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Kinked-Demand Equilibria and Weak Duopoly in the Hotelling Model of Horizontal Differentiation

  • Pierre R Mérel and Richard J. Sexton
Published/Copyright: April 5, 2010
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 10 Issue 1

The Hotelling model with finite consumer reservation price is, in its various forms, perhaps the canonical model of horizontal product differentiation. Yet the following key aspects of this model are little understood: (i) the existence of asymmetric price equilibria when consumers have unit demands and (ii) for a very broad set of model specifications, the non-monotonicity of price as a function of consumers' transportation cost, i.e., the degree of product differentiation in the market. We provide a complete characterization of the asymmetric equilibria, show that they exist for a comparatively "wide" range of markets, and argue that their existence is robust to various extensions of the prototype model. Introducing elasticity into consumer demands suppresses the kink in the firms' demand functions and ensures the uniqueness (and symmetry) of the price equilibrium. However, the key perverse comparative static of the symmetric kinked equilibrium, decreasing price as a function of transport cost, survives relaxation of the unit-demand assumption. Indeed the symmetric kinked equilibrium of the unit-demand case is a special case of a general but largely unexplored set of equilibria in the Hotelling model we call weak duopoly. Weak-duopoly equilibria exist for intermediate values of transportation cost for a very broad class of consumer demands. They occupy a comparatively wide range of the model parameter space, and firm behavior in weak duopoly differs fundamentally from that which occurs for lower values of the transportation cost, or when consumers have no reservation price.

Keywords: duopoly; Hotelling; kinked-demand equilibrium; asymmetric equilibria; transportation cost
Published Online: 2010-4-5

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston

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  2. Endogenous Investment and Pricing under Uncertainty
  3. Information Revelation in Markets with Pairwise Meetings: Complete Revelation in Dynamic Analysis
  4. Optimal Screening by Risk-Averse Principals
  5. Coordination under the Shadow of Career Concerns
  6. The Optimal Accuracy Level in Asymmetric Contests
  7. The Fragmentation of Reputation
  8. Sharing Risk Efficiently under Suboptimal Punishments for Defection
  9. Advice from Multiple Experts: A Comparison of Simultaneous, Sequential, and Hierarchical Communication
  10. Contractual Incompleteness for External Risks
  11. On Delegation in Contests and the Survival of Payoff Maximizing Behavior
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  32. Price Regulation under Demand Uncertainty
  33. Linear Demand Systems are Inconsistent with Discrete Choice
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  35. Relative Extinction of Heterogeneous Agents
  36. Profit-Maximizing Sale of a Discrete Public Good via the Subscription Game in Private-Information Environments
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  38. The Role of Replication-Invariance: Two Answers Concerning the Problem of Fair Division When Preferences Are Single-Peaked
  39. Collusive Behavior of Bidders in English Auctions: A Cooperative Game Theoretic Analysis
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  42. Bertrand Competition in Markets with Fixed Costs
  43. Regular Infinite Economies
  44. Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note
  45. Quantifying the Cost of Risk in Consumption
  46. On a Class of Contest Success Functions
  47. Revealed Preference with Stochastic Demand Correspondence
  48. Contracting for Dynamic Efficiency
  49. Existence Advertising, Price Competition and Asymmetric Market Structure
  50. Global Social Interactions with Sequential Binary Decisions: The Case of Marriage, Divorce, and Stigma
  51. First-Mover Advantage in a Dynamic Duopoly with Spillover
  52. Costly Renegotiation in Repeated Bertrand Games
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  54. Antitrust Evaluation of Horizontal Mergers: An Economic Alternative to Market Definition
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https://doi.org/10.2202/1935-1704.1619
Keywords for this article
duopoly; Hotelling; kinked-demand equilibrium; asymmetric equilibria; transportation cost

Articles in the same Issue

  1. Topics Article
  2. Endogenous Investment and Pricing under Uncertainty
  3. Information Revelation in Markets with Pairwise Meetings: Complete Revelation in Dynamic Analysis
  4. Optimal Screening by Risk-Averse Principals
  5. Coordination under the Shadow of Career Concerns
  6. The Optimal Accuracy Level in Asymmetric Contests
  7. The Fragmentation of Reputation
  8. Sharing Risk Efficiently under Suboptimal Punishments for Defection
  9. Advice from Multiple Experts: A Comparison of Simultaneous, Sequential, and Hierarchical Communication
  10. Contractual Incompleteness for External Risks
  11. On Delegation in Contests and the Survival of Payoff Maximizing Behavior
  12. Optimal Quality Scores in Sponsored Search Auctions: Full Extraction of Advertisers' Surplus
  13. A Theory of Credibility under Commitment
  14. Communication Breakdown: Consultation or Delegation from an Expert with Uncertain Bias
  15. Social Learning in Social Networks
  16. A Note on the Multidimensional Monopolist Problem and Intertemporal Price Discrimination
  17. A Note on Rationalizability and Restrictions on Beliefs
  18. Vote or Shout
  19. Asymmetry and Collusion in Sequential Procurement: A "Large Lot Last" Policy
  20. Status, Inequality and Intertemporal Choice
  21. Designing the Efficient Information-Processing Organization
  22. Ensuring Quality Provision through Capacity Regulation under Price Competition
  23. Successive Oligopolies and Decreasing Returns
  24. Advice by an Informed Intermediary: Can You Trust Your Broker?
  25. Advances Article
  26. Non-Bayesian Learning
  27. Markets versus Negotiations: The Predominance of Centralized Markets
  28. Crime Reporting: Profiling and Neighbourhood Observation
  29. Endogenous Two-Sided Markets with Repeated Transactions
  30. Position Auctions with Budgets: Existence and Uniqueness
  31. Walrasian Equilibrium and Reputation under Imperfect Public Monitoring
  32. Price Regulation under Demand Uncertainty
  33. Linear Demand Systems are Inconsistent with Discrete Choice
  34. Contributions Article
  35. Relative Extinction of Heterogeneous Agents
  36. Profit-Maximizing Sale of a Discrete Public Good via the Subscription Game in Private-Information Environments
  37. Kinked-Demand Equilibria and Weak Duopoly in the Hotelling Model of Horizontal Differentiation
  38. The Role of Replication-Invariance: Two Answers Concerning the Problem of Fair Division When Preferences Are Single-Peaked
  39. Collusive Behavior of Bidders in English Auctions: A Cooperative Game Theoretic Analysis
  40. Bad Government Can Be Good Politics: Political Reputation, Negative Campaigning, and Strategic Shirking
  41. Equilibrium Social Hierarchies: A Non-Cooperative Ordinal Status Game
  42. Bertrand Competition in Markets with Fixed Costs
  43. Regular Infinite Economies
  44. Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note
  45. Quantifying the Cost of Risk in Consumption
  46. On a Class of Contest Success Functions
  47. Revealed Preference with Stochastic Demand Correspondence
  48. Contracting for Dynamic Efficiency
  49. Existence Advertising, Price Competition and Asymmetric Market Structure
  50. Global Social Interactions with Sequential Binary Decisions: The Case of Marriage, Divorce, and Stigma
  51. First-Mover Advantage in a Dynamic Duopoly with Spillover
  52. Costly Renegotiation in Repeated Bertrand Games
  53. Policy and Perspective
  54. Antitrust Evaluation of Horizontal Mergers: An Economic Alternative to Market Definition
  55. Understanding UPP
  56. Upward Pricing Pressure in Horizontal Merger Analysis: Reply to Epstein and Rubinfeld
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