Price to Compete ... With Many: How to Identify Price Competition in High Dimensional Space

Abstract

The authors study price competition in markets with a large number (in magnitude of hundreds or thousands) of potential competitors, using the hotel industry as a test bed.The authors address two methodological challenges: simultaneity bias and high dimensionality. Simultaneity bias arises from joint determination of prices in competitive markets.The authors propose a new instrumental variable approach to address simultaneity bias in high dimensions. The novelty of the idea is to exploit online search and clickstream data to uncover demand shocks at a granular level, with sufficient variations both over time and across competitors in order to obtain valid instruments at a large scale.The authors then develop a methodology to identify relevant competitors in high dimensions combining the instrumental variable approach with high dimensional l-1 norm regularization.The authors apply this data-driven approach to study the patterns of hotel price competition in the New York City market. The authors find that engagement in competition-based revenue management is prevalent across branded and non-branded hotels and across all quality tiers. When choosing whose prices to follow, branded hotels are more confined by quality boundaries but less by geographical boundaries, as compared to independent hotels. Also, budget and luxury hotels are more confined by quality boundaries but less by geographical boundaries, as compared to economy and up-scale hotels.Lastly, the authors show that the competitive responses identified through our method can help hoteliers proactively manage their prices and promotions. The authors find that accounting for competitive responses will lead to more accurate price/promotions decisions (avoiding up to 11-20% of pricing errors and 11-23% missed growth targets for certain hotels and chains).