Price Competition with the Attraction Demand Model: Existence of Unique Equilibrium and Its Stability

Gallego, Guillermo; Huh, Woonghee Tim; Kang, Wanmo; Phillips, Robert L.

doi:10.1287/msom.1060.0115

Cited by 88 publications

(68 citation statements)

References 22 publications

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“…Some sample publications that extend the discrete choice one-period models considered in ( [2])are: in economics, [28], marketing, [7], and operations [18], [25], [33]. Talluri [33] points out the role of observability in a dynamic capacity RM allocation control game.…”

Section: Dynamic Models Of Competitionmentioning

confidence: 99%

Dynamic Price Competition with Fixed Capacities

Martínez‐de‐Albéniz

Talluri

2011

Management Science

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Many revenue management (RM) industries are characterized by (a) fixed capacities in the short term (e.g., hotel rooms, seats on an airline flight), (b) homogeneous products (e.g., two airline flights between the same cities at similar times), and (c) customer purchasing decisions largely influenced by price. Competition in these industries is also very high even with just two or three direct competitors in a market. However, RM competition is not well understood and practically all known implementations of RM software and most published models of RM do not explicitly model competition. For this reason, there has been considerable recent interest and research activity to understand RM competition. In this paper we study price competition for an oligopoly in a dynamic setting, where each of the sellers has a fixed number of units available for sale over a fixed number of periods. Demand is stochastic, and depending on how it evolves, sellers may change their prices at any time. This reflects the fact that firms constantly, and almost costlessly, change their prices (alternately, allocations at a price in quantity-based RM), reacting either to updates in their estimates of market demand, competitor prices, or inventory levels. We first prove existence of a unique subgame-perfect equilibrium for a duopoly. In equilibrium, in each state sellers engage in Bertrand competition, so that the seller with the lowest reservation value ends up selling a unit at a price that is equal to the equilibrium reservation value of the competitor. This structure hence extends the marginal-value concept of bid-price control, used in many RM implementations, to a competitive model. In addition, we show that the seller with the lowest capacity sells all its units first. Furthermore, we extend the results transparently to n firms and perform a number of numerical comparative statics exploiting the uniqueness of the subgame-perfect equilibrium.

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Section: Dynamic Models Of Competitionmentioning

confidence: 99%

Dynamic Price Competition with Fixed Capacities

Martínez‐de‐Albéniz

Talluri

2011

Management Science

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“…The Nash equilibrium p DPDP ¼ ðp DPDP 1 ; p DPDP 2 Þ can be found from stationary conditions ∂c 1 (p DPDP )/∂p 1 = ∂c 2 (p DPDP )/∂p 2 = 0. While there is no analytic solution to find the equilibrium in our example, Gallego et al (2006) describe a 'best-response' approach to find these solutions and show a linear convergence rate. We use a similar approach within the session to find p DPDP :The resulting prices and contributions depend on the bid prices for both airlines.…”

Section: Case 1: Al1 Rms Al2 Rmsmentioning

confidence: 98%

“…Obviously, this approach is impossible, and the standard solution is to analyze the existence and stability of a Nash equilibrium (no player can gain by unilaterally changing strategy). Gallego et al (2006) show that a unique Nash equilibrium exists for games with a multinomial logit (MNL) demand model under mild and realistic assumptions associated with the utility and cost functions.…”

Section: Game Theorymentioning

confidence: 99%

Dynamic pricing – The next revolution in RM?

Fiig¹,

Goyons

Adelving

et al. 2016

J Revenue Pricing Manag

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Thomas Fiig is director, chief scientist at Amadeus, where he is responsible for revenue management strategy and scientific methodologies. He holds a PhD in Theoretical Physics and Mathematics and a BA in Finance from the University of Copenhagen, Denmark. He has published several articles, recently focused on methodologies for origin-and-destination forecasting and optimization of simplified fare structures. He serves on the editorial board of the Journal of Revenue and Pricing Management.Oriana Goyons is a product definition analyst in the revenue management area at Amadeus. Currently, she is constructing the dynamic pricing product. She earned her master's degree in Operations Research from INPG Institut National Polytechnique and her engineering degree from ENSIMAG in Grenoble, France.Robin Adelving is a software development engineer at Amadeus, and a main contributor to the development of the Altéa Benchmarking Engine (ABE) simulation tool. Currently, he works in revenue management and operations research. He holds an engineering degree in Mathematics and Computer Science from ENSIMAG in Grenoble, France.Barry Smith is a freelance engineer specializing in pricing, revenue management and air transportation scheduling. While at American Airlines and Sabre, he developed many of the revenue management techniques used throughout the airline industry and pioneered the application of revenue management techniques in other industries. He holds patents in reservation system design, scheduling, pricing, operations and online retailing. He is an AGIFORS past president and Fellow. He led a team that received the Edelman Award and INFORMS Revenue Management Section Prize for their work on revenue management at American Airlines.ABSTRACT Existing revenue management systems (RMS) base their recommendations on historic observations and do not explicitly consider competition. This means that RMS recommendations often are not appropriate for real-time competitive situations. Dynamic pricing (DP) is an extension of RMS that dynamically calculates the optimal price, taking into account the airline's strategy, customer-specific information and realtime alternative offerings. By optimizing the contribution within the shopping session, DP has a more current and detailed view of demand and can improve RMS performance. We investigated the performance of DP using two simulators, Altéa Benchmarking Engine and Passenger Origin Destination Simulator and demonstrate that DP can deliver substantial revenue benefits with no modification to existing revenue management (RM) processes. However, the deployment of DP into the airline distribution process will be a challenge, because it affects all shopping and downstream processes, such as ticketing, servicing, revenue accounting, RM and interline settlement, that rely on information from existing fare aggregators. Nevertheless, the potential benefits of DP are so compelling that we believe the effort to bring this technology into practice is warranted.

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“…The Bernsten and Federgruen [7] investigate a similar problem in a decentralized system, both with and without market competition. Gallego et al [21] discuss a system under Bertrand competition with asymmetric nonlinear demand. Zhao [43] studies a supply chain with multiple retailers that compete in both price and inventory.…”

Section: Introductionmentioning

confidence: 99%