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The Clarke (aka. VCG ) mechanism [Clarke 71]

The Clarke (aka. VCG ) mechanism [Clarke 71]. The Clarke mechanism chooses some outcome o that maximizes Σ i v i ( θ i ’, o) θ i ’ = the type that i reports To determine the payment that agent j must make:

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The Clarke (aka. VCG ) mechanism [Clarke 71]

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  1. The Clarke(aka. VCG)mechanism[Clarke 71] • The Clarke mechanism chooses some outcome o that maximizes Σi vi(θi’, o) • θi’ = the type that i reports • To determine the payment that agent j must make: • Pretend j does not exist, and choose o-j that maximizes Σi≠j vi(θi’, o-j) • j pays Σi≠j vi(θi’, o-j) - Σi≠j vi(θi’, o)

  2. The Clarke mechanism is strategy-proof • Total utility for agent j is • vj(θj, o) + Σi≠j vi(θi’, o) - Σi≠j vi(θi’, o-j) • But agent j cannot affect the choice of o-j • Hence, j can focus on maximizing vj(θj, o) + Σi≠j vi(θi’, o) • The other agents’ types θi’ are out of j’s control • Agent j’s true type θj is also fixed • Agent j will try to report a type θj’ so that o maximizes vj(θj, o) + Σi≠j vi(θi’, o) • But mechanism chooses o to maximize Σi vi(θi’, o) • Hence, if θj’ = θj, o maximizes Σi vi(θi’, o) = vj(θj’, o) + Σi≠j vi(θi’, o). Therefore, if θj’ = θj, o maximizes vj(θj, o) + Σi≠j vi(θi’, o).

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