Evaluation of Payoff Matrices for Non-Cooperative Games via Processing Binary Expert Estimations

Open access


A problem of evaluating the non-cooperative game model is considered in the paper. The evaluation is understood in the sense of obtaining the game payoff matrices whose entries are single-point values. Experts participating in the estimation procedure make their judgments on all the game situations for every player. A form of expert estimations is suggested. The form is of binary type, wherein the expert’s judgment is either 1 or 0. This type is the easiest to be implemented in social networks. For most social networks, 1 can be a “like” (the currently evaluated situation is advantageous), and 0 is a “dislike” (disadvantageous). A method of processing expert estimations is substantiated. Two requirements are provided for obtaining disambiguous payoff averages along with the clustered payoff matrices.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] M. J. Osborne An introduction to game theory Oxford UK: Oxford University Press 2003.

  • [2] N. Nisan T. Roughgarden É. Tardos and V. V. Vazirani Algorithmic Game Theory Cambridge UK: Cambridge University Press 2007. https://doi.org/10.1017/CBO9780511800481

  • [3] J. Moon and T. Başar “Minimax estimation with intermittent observations” Automatica vol. 62 2015 pp. 122-133. https://doi.org/10.1016/j.automatica.2015.09.004

  • [4] C. Dong G. H. Huang Y. P. Cai and Y. Xu “An interval-parameter minimax regret programming approach for power management systems planning under uncertainty” Applied Energy vol. 88 iss. 8 pp. 2835-2845 2011. https://doi.org/10.1016/j.apenergy.2011.01.056

  • [5] V. V. Romanuke “Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game” Journal of Information and Organizational Sciences vol. 38 no. 2 pp. 125-143 2014.

  • [6] R. R. Dias and M. Scheepers “Selective games on binary relations” Topology and its Applications vol. 192 pp. 58-83 2015. https://doi.org/10.1016/j.topol.2015.05.071

  • [7] V. Knoblauch “A simple voting scheme generates all binary relations on finite sets” Journal of Mathematical Economics vol. 49 iss. 3 pp. 230-233 2013. https://doi.org/10.1016/j.jmateco.2013.01.002

  • [8] H. Ichihashi and I. B. Türksen “A neuro-fuzzy approach to data analysis of pairwise comparisons” International Journal of Approximate Reasoning vol. 9 iss. 3 pp. 227-248 1993. https://doi.org/10.1016/0888-613X(93)90011-2

  • [9] J. Ramík and P. Korviny “Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean” Fuzzy Sets and Systems vol. 161 iss. 11 pp. 1604-1613 2010. https://doi.org/10.1016/j.fss.2009.10.011

  • [10] E. Abbasi M. Ebrahim Shiri and M. Ghatee “Root-quatric mixture of experts for complex classification problems” Expert Systems with Applications vol. 53 pp. 192-203 2016. https://doi.org/10.1016/j.eswa.2016.01.040

  • [11] S. R. Kheradpisheh F. Sharifizadeh A. Nowzari-Dalini M. Ganjtabesh and R. Ebrahimpour “Mixture of feature specified experts” Information Fusion vol. 20 pp. 242-251 2014. https://doi.org/10.1016/j.inffus.2014.02.006

  • [12] I. Reychav M. Ndicu and D. Wu “Leveraging social networks in the adoption of mobile technologies for collaboration” Computers in Human Behavior vol. 58 pp. 443-453 2016. https://doi.org/10.1016/j.chb.2016.01.011

  • [13] T Kitagawa and C. Muris “Model averaging in semiparametric estimation of treatment effects” Journal of Econometrics vol. 193 iss. 1 pp. 271-289 2016. https://doi.org/10.1016/j.jeconom.2016.03.002

  • [14] X. Zeng J. Wu D. Wang X. Zhu and Y. Long “Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method” Journal of Hydrology vol. 538 pp. 689-704 2016. https://doi.org/10.1016/j.jhydrol.2016.04.038

  • [15] N. Betzler M. R. Fellows J. Guo R. Niedermeier and F. A. Rosamond “Fixed-parameter algorithms for Kemeny rankings” Theoretical Computer Science vol. 410 iss. 45 pp. 4554-4570 2009. https://doi.org/10.1016/j.tcs.2009.08.033

  • [16] V. V. Romanuke “Fast Kemeny consensus by searching over standard matrices distanced to the averaged expert ranking by minimal difference” Research Bulletin of NTUU “Kyiv Polytechnic Institute” no. 1 pp. 58-65 2016.

  • [17] F. Chiclana J. M. Tapia García M. J. del Moral and E. Herrera- Viedma “Analyzing consensus measures in group decision making” Procedia Computer Science vol. 55 pp. 1000-1008 2015. https://doi.org/10.1016/j.procs.2015.07.103

  • [18] A. Peiravi and H. T. Kheibari “A fast algorithm for connectivity graph approximation using modified Manhattan distance in dynamic networks” Applied Mathematics and Computation vol. 201 iss. 1-2 pp. 319-332 2008. https://doi.org/10.1016/j.amc.2007.12.026

  • [19] N. N. Vorobyov Game theory fundamentals. Noncooperative games. Moscow: Nauka 1984 (in Russian).

  • [20] D. J. Nott L. Marshall M. Fielding and S.-Y. Liong “Mixtures of experts for understanding model discrepancy in dynamic computer models” Computational Statistics & Data Analysis vol. 71 pp. 491-505 2014. https://doi.org/10.1016/j.csda.2013.04.020

  • [21] H. Valizadegan Q. Nguyen and M. Hauskrecht “Learning classification models from multiple experts” Journal of Biomedical Informatics vol. 46 iss. 6 pp. 1125-1135 2013. https://doi.org/10.1016/j.jbi.2013.08.007

  • [22] I. Palomares and L. Martínez “Low-dimensional visualization of experts’ preferences in urgent group decision making under uncertainty” Procedia Computer Science vol. 29 pp. 2090-2101 2014. https://doi.org/10.1016/j.procs.2014.05.193

  • [23] V. V. Romanuke “Finite approximation of unit-hypercubic infinite noncooperative game via dimension-dependent irregular samplings and reshaping the player’s payoffs into line array for simplification and speedup” Herald of Zaporizhzhya National University no. 2 pp. 201-221 2015.

  • [24] V. V. Romanuke “Uniform sampling of fundamental simplexes as sets of players’ mixed strategies in the finite noncooperative game for finding equilibrium situations with possible concessions” Journal of Automation and Information Sciences vol. 47 iss. 9 pp. 76-85 2015. https://doi.org/10.1615/JAutomatInfScien.v47.i9.70

  • [25] T. Nakata “Weak laws of large numbers for weighted independent random variables with infinite mean” Statistics & Probability Letters vol. 109 pp. 124-129 2016. https://doi.org/10.1016/j.spl.2015.11.017

  • [26] M. A. Kouritzin and Y.-X. Ren “A strong law of large numbers for super-stable processes” Stochastic Processes and their Applications vol. 124 iss. 1 pp. 505-521 2014. https://doi.org/10.1016/j.spa.2013.08.009

Journal information
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 164 63 2
PDF Downloads 94 32 1