Price competition, Sequential Search and Sellers’ rationality

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. Simulation Results show that Reinforcement Learning never converges to Nash equilibrium. However, using Nash equilibrium, one can predict how the two first order statistics vary with respect to market structure. Concerning the average posted price, we find that Nash predictions are well respected, 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. Yet, 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 of firms and the proportion of informed consumers is in a decrease of the accepted price of informed consumers although Nash predicts such a decrease only for the second parameter within the parameter range considered.