Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting

Abstract

This paper studies a dynamic model of perfectly competitive price posting under demand uncertainty. Firms must produce output in advance. After observing aggregate sales in prior periods, firms post prices for their unsold output. In each period, the demand of a new batch of consumers is randomly activated. Existing customers who have not yet bought and then new customers arrive at the market in random order, observe the posted prices, and either purchase at the lowest available price or delay their purchase decision. We construct a sequential equilibrium in which the output produced and its allocation across consumers is efficient. Thus consumers endogenously sort themselves efficiently, with the highest valuations purchasing first. Transaction prices in each period rise continuously, as firms become more optimistic about demand, followed by a market correction. By the last period, prices are market clearing.

Dynamic Price Dispersion of Seasonal Goods in Bertrand–Edgeworth Competition

“…They utilize variational inequality tools and conduct comparative statics on equilibrium prices as a function of demand-capacity ratios. (Deneckere & Peck, 2012) derive dynamic price dispersion in perfect competition by developing a dynamic version of Prescott's hotel model. Their model integrates price variation across periods, adjusting the demand function based on past revealed demand.…”

Information, Bertrand–Edgeworth competition and the law of one price

“…Alternative methods of delivering pure strategy equilibria include modifying the timing of the game (Deneckere and Kovenock, 1992;Deneckere and Peck, 2012;Dudey, 1992), allowing sellers to choose list prices and subsequent discount prices (Garcìa Díaz et al, 2009;Myatt and Ronayne, 2019), requiring integer pricing (Chowdhury, 2008), imposing a cost on firms that turn customers away (Dixon, 1990) and introducing a public social-surplus maximising seller (Rácz and Tasnádi, 2016).…”