Section 2: Combinatorial Auctions

Key Learning Points

• Define combinatorial auctions.
• Define the winner determination problem (WDP).
• Present a number of bidding languages that have been proposed for encoding bids and their relationships.

Activities

1. Read Section 11.3 of the text.
2. Do the following exercises:
   1. What is the set of winning bids given the following bids?

      Price	Bid items
      $1	Beast Boy
      $3	Robin
      $5	Raven, Starfire
      $6	Cyborg, Robin
      $4	Cyborg, Beast Boy
      $3	Raven, Beast Boy

   2. Consider the following combinatorial auction with 2 agents and 2 objects {a, b}. The valuation of agent 1 is v₁({a}) = 14, v₁({b}) = 1 and the valuation of agent 2 is v₂({a}) = 10, v₂({b}) = 10, v₂({a, b}) = 30. What is the allocation and payments for the VCG mechanism?