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A Complementarity Framework for Forward Contracting Under Uncertainty

Author

Listed:
  • Uday V. Shanbhag

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Gerd Infanger

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Peter W. Glynn

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

We consider a particular instance of a stochastic multi-leader multi-follower equilibrium problem in which players compete in the forward and spot markets in successive periods. Proving the existence of such equilibria has proved difficult, as has the construction of globally convergent algorithms for obtaining such points. By conjecturing a relationship between forward and spot decisions, we consider a variant of the original game and relate the equilibria of this game to a related simultaneous stochastic Nash game where forward and spot decisions are made simultaneously. We characterize the complementarity problem corresponding to the simultaneous Nash game and prove that it is indeed solvable. Moreover, we show that an equilibrium to this Nash game is a local Nash equilibrium of the conjectured variant of the multi-leader multi-follower game of interest. Numerical tests reveal that the difference between equilibrium profits between the original and constrained games are small. Under uncertainty, the equilibrium point of interest is obtainable as the solution to a stochastic mixed-complementarity problem. Based on matrix-splitting methods, a globally convergent decomposition method is suggested for such a class of problems. Computational tests show that the effort grows linearly with the number of scenarios. Further tests show that the method can address larger networks as well. Finally, some policy-based insights are drawn from utilizing the framework to model a two-settlement six-node electricity market.

Suggested Citation

  • Uday V. Shanbhag & Gerd Infanger & Peter W. Glynn, 2011. "A Complementarity Framework for Forward Contracting Under Uncertainty," Operations Research, INFORMS, vol. 59(4), pages 810-834, August.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:4:p:810-834
    DOI: 10.1287/opre.1110.0947
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    References listed on IDEAS

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    Cited by:

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    2. Lorenczik, Stefan & Malischek, Raimund & Trüby, Johannes, 2017. "Modeling strategic investment decisions in spatial markets," European Journal of Operational Research, Elsevier, vol. 256(2), pages 605-618.
    3. Chun, So Yeon & Kleywegt, Anton J & Shapiro, Alexander, 2011. "Revenue management in resource exchange seller alliances," MPRA Paper 34657, University Library of Munich, Germany.
    4. So Yeon Chun & Anton J. Kleywegt & Alexander Shapiro, 2017. "When Friends Become Competitors: The Design of Resource Exchange Alliances," Management Science, INFORMS, vol. 63(7), pages 2127-2145, July.
    5. Jinlong Lei & Uday V. Shanbhag & Jong-Shi Pang & Suvrajeet Sen, 2020. "On Synchronous, Asynchronous, and Randomized Best-Response Schemes for Stochastic Nash Games," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 157-190, February.
    6. Bakker, Craig & Zaitchik, Benjamin F. & Siddiqui, Sauleh & Hobbs, Benjamin F. & Broaddus, Elena & Neff, Roni A. & Haskett, Jonathan & Parker, Cindy L., 2018. "Shocks, seasonality, and disaggregation: Modelling food security through the integration of agricultural, transportation, and economic systems," Agricultural Systems, Elsevier, vol. 164(C), pages 165-184.
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    8. Heikki Peura & Derek W. Bunn, 2021. "Renewable Power and Electricity Prices: The Impact of Forward Markets," Management Science, INFORMS, vol. 67(8), pages 4772-4788, August.
    9. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.

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