3 Presentations

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  04:00 PM - 04:30 PM

  A Supply Chain Network Game Theoretic Framework for Time-Based Competition with Transportation Costs and Product Differentiation

  • Anna Nagurney, presenter, Isenberg School of Management
  • Min Yu, Pamplin School of Business Administration, University of Portland, Portland, Oregon 97203

  In this paper, we developed a supply chain network game theory model with differentiated products and transportation costs in the case of time-based oligopolistic competition. The firms are profit-maximizers and have, as their strategic variables, the product shipments and the guaranteed delivery times to the consumers at the demand markets with the guaranteed delivery times never exceeding the sum of the production time and the transportation time. The demand price functions are functions of the demands for the products at the different demand markets as well as their guaranteed delivery times. The governing Nash equilibrium conditions are formulated as alternative variational inequalities. An algorithm is proposed, which yields closed form expressions, at each iteration, for the product shipments, the guaranteed delivery times, as well as the associated Lagrange multipliers. Supply chain network numerical examples are given to illustrate the modeling and the computational approach.

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  04:30 PM - 05:00 PM

  Interdiction Games on Markovian PERT Networks

  • Daniel Kuhn, presenter, Imperial College London

  We study stochastic interdiction games where an interdictor endeavors to maximally delay the expected completion time of a project that is managed according to the early start policy. The interdictor can deploy a non-renewable resource to interdict individual project tasks, thereby prolonging their uncertain durations. Given limited resource availability, the goal is to decide when to interdict which tasks in order to inflict maximum disruption to the project. We formulate the interdictor's decision problem as a multiple optimal stopping problem in continuous time and with decision-dependent information. Under a memoryless probabilistic model, we prove that this problem is equivalent to a Markov Decision Process (MDP) in discrete time that can be solved via efficient value iteration. The basic model is then generalized to account for implementation uncertainty. We also discuss a crashing game where the project manager can use a limited renewable resource to expedite certain tasks in order to counterbalance the interdictor's efforts. The resulting optimal stopping problem can be reformulated as a robust MDP.

• 
  05:00 PM - 05:30 PM

  Competitors Are Welcome: Why Incumbents Might Embrace Entrants?

  • Barna Bako, presenter, Corvinus University of Budapest

  Picture an industry where a monopolist operates initially and serves consumers who differ in their quality valuation and price elasticity. Will an entry jeopardize the incumbent’s profit or should the monopolist accommodate the entry? One of the main propositions of economic theory is that competition leads to lower prices and profits. In this article we present a simple model with product differentiation where exactly the opposite happens.
  We consider the following set-up: there are two segments of consumers differing in their valuation of quality and price-elasticity. A single product firm operates at the market without being able to price discriminate among segments. Our results show that if a low quality firm enters the market and captures a part of the price sensitive segment it might lead to price and profit increase. More specifically, if the difference in quality valuation is high enough the incumbent is better off after entry. Furthermore, we show that as the price-sensitive segment decreases the equilibrium prices increase. Hence, the incumbent may benefit from excluding some of its most price-sensitive consumers. Our main finding suggests that a high-quality firm quits the low-end market entirely if the quality valuation is high enough and the price-sensitive segment size is sufficiently low. These results indicate that an entry can be beneficial for the incumbent firm.
  This paper contributes to the literature on price-increasing competition. The main body of this literature (e.g. Rosenthal (1985), Inderst (2002), Chen and Riordan (2008)) concentrates mostly on price changes after competition picks up. The literature closest to our article deals with the profit increasing effect of the competition and the strategies an incumbent can pursue in order to increase competition and its profit.
  A few other papers show findings similar to our results. By using a model with a single manufacturer serving a market through a strategic retailer Kumar and Ruan (2006) show that a manufacturer by complementing the retail channel with an online channel effectively can induce retailers to enhance their support level for the manufacturer‘s product which increases demand and consequently its profit. Similar findings were presented by Ishibashi and Matsushima (2009), who analyzed the competition between low-end and high-end firms. In both quantity and price competition they show that if the low-end firms can capture the whole elastic segment of consumers that could lead to higher profits for the incumbents. In their model the existence of low-end firms functions as a credible threat which induces high-end firms not to overproduce. In our model we show that the existence of these kind of threats is not necessary to achieve this result.
  Alexandrov (2012) analyzes the question of de-marketing in a segmented market and arrives to the conclusion that horizontally differentiated firms can be better off by forbidding a group of consumers from patronizing the firm and leaving that segment to be served by the other firm or a new entrant. However quitting the low-end segment by all the firms does not constitute an equilibrium. If a firm stops serving the price-sensitive consumer group, the firm‘s competitor is much better off since she benefits from higher margins together with higher volumes. Thus, firms opt for a unilateral quit by their competitor and might end up serving all consumer segments which gives rise of the problem of coordination. To solve this problem we introduce asymmetric firms and analyze the effects of de-marketing in a more general model.