Mathematical Programming

, Volume 101, Issue 1, pp 57–94 | Cite as

Spatial oligopolistic equilibria with arbitrage, shared resources, and price function conjectures

  • Benjamin F. Hobbs
  • Jong-Shi PangEmail author


This paper considers equilibria among multiple firms that are competing non-cooperatively against each other to sell electric power and buy resources needed to produce that power. Examples of such resources include fuels, power plant sites, and emissions allowances. The electric power market is a spatial market on a network in which flows are constrained by Kirchhoff’s current and voltage laws. Arbitragers in the power market erase spatial price differences that are non-cost based. Power producers can compete in power markets à la Cournot (game in quantities), or in a generalization of the Cournot game (termed the conjectured supply function game) in which they anticipate that rivals will respond to price changes. In input markets, producers either compete à la Bertrand (price-taking behavior) or they can conjecture that price will increase with consumption of the resource. The simultaneous competition in power and input markets presents opportunities for strategic price behavior that cannot be analyzed using models of power markets alone. Depending on whether the producers treat the arbitrager endogenously or exogenously, we derive two mixed nonlinear complementarity formulations of the oligopolistic problem. We establish the existence and uniqueness of solutions as well as connections among the solutions to the model formulations. A numerical example is provided for illustrative purposes.


Power Market Supply Function Price Function Emission Allowance Spatial Price 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Geography and Environmental EngineeringThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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