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An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

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  • Huppmann, Daniel
  • Siddiqui, Sauleh

Abstract

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first-order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program.

Suggested Citation

  • Huppmann, Daniel & Siddiqui, Sauleh, 2018. "An exact solution method for binary equilibrium problems with compensation and the power market uplift problem," European Journal of Operational Research, Elsevier, vol. 266(2), pages 622-638.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:622-638
    DOI: 10.1016/j.ejor.2017.09.032
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    More about this item

    Keywords

    Binary Nash game; Non-cooperative equilibrium; Incentive compatibility; Electricity market; Uplift payments;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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