Limitations of VCG-Based Mechanisms. Shahar Dobzinski Joint work with Noam Nisan. Combinatorial Auctions. m items, n bidders, each bidder i has a valuation function v i :2 M ->R + . Common assumptions: Normalization : v i ( )=0 Monotonicity : S T v i (T) ≥ v i (S)
Limitations of VCG-Based Mechanisms
Joint work with Noam Nisan
for every S,T M: v(S)+v(T) ≥ v(ST)
(but all of our results also hold for submodular valuations)
Many truthful Mechanisms
MIR are the only truthful mechanisms
E.g., combinatorial auctions
Very rich domains
Single parameter domains
A Truthful Mechanism
Conjecture: Every mechanism for “rich enough” domain must be affine maximizer.
A way to set lower bounds on the only technique we have
The Power of Efficient MIR Algorithms
a m1/6 lower bound for CAs with subadditive bidders using MIR algorithms.
For each index i with ai=1, set vA(S)=2 for all Ai S. Otherwise vA(S)=1. Similar valuation for Bob.