub2e4.
    \uc608\ub97c \ub4e4\uc5b4 \uc774\uc804\uc758 \ub77c\uc6b0\ud305 \ubb38\uc81c\ub97c \ub2e4\uc2dc \ubcf4\uc790.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    VCG can end up paying arbitrarily more than an agent is willing to accept<\/strong> (or equivalently charging arbitrarily less than an agent is willing to pay)<\/p>\n\n\n\n

    Consider the effect of AC’s cost on the payment to AB.<\/p>\n\n\n\n

      \n
    • If the cost of this edge increased to 8, our payment to AB would increase to \\(p_{AB} = (-12) – (-2) = -10\\).<\/li>\n\n\n\n
    • If the cost were any \\(x \\geq 2\\), we would select the path ABEF and would have to make a payment to AB of \\(p_{AB} = (-4-x) – (-2) = -(x+2)\\).<\/li>\n\n\n\n
    • The gap between agents’ true costs and the payments that they could receive under VCG is unbounded.<\/li>\n<\/ul>\n\n\n\n

      \ucd5c\ub2e8 \uacbd\ub85c\uc758 \ube44\uc6a9\uc774 5\uc774\uace0, \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \ube44\uc6a9\uc774 6\uc774\ub77c\uace0 \ud558\uc790.<\/p>\n\n\n\n

      \uc774\ub54c \uc5b4\ub5a4 \ub9c1\ud06c(\uc608: AB)\uc758 \uc18c\uc720\uc790\uc5d0\uac8c \uc9c0\ubd88\ub418\ub294 \uae08\uc561\uc740 \uc790\uc2e0\uc758 \ubcf4\uace0\uc640 \ubb34\uad00\ud558\uac8c, \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \ube44\uc6a9\uc5d0 \ub530\ub77c \uacb0\uc815\ub41c\ub2e4.
      \uc608\ub97c \ub4e4\uc5b4, AC\uc758 \ube44\uc6a9\uc774 2\uc5d0\uc11c 8\ub85c \uc99d\uac00\ud558\uba74, \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c\ub294 12\uac00 \ub418\uba70, \uadf8\uc5d0 \ub530\ub77c AB\uac00 \ubc1b\ub294 \uae08\uc561\ub3c4 6\ub9cc\ud07c \uc99d\uac00\ud558\uac8c \ub41c\ub2e4.
      \uc989, \ub2e4\ub978 \uc0ac\ub78c\uc758 \ube44\uc6a9 \ubcc0\ud654\uac00 \ubcf8\uc778\uc758 \uc218\uc775\uc5d0 \uc601\ud5a5\uc744 \ubbf8\uce58\ub294 \uad6c\uc870\uc774\ub2e4.
      \uc774\ub294 \uc9c0\ubd88\uc561\uacfc \uc2e4\uc81c \ube44\uc6a9 \uac04\uc758 \ucc28\uc774\uac00 \ubb34\ud55c\uc815 \ucee4\uc9c8 \uc218 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\n\n\n\n

      \ub610\ud55c, \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c\uc640\uc758 \ucc28\uc774\ub97c \uae30\ubc18\uc73c\ub85c \uc9c0\ubd88\uc561\uc744 \ucd94\uc815\ud558\ub824 \ud574\ub3c4, \uc9c0\ubd88\uc561\uc740 \uc5ec\uc804\ud788 \ud574\ub2f9 \uacbd\ub85c\ubcf4\ub2e4 \ud6e8\uc52c \ud074 \uc218 \uc788\uc74c\uc774 \uc218\ud559\uc801\uc73c\ub85c \uc785\uc99d\ub41c\ub2e4.
      \uacb0\uacfc\uc801\uc73c\ub85c, VCG\ub294 \ube44\uc6a9 \ub300\ube44 \uacfc\ub3c4\ud55c \ubcf4\uc0c1\uc744 \uc720\ubc1c\ud560 \uc218 \uc788\ub294 \uad6c\uc870\uc774\ub2e4.<\/p>\n\n\n\n

      Are VCG’s payment at least close to the cost of the second shortest disjoint path?<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      The top path has a total cost of c.
      VCG picks it, pays each of the k agents \\(c(1+\\epsilon) – (k-1)\\frac{c}{k}\\).
      Hence VCG’s total payment is \\(c(1+k \\epsilon)\\).
      For fixed \\(\\epsilon\\), VCG’s payment is \\(\\Theta(k)\\) times (i.e., only a constant away from k times) the cost of the second shortest disjoint path.<\/p>\n\n\n\n

      \uc5d0\uc774\uc804\ud2b8 i\uc758 \uc81c\uac70\uac00 \uc0ac\ud68c\uc801 \ube44\uc6a9\uc5d0 \ub07c\uce58\ub294 \uc601\ud5a5\uc740?<\/p>\n\n\n\n

      \uc5d0\uc774\uc804\ud2b8 i\uac00 \uc5c6\uc73c\uba74, \uc704\ucabd \uacbd\ub85c \uc0ac\uc6a9 \ubd88\uac00\ub2a5\ud558\ubbc0\ub85c, \uc804\uccb4 \uacbd\ub85c\ub294 \uc544\ub798\ucabd \uacbd\ub85c \\((s \\to t)\\)\ub85c \ubc14\ub01c
      \uc544\ub798\ucabd \uacbd\ub85c\uc758 \ube44\uc6a9\uc740: \\(c(1 + \\varepsilon)\\)
      \uc5d0\uc774\uc804\ud2b8 i\ub97c \uc81c\uc678\ud55c \uc704\ucabd \uacbd\ub85c\uc758 \ub098\uba38\uc9c0 k-1 \uc5d0\uc774\uc804\ud2b8\uc758 \ube44\uc6a9\uc740:
      \\((k-1)\\cdot \\frac{c}{k} = \\frac{(k-1)c}{k}\\)<\/p>\n\n\n\n

      \ub530\ub77c\uc11c VCG\uac00 \uc5d0\uc774\uc804\ud2b8 i\uc5d0\uac8c \uc9c0\ubd88\ud558\ub294 \uae08\uc561\uc740: <\/p>\n\n\n\n

      \\(p_i = c\\left(1 + \\varepsilon – \\frac{k-1}{k}\\right) = c\\left(1 + \\varepsilon – 1 + \\frac{1}{k}\\right) = c\\left(\\varepsilon + \\frac{1}{k}\\right)\\)<\/p>\n\n\n\n

      \uac01 \uc5d0\uc774\uc804\ud2b8\ub9c8\ub2e4 \ub3d9\uc77c\ud55c \uae08\uc561\uc744 \ubc1b\uc73c\ubbc0\ub85c, \ucd1d \uc9c0\uae09\uc561\uc740: <\/p>\n\n\n\n

      \\(\\text{Total payment} = k \\cdot p_i = k \\cdot c\\left(\\varepsilon + \\frac{1}{k}\\right) = c(k\\varepsilon + 1) = c(1 + k\\varepsilon)\\)<\/p>\n\n\n\n

      \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c(\uc544\ub798\ucabd \uacbd\ub85c)\uc758 \ube44\uc6a9\uc740 \\(c(1+\\epsilon)\\)
      VCG \ucd1d \uc9c0\ubd88\uc561\uc740 \\(c(1+k \\epsilon)\\)<\/p>\n\n\n\n

      \ub530\ub77c\uc11c, \\(\\frac{\\text{VCG total payment}}{\\text{2nd shortest path cost}} = \\frac{c(1 + k\\varepsilon)}{c(1 + \\varepsilon)} \\approx \\Theta(k)\\)<\/p>\n\n\n\n

      \u2192 \\(\\epsilon\\)\uc774 \uc791\uc744\uc218\ub85d VCG\uc758 \ube44\uc6a9\uc740 \ub450 \ubc88\uc9f8 \ucd5c\ub2e8 \uacbd\ub85c \ube44\uc6a9\uc758 \uc57d k\ubc30\uae4c\uc9c0 \ub298\uc5b4\ub0a0 \uc218 \uc788\uc74c<\/p>\n\n\n\n

      \n\n\n\n

      4. \uc218\uc775 \ub2e8\uc870\uc131 \uc704\ubc30 (Revenue Monotonicity Violated)<\/h4>\n\n\n\n

      Revenue monotonicity: revenue always weakly increases as agents are added.<\/p>\n\n\n\n

      \uc9c1\uad00\uc801\uc73c\ub85c\ub294, \uba54\ucee4\ub2c8\uc998\uc5d0 \ub354 \ub9ce\uc740 \ucc38\uac00\uc790\ub97c \ucd94\uac00\ud558\uba74 \ucd1d \uc218\uc775\uc774 \uc99d\uac00\ud574\uc57c \ud55c\ub2e4\uace0 \uc0dd\uac01\ud558\uae30 \uc27d\ub2e4. \ud558\uc9c0\ub9cc VCG\ub294 \uadf8\ub807\uc9c0 \uc54a\ub2e4.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      \uc608\ub97c \ub4e4\uc5b4 \ub3c4\ub85c \uac74\uc124 \uc608\uc2dc\uc5d0\uc11c,<\/p>\n\n\n\n

      – \uac74\uc124 \uc2dc \ucd1d \ud6a8\uc6a9\uc740 100
      – \ube44\uac74\uc124 \uc2dc \ucd1d \ud6a8\uc6a9\uc740 90<\/p>\n\n\n\n

      \uc774\ubbc0\ub85c \ub3c4\ub85c\uac00 \uac74\uc124\ub41c\ub2e4.<\/p>\n\n\n\n

      \uc774\ub54c Agent 2\ub294 Agent 1\uc774 \uc5c6\uc744 \uacbd\uc6b0 90\uc758 \ud6a8\uc6a9\uc744 \ubc1b\uc73c\ubbc0\ub85c, Agent 2\ub294 90\uc744 \uc9c0\ubd88\ud558\uac8c \ub41c\ub2e4.
      \ud558\uc9c0\ub9cc Agent 3\ub97c \ucd94\uac00\ub85c \ud22c\uc785\ud558\uc5ec, \uadf8\uac00 Agent 2\uc640 \ub3d9\uc77c\ud55c \ud6a8\uc6a9\uc744 \uac00\uc9c4\ub2e4\uace0 \ud558\uba74, \ub450 \uc5d0\uc774\uc804\ud2b8 \uc911 \ub204\uad6c\ub97c \uc81c\uc678\ud558\ub354\ub77c\ub3c4 \ub3c4\ub85c\ub294 \uc5ec\uc804\ud788 \uac74\uc124\ub41c\ub2e4.
      \uc989, \ub458 \ub2e4 \ud53c\ubc97 \uc5d0\uc774\uc804\ud2b8\uac00 \uc544\ub2c8\ubbc0\ub85c, \uc9c0\ubd88\ud558\uc9c0 \uc54a\ub294\ub2e4. \uacb0\uacfc\uc801\uc73c\ub85c \ucd1d \uc218\uc775\uc740 90\uc5d0\uc11c 0\uc73c\ub85c \uac10\uc18c\ud55c\ub2e4.<\/p>\n\n\n\n

      \uac8c\ub2e4\uac00 \uc5d0\uc774\uc804\ud2b8\uac00 \uc790\uc2e0\uc744 \ub458\ub85c \ub098\ub204\uc5b4 \ubcf4\uace0\ud558\uba74, \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc790\uc2e0\uc758 \uc9c0\ubd88\uc744 \uc5c6\uc568 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

      \ud558\uc9c0\ub9cc Agent 3\uac00 \ucd94\uac00\ub420 \uacbd\uc6b0 \uc544\ubb34\uac83\ub3c4 \uc9c0\ubd88\ud560 \ud544\uc694\uac00 \uc5c6\ub2e4.<\/p>\n\n\n\n

      Adding agent 3 causes VCG to make the same choice but to collect zero revenue!
      Agent 2 could pretend to be two agents and eliminate his payment.<\/p>\n\n\n\n

      \n\n\n\n

      5. \uc218\uc775 \ud658\uae09 \ubd88\uac00\ub2a5 (Cannot Return All Revenue to Agents)<\/h4>\n\n\n\n