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 by Holzman, Kfir-Dahav, Monderer, and Tennenholtz (2003), according to which, the symmetric bundling equilibria are precisely those defined by a quasi-field.