Characterization of ex post equilibrium in the VCG combinatorial auctions

We prove that when the number of (potential) buyers is at least three, every ex post equilibrium in the Vickrey-Clarke-Groves combinatorial auction mechanisms is a bundling equilibrium and is symmetric. This complements a theorem proved in Holzman, Kfir-Dahav, Monderer, and Tennenholtz [6], according to which, the symmetric bundling equilibria are precisely those defined by a quasi field.