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)
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Limitations of VCG-Based Mechanisms
Shahar Dobzinski
Joint work with Noam Nisan
Common assumptions:
for every S,T M: v(S)+v(T) ≥ v(ST)
(but all of our results also hold for submodular valuations)
No
Probably Not
Many truthful Mechanisms
MIR are the only truthful mechanisms
???
E.g., combinatorial auctions
Very rich domains
Single parameter domains
LMN
A Truthful Mechanism
Affine Maximizer
Conjecture: Every mechanism for “rich enough” domain must be affine maximizer.
A way to set lower bounds on the only technique we have
Nisan-Ronen
MIR Algorithm
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.