Dynamic pricing under first order Markovian competition

We evaluate the effect of competition on prices, profits, and consumers' surplus in multiperiod, finite horizon, dynamic pricing settings. In our base model, a single myopic consumer visits two competing retailers, who offer identical goods, in a (first order Markovian) probabilistic fashion–if the posted price exceeds the consumer's valuation for the good, he returns to the same store in the following period with a certain probability. We find that even a small reduction in the return probability from one–which corresponds to the monopoly case at which prices decline linearly–is sufficient to revert the price decline from a linear into an exponential shape. Each retailer's profit is particularly sensitive to changes in his return probability when it is relatively high, and is maximized under complete loyalty behavior (i.e., return probability is one). On the other hand, consumer surplus is maximized under complete switching behavior (i.e., return probability is zero). In the presence of many similar consumers, the insights remain valid. We further focus on the extreme scenario where all consumers follow a complete switching behavior, to derive sharp bounds, and also consider the instance where, in this setting, myopic consumers are replaced with strategic consumers.