Abstract
We study dynamic games between two providers — an entrant and an incumbent — each with fixed capacity, who compete to sell in both a forward market and a spot market. We analyse two types of games between the providers: (a) a sequential game where the incumbent plays first followed by the entrant and (b) a repeated game where both providers make simultaneous decisions but do this repeatedly an infinite number of times. Demand is either from a single buyer or a population of independent consumers. We identify outcomes for the sequential game for varying levels of demand. For the repeated game, we identify the existence of subgame-perfect Nash equilibria and show how the two providers can obtain higher average revenues by implicit collusion. The study has implications for revenue management markets where providers have dynamic competitive interactions rather then a single static interaction.
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1 Guillermo Gallego is Chairman of the IEOR Department at Columbia University. He has consulted extensively in the areas of manufacturing, supply chain, revenue management and distance learning. He has been Associate Editor, Departmental Editor and Senior Editor of several of the flagship journals of his field and has been an invited speaker at almost all national and international universities with strong programmes in operations research and operations management. He has been the recipient of seven NSF grants and of several industrial grants to support his research activities. He has published over 50 papers in prestigious journals including seminal papers in supply chain, inventory theory and revenue management.
2 Srinivas Krishnamoorthy is an Assistant Professor at the Ivey School of Business, The University of Western Ontario. He obtained his PhD from the Graduate School of Business, Columbia University. Prior to his PhD, he worked in the mutual fund and banking industries in India. He also has a BTech in Mechanical Engineering from the Indian Institute of Technology and a PGDM (MBA) from the Indian Institute of Management.
3 Robert Phillips is co-founder and CTO of Nomis Solutions and a Lecturer at Stanford University Graduate School of Business. Prior to Nomis, he served as Chief Technology Officer of publicly held Manugistics where he was the key visionary for Manugistics Pricing and Revenue Optimization and Enterprise Profit Optimization solutions. He was also the founder and CEO of Talus Solutions and was a visiting professor at Columbia University Graduate School of Business. Over the past 15 years, he has helped leading companies optimise price and revenue within a wide variety of industries including airlines, rental cars, hotels, electric power, freight and manufacturing. His book, titled Pricing and Revenue Optimization, provides a comprehensive introduction to the concepts, theories and applications of pricing and revenue optimisation.
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Gallego, G., Krishnamoorthy, S. & Phillips, R. Dynamic revenue management games with forward and spot markets. J Revenue Pricing Manag 5, 10–31 (2006). https://doi.org/10.1057/palgrave.rpm.5160020
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DOI: https://doi.org/10.1057/palgrave.rpm.5160020