In a model of competition with imperfect consumer price information and incomplete price search, some consumers may end up comparing prices originating from the same supplier: either because one firm sets multiple prices or because a group of firms colludes. This leads to added monopoly power for these firms, and average prices in the mixed strategy equilibrium become higher. There is a shift in welfare from consumers to producers, both with exogenous and endogenous consumer search behaviour. However consumers might search more or less with multiple prices. The implications for the price-setting equilibrium, competition policy and recent judgements are considered.