We consider a sequential search model with two types of consumers: ('high cost's) consumers who incur a positive search cost at each visit and informed consumers who visit all the firms at no cost. The objective is to compare Nash market predictions with a market with adaptive sellers using reinforcement learning. Results show that, reinforcement learning never converges to Nash. However, Nash predictions are not rejected for first order statistics notably average posted prices albeit variations are in general less pronounced with reinforcement learners. Concerning price dispersion, only variations with respect to the number of firms follow the same shape as Nash. But increasing the proportion of informed consumers seems to have contradicting effects on price dispersion although Nash predicts in general a decrease of price dispersion in the case of study. The impact of the number firms and the proportion of informed consumers is in a decrease of the accepted price of informed consumers although Nash predict such a decrease only for the second parameter.
