Table of Contents
Game Theory
Volume 2013, Article ID 290427, 5 pages
http://dx.doi.org/10.1155/2013/290427
Research Article

A Necessary Condition for Nash Equilibrium in Two-Person Zero-Sum Constrained Stochastic Games

Department of Computer Science and Engineering, Sogang University, Seoul 121-742, Republic of Korea

Received 15 September 2013; Accepted 19 November 2013

Academic Editor: Peijun Guo

Copyright © 2013 Hyeong Soo Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Altman and A. Shwartz, “Constrained Markov games: Nash equilibria,” in Annals of the International Society of Dynamic Games, V. Gaitsgory, J. Filar, and K. Mizukami, Eds., vol. 5, pp. 303–323, Birkhäauser, Boston, Mass, USA, 2000. View at Google Scholar
  2. J. Alvarez-Mena and O. Hernández-Lerma, “Existence of nash equilibria for constrained stochastic games,” Mathematical Methods of Operations Research, vol. 63, no. 2, pp. 261–285, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. E. Altman, K. Avrachenkov, R. Marquez, and G. Miller, “Zero-sum constrained stochastic games with independent state processes,” Mathematical Methods of Operations Research, vol. 62, no. 3, pp. 375–386, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. E. Altman, K. Avrachenkov, N. Bonneau, M. Debbah, R. El-Azouzi, and D. S. Menasche, “Constrained cost-coupled stochastic games with independent state processes,” Operations Research Letters, vol. 36, no. 2, pp. 160–164, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. N. Shimkin, “Stochastic games with average cost constraints,” in Annals of the International Society of Dynamic Games, T. Basar and A. Haurie, Eds., vol. 1 of Advances in Dynamic Games and Applications, Birkhäauser, Boston, Mass, USA, 1994. View at Google Scholar
  6. J. Filar and K. Vrieze, Competitive Markov Decision Processes, Springer, New York, NY, USA, 1996.
  7. C. Alós-Ferrer and A. B. Ania, “Local equilibria in economic games,” Economics Letters, vol. 70, no. 2, pp. 165–173, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. D. S. Hochbaum, “Approximating clique and biclique problems,” Journal of Algorithms, vol. 29, no. 1, pp. 174–200, 1998. View at Google Scholar · View at Scopus
  9. M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, John Wiley & Sons, New York, NY, USA, 1994.