Advertising, brand loyalty and pricing

I consider an oligopoly model where, prior to price competition, firms invest in persuasive advertising and induce brand loyalty in consumers who would otherwise buy the cheapest alternative on the market. This setting, in which persuasive advertising is introduced to homogeneous product markets, provides an alternative explanation for price dispersion phenomena. Despite ex ante symmetry, the equilibrium profile of advertising outlays is asymmetric. It follows that endogenously determined brand loyal consumer bases are not symmetric across firms. This raises a robustness question regarding Varian's "model of sales" where symmetry is exogenously assumed.