|
| 1 | +Nash equilibria in binary strategies |
| 2 | +==================================== |
| 3 | + |
| 4 | +Abstract |
| 5 | +-------- |
| 6 | +We propose a novel method to find Nash equilibria in games with binary decision variables |
| 7 | +by including compensation payments and incentive-compatibility constraints from non-cooperative game theory |
| 8 | +directly into an optimization framework in lieu of using first order conditions of a linearization, |
| 9 | +or relaxation of integrality conditions. |
| 10 | + |
| 11 | +The reformulation offers a new approach to obtain and interpret dual variables to binary constraints |
| 12 | +using the benefit or loss from deviation rather than marginal relaxations. |
| 13 | +The method endogenizes the trade-off between overall (societal) efficiency |
| 14 | +and compensation payments necessary to align incentives of individual players. |
| 15 | + |
| 16 | +The manuscript with the theoretical background of dual variables in integer programs |
| 17 | +and the mathematical explanation of our method is published |
| 18 | +in the [European Journal of Operational Research](https://doi.org/10.1016/j.ejor.2017.09.032). |
| 19 | +Preprints and working versions can be downloaded |
| 20 | +from [arXiv](http://arxiv.org/abs/1504.05894) |
| 21 | +and [OptimizationOnline](http://www.optimization-online.org/DB_HTML/2015/04/4874.html). |
| 22 | + |
| 23 | +Content |
| 24 | +------- |
| 25 | +This repository contains the GAMS codes for the numerical results for the electricity market example |
| 26 | +presented in Chapter 4 and the Appendix of the manuscript (including all data), |
| 27 | +as well as an additional illustrative example of a natural gas investment and operation game. |
| 28 | + |
| 29 | +- ``MOPBQE_power_market_example``: |
| 30 | + A stylized electricity network with 6 nodes, 9 generations and 2 time periods |
| 31 | + to illustrate the binary equilibrium method. The results are presented in Chapter 4 of the manuscript. <br /> |
| 32 | + Data modified from Example 5.1 in |
| 33 | + Steven Gabriel, Antonio Conejo, Carlos Ruiz & Sauleh Siddiqui. |
| 34 | + "Solving discretely-constrained, Mixed Complementarity Problems with Applications in Energy", |
| 35 | + *Computers & Operations Research*, 40(5):1339-1350, 2013. |
| 36 | + [DOI: 10.1016/j.cor.2012.10.017](http://dx.doi.org/10.1016/j.cor.2012.10.017). |
| 37 | + |
| 38 | +- ``MOPBQE_power_market_numerical_tests``: |
| 39 | + A large-scale electricity network dataset for the numerical tests |
| 40 | + presented in the Appendix of the manuscript. <br /> |
| 41 | + Data based on: |
| 42 | + H. Pandzic, Y. Dvorkin, T. Qiu, Y. Wang, and D. Kirschen. |
| 43 | + Unit Commitment under Uncertainty - GAMS Models |
| 44 | + Library of the Renewable Energy Analysis Lab (REAL) |
| 45 | + University of Washington, Seattle, USA. |
| 46 | + http://www.ee.washington.edu/research/real/gams_code.html. |
| 47 | + |
| 48 | + - ``MOPBQE_resource_market_example``: |
| 49 | + A stylized natural gas investment and operation game to illustrate the versatility |
| 50 | + of the binary-equilibrium approach and its applicability to problems |
| 51 | + beyond the electricity sector. |
| 52 | + |
| 53 | +Bibliography info |
| 54 | +----------------- |
| 55 | +*Please cite as:* <br /> |
| 56 | +Daniel Huppmann and Sauleh Siddiqui. |
| 57 | +"An exact solution method for binary equilibrium problems with compensation and the power market uplift problem", |
| 58 | +*European Journal of Operational Research*, 2017, |
| 59 | +[DOI: 10.1016/j.ejor.2017.09.032](https://doi.org/10.1016/j.ejor.2017.09.032). |
| 60 | + |
| 61 | +Classification |
| 62 | +-------------- |
| 63 | +### Keywords |
| 64 | +binary Nash game, non-cooperative equilibrium, multi-objective optimisation, |
| 65 | +compensation, incentive compatibility, electricity market, power market, uplift payments |
| 66 | + |
| 67 | +### Journal of Economic Literature Classification [JEL Codes](https://www.aeaweb.org/econlit/jelCodes.php?view=jel) |
| 68 | +C72, C61, L13, L94 |
| 69 | + |
| 70 | +### Mathematics Subject Classification [MSC](https://cran.r-project.org/web/classifications/MSC.html) |
| 71 | +90C11, 90C46, 91B26 |
| 72 | + |
| 73 | +Authors and Contributors |
| 74 | +------------------------ |
| 75 | +This method and the codes were developed by @danielhuppmann and @ssaul3h. |
| 76 | + |
| 77 | +License |
| 78 | +------- |
| 79 | +This work is licensed under a [Creative Commons Attribution 4.0 International License](http://creativecommons.org/licenses/by/4.0/) |
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