Have a personal or library account? Click to login
Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game Cover

Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game

Applied Computer Systems
Volume 20 (2016): Issue 1 (December 2016)
By: Vadim V. Romanuke and  Vladimir V. Kamburg  
Open Access
|Jan 2017

References

  1. [1] M. J. Osborne, An introduction to game theory. Oxford: Oxford University Press, 2003.
    Search in Google ScholarBack to article
  2. [2] N. N. Vorobyov, Game theory fundamentals. Noncooperative games. Moscow: Nauka, 1984 (in Russian).
    Search in Google ScholarBack to article
  3. [3] J. Bergin, “A characterization of sequential equilibrium strategies in infinitely repeated incomplete information games,” Journal of Economic Theory, vol. 47, iss. 1, pp. 51–65, Feb. 1989. https://doi.org/10.1016/0022-0531(89)90102-610.1016/0022-0531(89)90102-6
    Search in Google ScholarBack to article
  4. [4] B. Chen and S. Takahashi, “A folk theorem for repeated games with unequal discounting,” Games and Economic Behavior, vol. 76, iss. 2, pp. 571–581, Nov. 2012. https://doi.org/10.1016/j.geb.2012.07.01110.1016/j.geb.2012.07.011
    Search in Google ScholarBack to article
  5. [5] V. V. Romanuke, “Method of practicing the optimal mixed strategy with innumerable set in its spectrum by unknown number of plays,” Measuring and Computing Devices in Technological Processes, no. 2, pp. 196–203, 2008.
    Search in Google ScholarBack to article
  6. [6] P. V. Reddy and J. C. Engwerda, “Pareto optimality in infinite horizon linear quadratic differential games,” Automatica, vol. 49, iss. 6, pp. 1705–1714, June 2013. https://doi.org/10.1016/j.automatica.2013.03.00410.1016/j.automatica.2013.03.004
    Search in Google ScholarBack to article
  7. [7] X. Chen and X. Deng, “Recent development in computational complexity characterization of Nash equilibrium,” Computer Science Review, vol. 1, iss. 2, pp. 88–99, Dec. 2007. https://doi.org/10.1016/j.cosrev.2007.09.00210.1016/j.cosrev.2007.09.002
    Search in Google ScholarBack to article
  8. [8] D. Friedman, “On economic applications of evolutionary game theory,” Journal of Evolutionary Economics, vol. 8, iss. 1, pp. 15–43, March 1998. https://doi.org/10.1007/s00191005005410.1007/s001910050054
    Search in Google ScholarBack to article
  9. [9] S. Brusco, “Perfect Bayesian implementation in economic environments,” Journal of Economic Theory, vol. 129, iss. 1, pp. 1–30, July 2006. https://doi.org/10.1016/j.jet.2004.12.00210.1016/j.jet.2004.12.002
    Search in Google ScholarBack to article
  10. [10] R. Calvert, M. D. McCubbins, and B. R. Weingast, “A Theory of Political Control and Agency Discretion,” American Journal of Political Science, vol. 33, iss. 3, pp. 588–611, Aug. 1989. https://doi.org/10.2307/211106410.2307/2111064
    Search in Google ScholarBack to article
  11. [11] H. Xie and Y.-J. Lee, “Social norms and trust among strangers,” Games and Economic Behavior, vol. 76, iss. 2, pp. 548–555, Nov. 2012. https://doi.org/10.1016/j.geb.2012.07.01010.1016/j.geb.2012.07.010
    Search in Google ScholarBack to article
  12. [12] L. Forni, “Social security as Markov equilibrium in OLG models,” Review of Economic Dynamics, vol. 8, iss. 1, pp. 178–194, Jan. 2005. https://doi.org/10.1016/j.red.2004.10.00310.1016/j.red.2004.10.003
    Search in Google ScholarBack to article
  13. [13] R. Zhao, G. Neighbour, J. Han, M. McGuire, and P. Deutz, “Using game theory to describe strategy selection for environmental risk and carbon emissions reduction in the green supply chain,” Journal of Loss Prevention in the Process Industries, vol. 25, iss. 6, pp. 927–936, Nov. 2012. https://doi.org/10.1016/j.jlp.2012.05.00410.1016/j.jlp.2012.05.004
    Search in Google ScholarBack to article
  14. [14] J. Scheffran, “The dynamic interaction between economy and ecology: Cooperation, stability and sustainability for a dynamic-game model of resource conflicts,” Mathematics and Computers in Simulation, vol. 53, iss. 4 – 6, pp. 371–380, Oct. 2000. https://doi.org/10.1016/S0378-4754(00)00229-910.1016/S0378-4754(00)00229-9
    Search in Google ScholarBack to article
  15. [15] M. Braham and F. Steffen, “Voting rules in insolvency law: a simple-game theoretic approach,” International Review of Law and Economics, vol. 22, iss. 4, pp. 421–442, Dec. 2002. https://doi.org/10.1016/S0144-8188(02)00113-810.1016/S0144-8188(02)00113-8
    Search in Google ScholarBack to article
  16. [16] G. Stoltz and G. Lugosi, “Learning correlated equilibria in games with compact sets of strategies,” Games and Economic Behavior, vol. 59, iss. 1, pp. 187–208, Apr. 2007. https://doi.org/10.1016/j.geb.2006.04.00710.1016/j.geb.2006.04.007
    Search in Google ScholarBack to article
  17. [17] E. Bajoori, J. Flesch, and D. Vermeulen, “Perfect equilibrium in games with compact action spaces,” Games and Economic Behavior, vol. 82, pp. 490–502, Nov. 2013. https://doi.org/10.1016/j.geb.2013.08.00210.1016/j.geb.2013.08.002
    Search in Google ScholarBack to article
  18. [18] J. Gabarró, A. García, and M. Serna, “The complexity of game isomorphism,” Theoretical Computer Science, vol. 412, iss. 48, pp. 6675–6695, Nov. 2011. https://doi.org/10.1016/j.tcs.2011.07.02210.1016/j.tcs.2011.07.022
    Search in Google ScholarBack to article
  19. [19] C. E. Lemke and J. T. Howson, “Equilibrium points of bimatrix games,” SIAM Journal on Applied Mathematics, vol. 12, iss. 2, pp. 413–423, 1964. https://doi.org/10.1137/011203310.1137/0112033
    Search in Google ScholarBack to article
  20. [20] N. Nisan, T. Roughgarden, É. Tardos and V. V. Vazirani, eds., Algorithmic Game Theory. Cambridge, UK: Cambridge University Press, 2007. https://doi.org/10.1017/CBO978051180048110.1017/CBO9780511800481
    Search in Google ScholarBack to article
  21. [21] N. N. Vorobyov, “Situations of equilibrium in bimatrix games,” Probability theory and its applications, no. 3, pp. 318–331, 1958 (in Russian).10.1137/1103024
    Search in Google ScholarBack to article
  22. [22] H. W. Kuhn, “An algorithm for equilibrium points in bimatrix games,” Proceedings of the National Academy of Sciences of the United States of America, vol. 47, pp. 1657–1662, 1961. https://doi.org/10.1073/pnas.47.10.165710.1073/pnas.47.10.165722318816590888
    Search in Google ScholarBack to article
  23. [23] S. C. Kontogiannis, P. N. Panagopoulou and P. G. Spirakis, “Polynomial algorithms for approximating Nash equilibria of bimatrix games,” Theoretical Computer Science, vol. 410, iss. 15, pp. 1599–1606, Apr. 2009. https://doi.org/10.1016/j.tcs.2008.12.03310.1016/j.tcs.2008.12.033
    Search in Google ScholarBack to article
  24. [24] P. J. Reny, “On the Existence of Pure and Mixed Strategy Equilibria in Discontinuous Games,” Econometrica, vol. 67, iss. 5, pp. 1029–1056, Sep. 1999. https://doi.org/10.1111/1468-0262.0006910.1111/1468-0262.00069
    Search in Google ScholarBack to article
  25. [25] P. Bernhard and J. Shinar, “On finite approximation of a game solution with mixed strategies,” Applied Mathematics Letters, vol. 3, iss. 1, pp. 1–4, 1990. https://doi.org/10.1016/0893-9659(90)90054-F10.1016/0893-9659(90)90054-F
    Search in Google ScholarBack to article
  26. [26] S. C. Kontogiannis and P. G. Spirakis, “On mutual concavity and strategically-zero-sum bimatrix games,” Theoretical Computer Science, vol. 432, pp. 64–76, May 2012. https://doi.org/10.1016/j.tcs.2012.01.01610.1016/j.tcs.2012.01.016
    Search in Google ScholarBack to article
  27. [27] D. Friedman and D. N. Ostrov, “Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games,” Journal of Economic Theory, vol. 148, iss. 2, pp. 743–777, March 2013. https://doi.org/10.1016/j.jet.2012.07.00410.1016/j.jet.2012.07.004
    Search in Google ScholarBack to article
  28. [28] R. Laraki, A. P. Maitra, and W. D. Sudderth, “Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff,” Dynamic Games and Applications, vol. 3, iss. 2, pp. 162–171, June 2013. https://doi.org/10.1007/s13235-012-0054-710.1007/s13235-012-0054-7
    Search in Google ScholarBack to article
  29. [29] R. Gu, X. Yang, J. Yan, Y. Sun, B. Wang, C. Yuan and Y. Huang, “SHadoop: Improving MapReduce performance by optimizing job execution mechanism in Hadoop clusters,” Journal of Parallel and Distributed Computing, vol. 74, iss. 3, pp. 2166–2179, March 2014. https://doi.org/10.1016/j.jpdc.2013.10.00310.1016/j.jpdc.2013.10.003
    Search in Google ScholarBack to article
  30. [30] H. Moulin, Théorie des jeux pour l’économie et la politique. Paris: Hermann, 1981 (in French).
    Search in Google ScholarBack to article
  31. [31] G. Tian, “Implementation of balanced linear cost share equilibrium solution in Nash and strong Nash equilibria,” Journal of Public Economics, vol. 76, iss. 2, pp. 239–261, May 2000. https://doi.org/10.1016/S0047-2727(99)00041-910.1016/S0047-2727(99)00041-9
    Search in Google ScholarBack to article
  32. [32] S.-C. Suh, “An algorithm for verifying double implementability in Nash and strong Nash equilibria,” Mathematical Social Sciences, vol. 41, iss. 1, pp. 103–110, Jan. 2001. https://doi.org/10.1016/S0165-4896(99)00057-810.1016/S0165-4896(99)00057-8
    Search in Google ScholarBack to article
  33. [33] V. Scalzo, “Pareto efficient Nash equilibria in discontinuous games,” Economics Letters, vol. 107, iss. 3, pp. 364–365, 2010. https://doi.org/10.1016/j.econlet.2010.03.01010.1016/j.econlet.2010.03.010
    Search in Google ScholarBack to article
  34. [34] D. Gąsior and M. Drwal, “Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks,” Computer Networks, vol. 57, iss. 14, pp. 2817–2832, Oct. 2013. https://doi.org/10.1016/j.comnet.2013.06.01210.1016/j.comnet.2013.06.012
    Search in Google ScholarBack to article
  35. [35] E. Kohlberg and J.-F. Mertens, “On the Strategic Stability of Equilibria,” Econometrica, vol. 54, no. 5, pp. 1003–1037, 1986. https://doi.org/10.2307/191232010.2307/1912320
    Search in Google ScholarBack to article
  36. [36] R. Selten, “Reexamination of the perfectness concept for equilibrium points in extensive games,” International Journal of Game Theory, vol. 4, iss. 1, pp. 25–55, March 1975. https://doi.org/10.1007/BF0176640010.1007/BF01766400
    Search in Google ScholarBack to article
  37. [37] E. van Damme, “A relation between perfect equilibria in extensive form games and proper equilibria in normal form games,” International Journal of Game Theory, vol. 13, iss. 1, pp. 1–13, March 1984. https://doi.org/10.1007/BF0176986110.1007/BF01769861
    Search in Google ScholarBack to article
  38. [38] D. Fudenberg and J. Tirole, “Perfect Bayesian equilibrium and sequential equilibrium,” Journal of Economic Theory, vol. 53, iss. 2, pp. 236–260, Apr. 1991. https://doi.org/10.1016/0022-0531(91)90155-W10.1016/0022-0531(91)90155-W
    Search in Google ScholarBack to article
  39. [39] S. Castro and A. Brandão, “Existence of a Markov perfect equilibrium in a third market model,” Economics Letters, vol. 66, iss. 3, pp. 297–301, March 2000. https://doi.org/10.1016/S0165-1765(99)00208-610.1016/S0165-1765(99)00208-6
    Search in Google ScholarBack to article
  40. [40] H. Haller and R. Lagunoff, “Markov Perfect equilibria in repeated asynchronous choice games,” Journal of Mathematical Economics, vol. 46, iss. 6, pp. 1103–1114, Nov. 2010. https://doi.org/10.1016/j.jmateco.2009.09.00310.1016/j.jmateco.2009.09.003
    Search in Google ScholarBack to article
  41. [41] K. Tanaka and K. Yokoyama, “On ε-equilibrium point in a noncooperative n-person game,” Journal of Mathematical Analysis and Applications, vol. 160, iss. 2, pp. 413–423, Sep. 1991. https://doi.org/10.1016/0022-247X(91)90314-P10.1016/0022-247X(91)90314-P
    Search in Google ScholarBack to article
  42. [42] T. Radzik, “Pure-strategy ε-Nash equilibrium in two-person non-zero-sum games,” Games and Economic Behavior, vol. 3, iss. 3, pp. 356–367, Aug. 1991. https://doi.org/10.1016/0899-8256(91)90034-C10.1016/0899-8256(91)90034-C
    Search in Google ScholarBack to article
DOI: https://doi.org/10.1515/acss-2016-0009 | Journal eISSN: 2255-8691 | Journal ISSN: 2255-8683
Journal RSS Feed
Language: English
Page range: 5 - 14
Published on: Jan 23, 2017
Published by: Riga Technical University
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Approximate solution,
equilibrium strategy support,
game isomorphism,
multidimensional matrix,
solution consistency,
two-person non-cooperative games,
unit hypercube
Related subjects:
Computer sciences,
Artificial intelligence,
Information technology,
Project management,
Software development

© 2017 Vadim V. Romanuke, Vladimir V. Kamburg, published by Riga Technical University
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 20 (2016): Issue 1 (December 2016)Next article