This paper considers markets in which consumers are imperfectly informed about both product prices and quality levels offered by firms. We characterize necessary and sufficient conditions for existence of the various equilibrium configurations of price and quality that can arise in two paradigm cases; when all consumers prefer higher quality and when all consumers prefer lower quality. Our results suggest that firms will exploit imperfect information by charging noncompetitive prices as well as by offering other than ideal quality in the former case, but only by changing noncompetitive prices in the latter case.

Louis L. Wilde, Alan Schwartz; Equilibrium Comparison Shopping, The Review of Economic Studies, Volume 46, Issue 3, 1 July 1979, Pages 543–553, https://doi

This paper reports experimental tests of three search equilibrium models. These models which differ only in the search strategies available to the buyers have qualitatively different predictions, that is, equilibria: price distributions, single price equilibria at the competitive price and at the monopoly price and two price equilibria. The experimental outcomes generally were consistent with the models' predictions. This suggests that debate on the utility of this class of models should shift to the realism of the models' assumptions rather than focus on their ability to characterize market outcomes. Also, since the basic models have been validated, the project of analysing experimentally the results of relaxing some of their assumptions seems worthwhile.