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VCG Mechanism Allocation and Transfers for 3 Players

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The table above shows, for instance, that player 1 has valuations va1=2,vb1=5 and va,b1=6. If the valuations of the three players are as depicted in the table above, and if all players report truthfully a) What is the allocation of the two objects that maximizes the sum of values(utilities) across all players, for this valuation profile? (Who gets what?) b) What are the transfers according to the VCG mechanism for this valuation profile? (Note: You are only required to state the allocation and transfers for this particular valuation profile and not for any general valuation profile. The correct answer involves explicit numbers and not algebraic expressions.) c) Suppose Player 3 lies and reports va3=9,vb3=9 and va,b3=15 and the VCG mechanism determines the corresponding allocation and transfers. What is Player 3's payoff from such a lie?.

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The table above shows, for instance, that player 1 has valuations va1=2,vb1=5 and va,b1=6. If the valuations of the three players are as depicted in the table above, and if all players report truthfully a) What is the allocation of the two objects that maximizes the sum of values(utilities) across all players, for this valuation profile? (Who gets what?) b) What are the transfers according to the VCG mechanism for this valuation profile? (Note: You are only required to state the allocation and transfers for this particular valuation profile and not for any general valuation profile. The correct answer involves explicit numbers and not algebraic expressions.) c) Suppose Player 3 lies and reports va3=9,vb3=9 and va,b3=15 and the VCG mechanism determines the corresponding allocation and transfers. What is Player 3's payoff from such a lie?

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VCG Mechanism Allocation and Transfers for 3 Players

  • 1. The table above shows, for instance, that player 1 has valuations va1=2,vb1=5 and va,b1=6. If the valuations of the three players are as depicted in the table above, and if all players report truthfully a) What is the allocation of the two objects that maximizes the sum of values(utilities) across all players, for this valuation profile? (Who gets what?) b) What are the transfers according to the VCG mechanism for this valuation profile? (Note: You are only required to state the allocation and transfers for this particular valuation profile and not for any general valuation profile. The correct answer involves explicit numbers and not algebraic expressions.) c) Suppose Player 3 lies and reports va3=9,vb3=9 and va,b3=15 and the VCG mechanism determines the corresponding allocation and transfers. What is Player 3's payoff from such a lie?