359
Views
4
CrossRef citations to date
0
Altmetric
Articles

A survey on potential evolutionary game and its applications

, &
Pages 26-45 | Received 21 Aug 2014, Accepted 11 Nov 2014, Published online: 27 Feb 2015

References

  • Blume, L. E. (1993). The statistical mechanics of strategic interaction. Games and Economic Behavior, 5, 387–424.
  • Cheng, D. (2014). On finite potential game. Automatica, 50, 1793–1801.
  • Cheng, D., He, F., Qi, H., Qi, H., & He, F. (in press). Modeling, analysis and control of networked evolutionary games. Retrieved from http://lsc.amss.ac.cn/dcheng/preprint/NTGAME02.pdf ( IEEE TAC).
  • Cheng, D., & Qi, H. (2007). Semi-tensor product of matrices – theory and applications (2nd ed. 2011). Beijing: Science Press ( in Chinese).
  • Cheng, D., Qi, H., & Li, Z. (2011). Analysis and control of boolean networks – a semi-tensor product approach. London: Springer.
  • Cheng, D., Qi, H., Wang, Y., & Liu, T. (in press). Vector space structure of finite evolutionary games. Retrieved from http://lsc.amss.ac.cn/dcheng/preprint/VSGAME01.pdf ( Submitted for publication).
  • Cheng, D., Qi, H., & Zhao, Y. (2012). An introduction to semi-tensor product of matrices and its applications. Singapore: World Scientific.
  • Fornasini, E., & Valcher, M. E. (2014). Optimal control of boolean control networks. IEEE Transactions on Automatic Control, 59, 1258–1270.
  • Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge, MA: MIT Press.
  • Gale, D., & Shapley, L. S. (1962). Colle admissions and the stability of marriage. American Mathematical Monthly, 69, 9–15.
  • Hart, S., & Mas-Colell, A. (1989). Potential, value, and consistency. Econometrica, 57, 589–614.
  • Heikkinen, T. (2006). A potential game approach to distributed power control and scheduling. Computer Networks, 50, 2295–2311.
  • Jackson, M. O., & Zenou, Y. (2014, January 1). Games on networks. In , P. Young & Zamir, S. (Eds.), Handbook of game theory. Elsevier Science. 2014 July. Retrieved from SSRN http://ssrn.com/abstract=2136179
  • Jiang, L., Perc, M., Wang, W., Lai, Y., & Wang, B. (2011). Impact of link deletions on public cooperation in scale-free networks. Europhysics Letters, 93. Article ID: 40001. Retrieved from http://iopscience.iop.org/0295-5075/93/4/40001
  • Khatri, C. G., & Rao, C. R. (1968). Solutions to some functional equations and their applications to characterization of probability distributions. The Indian Journal of Statistics, Series A, 30, 167–180.
  • Laschov, D., & Margaliot, M. (2013). Minimum-time control of boolean networks. SIAM Journal on Control and Optimization, 51, 2869–2892.
  • Marden, J. R., Arslan, G., & Shamma, J. S. (2009). Cooperative control and potential games. IEEE Transactions on Systems, Man, and Cybernetcs, Part B, 39, 1393–1407.
  • Milchtaich, I. (1996). Congestion games with player-specific payoff functions. Games and Economic Behavior, 13, 111–124.
  • Monderer, D., & Shapley, L. S. (1996a). Fictitious play property for games with identical interests. Journal of Economic Theory, 1, 258–265.
  • Monderer, D., & Shapley, L. S. (1996b). Potential games. Games and Economic Behavior, 14, 124–143.
  • Nash, J. (1951). Non-cooperative game. The Annals of Mathematics, 54, 286–295.
  • Perc, M., Gardeñes, J. G., Szolnoki, A., Floria, L. M., & Moreno, Y. (2013). Evolutionary dynamics of group interactions on structured populations: A review. Journal of the Royal Society Interface, 10, 20120997.
  • Rosenthal, R. W. (1973). A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory, 2, 65–67.
  • Smith, J. M. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.
  • Szolnoki, A., & Perc, M. (2009). Resolving social dilemmas on evolving random networks. Europhysics Letters, 86, 30007.
  • von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton: Princeton University Press.
  • Wang, X., Xiao, N., Wongpiromsarn, T., Xie, L., Frazzoli, E., & Rus, D. (2013). Distributed consensus innoncooperative congestion games: An application to road pricing. In Proceedings of 10th IEEE International Conference on Control and Automation (pp. 1668–1673). Hangzhou, China.
  • Wang, Y., Zhang, C., & Liu, Z. (2012). A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 48, 1227–1236.
  • Yazicioglu, A. Y., Egerstedt, M., & Shamma, J. S. (2013). A game theoretic approach to distributed coverage of graphs by heterogeneous mobile agents. Estimation and Control of Networked Systems, 4, 309–315.
  • Zhao, Y., Kim, J., & Filippone, M. (XXXX). Control of large-Scale Boolean networks via network aggregation. IEEE Transactions on Neural Network and Lineasr Systems (Under revision).
  • Zhao, Y., Kim, J., & Filippone, M. (2013). Aggregation algorithm towards large-scale Boolean network analysis. IEEE Transactions on Automatic Control, 58, 1976–1985.
  • Zhu, M., & Martinez, S. (2013). Distributed coverage games for energy-aware mobile sensor networks. SIAM Journal on Control and Optimization, 51(1), 1–27.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.