[en] We introduce in this paper a new approach for efficiently identifying Nash equilibria for games composed of large numbers of players having discrete and not too large strategy spaces. The approach is based on a characterization of Nash equilibria in terms of minima of a function and relies on stochastic optimization algorithms to find these minima. The approach is applied to compute Nash equilibria of some electricity markets and, based on the simulation results, its performances are discussed.
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
E.H.L. Aarts and J.H.M. Korst. Simulated Annealing and Boltzmann Machines. John Wiley & Sons, 1989.
B. Adenso-Diaz and Manuel Laguna. Fine-tuning of algorithms using fractional experimental design and local search. Operation Research, 54(1):99-114, 2006.
C.A. Berry, B.F. Hobbs, W.A. Meroney, and R.P. O'Neill. Understanding how market power can arise in network competition: a game theoretic approach. Utility Policy, 8(3):139-158, September 1999.
M. Blesa and F. Xhafa. Using parallelism in experimenting and fine tuning of parameters for metaheuristics. In Computational science - ICCS 2004, volume 3036 of Lecture Notes in Computer Science, pages 429-432. Springer Berlin / Heidelberg, 2004.
D. Chattopadhyay. Multicommodity spatial sournot model for generator bidding analysis. IEEE Transactions on Power Systems, 19(1):267-275, February 2004.
M. Coli, G. Gennuso, and P. Palazzari. A New Crossover Operator for Genetic Algorithms. Proceeding of the IEEE International Conference on Evolutonary Computation ICEC 96, pages 201-206, May 1996.
J. Contreras, M. Klusch, and J. B. Krawczyk. Numerical solutions to Nash Cournot equilibria in coupled constraint electricity markets. IEEE Transactions on Power Systems, 19(1):195-206, February 2004.
Pedro F. Correia, Thomas J. Overbye, and Ian A. Hiskens. Searching for noncooperative equilibria in centralized electricity markets. IEEE Transactions on Power Systems, 18(4):1417-1424, November 2003.
Lance B. Cunningham, Ross Baldick, and Martin L. Baughman. An empirical study of applied game theory : transmission constrained Cournot behavior. IEEE Transactions on Power Systems, 17(1):166-172, February 2002.
M. Dorigo, V. Maniezzo, and A. Colorni. The ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics - Part B, 26(1):26-41, 1996.
F. Glover. Tabu search - part ii. ORSA Journal on Computing, 2:4-32, 1990.
D.E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989.
R. Green and D. M. Newbery. Competition in the British electricity spot market. Journal of Political Economy, 100(5):929-953, October 1992.
J. H. Holland. Adaptation in Natural and Artificial Systems. MIT Press, Cambridge, MA, USA, 1992.
Kwang-Ho Lee and Ross Baldick. Solving three - player games by the matrix approach with application to an electric power market. IEEE Transactions on Power Systems, 18(4):1573-1580, Nov. 2003.
Kwang-Ho Lee and Ross Baldick. Tuning of discretization in bimatrix game approach to power pystem market analysis. IEEE Transactions on Power Systems, 18(2):830-836, May 2003.
R.D. McKelvey and A. McLennan. Handbook of computational economics, volume 1, chapter Computation of equilibria in finite games, pages 87-142. North-Holland, 1996.
A. Minoia, D. Ernst, M. Dicorato, M. Trovato, and M. Ilic. Reference transmission network: a game theory approach. IEEE Transactions on Power Systems, 21:249-259, February 2006.
L. Shi and S. Olafsson. Nested partitioning for global optimization. Operations Research, 48(3):390-407, 2000.
You Seok Son and Ross Baldick. Hybrid coevolutionary programming for Nash equilibrium search in games with local optima. IEEE Transactions on Evolutionary Computation, 8(4):305-315, August 2004.
W. Xian, L. Yuzeng, and Z. Shaohua. Oligopolistic equilibrium analysis for electricity markets: a nonlinear complementarity approach. IEEE Transactions on Power Systems, 19(3):1348-1355, August 2004.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
