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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Worst Case ELR Comput<strong>at</strong>ion - Example<br />
Buyer 1<br />
1‐p p 0 < L < H<br />
r = H/L<br />
L H<br />
If pr < 1, <strong>the</strong>n w(L) > 0. The optimal alloc<strong>at</strong>ions is efficient.<br />
If pr ≥ 1, <strong>the</strong>n w(L) ≤ 0. The buyer wins only if he bids H.<br />
For pr ≥ 1, <strong>the</strong> RSW = pH, while <strong>the</strong> MSW = pH + (1 − p)L.<br />
ELR = (1 − p)/(pr + 1 − p).<br />
ELR is maximized by setting p = 1/r.<br />
Hence, η = (r − 1)/(2r − 1).