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

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