Review for NeurIPS paper: No-regret Learning in Price Competitions under Consumer Reference Effects

Summary and Contributions: This paper studies a multi-period model: in each period, each of two firms posts a price for each product. The consumers demand for each of the products is linear in both prices and in addition linear in the reference price which captures past prices. Specifically, it is a weighted average of the previous-period reference price and the two previous-period posted prices. The firms do not know the specific demand function and have access only to the derivative of their revenue (a function that maps a price to revenue which is equal to demand times price) which is denoted by g_i(p_i). Note that g_i() depends on the other parameters but the firm views them as constants and is able to feed g_i with a possible choice of p_i and then get the revenue derivative for that price choice.