On Revenue Optimal Combinatorial Auctions - IFP Group at the ...

Simplifying OAP
Revenue(π) maximum revenue to the seller for a given π,
[ N
]
∑
= E q n (X n )w n (X n ) (from single buyer analysis),
n=1
[ ∑
= E π A (X) ( ∑
w n (X n ) )] (by relating q n ’s to π).
A∈A
n∈A
Suggests allocating from argmax
A∈A
[ ∑
w n (v n ) ] , for a bid vector v.
n∈A
Works if w n (x 1 n ) ≤ w n (x 2 n ) ≤ . . . ≤ w n (x Kn
n ).
Otherwise, the resulting q n ’s need not be monotone.