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