We have three bidders (A, B and C) and three goods (x, y and z). The valuations are:

vA(x) = 17 vB(x) = 13 vC(x) = 5

vA(y) = 9 vB(y) = 15 vC(y) = 7

vA(z) = 1 vB(z) = 1 vC(z) = 21

vA(xy) = 33 vB(xy) = 25 vC(xz) = 1

vA(xz) = 15 vB(xz) = 11 vC(xy) = 19

All the valuations that are missing are assumed to be equal to 0 (so for instance we have vA(xyz) = 0, vi() = 0 for any bidder i = A, B, C, etc.).

Find the allocation and the price paid by each bidder with the VCG auction.