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README.md

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Nash equilibria in binary strategies
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====================================
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Abstract
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--------
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We propose a novel method to find Nash equilibria in games with binary decision variables
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by including compensation payments and incentive-compatibility constraints from non-cooperative game theory
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directly into an optimization framework in lieu of using first order conditions of a linearization,
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or relaxation of integrality conditions.
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The reformulation offers a new approach to obtain and interpret dual variables to binary constraints
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using the benefit or loss from deviation rather than marginal relaxations.
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The method endogenizes the trade-off between overall (societal) efficiency
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and compensation payments necessary to align incentives of individual players.
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The manuscript with the theoretical background of dual variables in integer programs
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and the mathematical explanation of our method is published
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in the [European Journal of Operational Research](https://doi.org/10.1016/j.ejor.2017.09.032).
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Preprints and working versions can be downloaded
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from [arXiv](http://arxiv.org/abs/1504.05894)
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and [OptimizationOnline](http://www.optimization-online.org/DB_HTML/2015/04/4874.html).
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Content
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-------
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This repository contains the GAMS codes for the numerical results for the electricity market example
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presented in Chapter 4 and the Appendix of the manuscript (including all data),
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as well as an additional illustrative example of a natural gas investment and operation game.
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- ``MOPBQE_power_market_example``:
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A stylized electricity network with 6 nodes, 9 generations and 2 time periods
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to illustrate the binary equilibrium method. The results are presented in Chapter 4 of the manuscript. <br />
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Data modified from Example 5.1 in
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Steven Gabriel, Antonio Conejo, Carlos Ruiz & Sauleh Siddiqui.
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"Solving discretely-constrained, Mixed Complementarity Problems with Applications in Energy",
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*Computers & Operations Research*, 40(5):1339-1350, 2013.
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[DOI: 10.1016/j.cor.2012.10.017](http://dx.doi.org/10.1016/j.cor.2012.10.017).
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- ``MOPBQE_power_market_numerical_tests``:
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A large-scale electricity network dataset for the numerical tests
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presented in the Appendix of the manuscript. <br />
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Data based on:
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H. Pandzic, Y. Dvorkin, T. Qiu, Y. Wang, and D. Kirschen.
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Unit Commitment under Uncertainty - GAMS Models
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Library of the Renewable Energy Analysis Lab (REAL)
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University of Washington, Seattle, USA.
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http://www.ee.washington.edu/research/real/gams_code.html.
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- ``MOPBQE_resource_market_example``:
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A stylized natural gas investment and operation game to illustrate the versatility
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of the binary-equilibrium approach and its applicability to problems
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beyond the electricity sector.
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Bibliography info
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-----------------
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*Please cite as:* <br />
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Daniel Huppmann and Sauleh Siddiqui.
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"An exact solution method for binary equilibrium problems with compensation and the power market uplift problem",
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*European Journal of Operational Research*, 2017,
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[DOI: 10.1016/j.ejor.2017.09.032](https://doi.org/10.1016/j.ejor.2017.09.032).
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Classification
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--------------
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### Keywords
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binary Nash game, non-cooperative equilibrium, multi-objective optimisation,
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compensation, incentive compatibility, electricity market, power market, uplift payments
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### Journal of Economic Literature Classification [JEL Codes](https://www.aeaweb.org/econlit/jelCodes.php?view=jel)
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C72, C61, L13, L94
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### Mathematics Subject Classification [MSC](https://cran.r-project.org/web/classifications/MSC.html)
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90C11, 90C46, 91B26
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Authors and Contributors
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------------------------
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This method and the codes were developed by @danielhuppmann and @ssaul3h.
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License
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-------
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This work is licensed under a [Creative Commons Attribution 4.0 International License](http://creativecommons.org/licenses/by/4.0/)

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