On Revenue Optimal Combinatorial Auctions - IFP Group at the ...
On Revenue Optimal Combinatorial Auctions - IFP Group at the ...
On Revenue Optimal Combinatorial Auctions - IFP Group at the ...
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The Sufficient Condition<br />
Hazard r<strong>at</strong>e order<br />
Let Z 1 , Z 2 be nonneg<strong>at</strong>ive random variables. Z 1 ≤ h Z 2 , if<br />
Prob(Z 1 > z|Z 1 > ẑ) ≤ Prob(Z 2 > z|Z 2 > ẑ) for all z ≥ ẑ.<br />
Stronger than <strong>the</strong> first order stochastic dominance.<br />
The sufficient condition<br />
Let s ⊆ t be two bundles. Then (X n |B n = s) ≤ h (X n |B n = t).<br />
The larger bundle is likely to have higher value.<br />
The condition is intuitive for single-minded buyers.
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