Finite Mixed Extension of Dyadic Games and their Fair Solutions

[1] K. Leyton-Brown and Y. Shoham, Essentials of Game Theory: A Concise, Multidisciplinary Introduction. Morgan & Claypool Publishers, 2008. https://doi.org/10.2200/S00108ED1V01Y200802AIM003 Search in Google Scholar

[2] R. B. Myerson, Game Theory: Analysis of Conflict. Harvard University Press, 1997. Search in Google Scholar

[3] V. V. Romanuke, “Pure strategies Pareto efficient situations versus pure strategies Nash equilibrium situations by their stochastically constrained payoffs in dyadic game modeling of resources rational usage with alternative choice of action,” Herald of Khmelnytskyi national university. Technical sciences, no. 6, pp. 140–143, 2014. Search in Google Scholar

[4] T. C. Schelling, The Strategy of Conflict. Harvard University, 1980. Search in Google Scholar

[5] J. Sostrin, The Manager’s Dilemma: Balancing the Inverse Equation of Increasing Demands and Shrinking Resources. New York, Palgrave Macmillan, 2015. https://doi.org/10.1057/9781137485809 Search in Google Scholar

[6] M. A. Ramírez, M. Smerlak, A. Traulsen, and J. Jost, “Diversity enables the jump towards cooperation for the Traveler’s Dilemma,” Scientific Reports, vol. 13, Jan. 2023, Art. no. 1441. https://doi.org/10.1038/s41598-023-28600-5 Search in Google Scholar

[7] D. Redhead, M. Gervais, K. Kajokaite, J. Koster, A. H. Manyoma, D. H. Manyoma, R. McElreath, and C. T. Ross, “Evidence of direct and indirect reciprocity in network-structured economic games,” Communications Psychology, vol. 2, May 2024, Art. no. 44. https://doi.org/10.1038/s44271-024-00098-1 Search in Google Scholar

[8] R. Xue and L. Xiong, “Two-stage evolutionary game model on complex networks for emergency logistics based on blockchain platform,” Expert Systems with Applications, vol. 256, Dec. 2024, Art. no. 124925. https://doi.org/10.1016/j.eswa.2024.124925 Search in Google Scholar

[9] Y. Zhang and H. Zhao, “A multi-agent model for decision making on environmental regulation in urban agglomeration,” The Journal of Supercomputing, vol. 78, pp. 5588–5609, Mar. 2022. https://doi.org/10.1007/s11227-021-04094-8 Search in Google Scholar

[10] V. V. Romanuke, “Ecological-economic balance in fining environmental pollution subjects by a dyadic 3-person game model,” Applied Ecology and Environmental Research, vol. 17, no. 2, pp. 1451–1474, 2019. https://doi.org/10.15666/aeer/1702_14511474 Search in Google Scholar

[11] R. Christmann, “Plea bargaining and investigation effort: inquisitorial criminal procedure as a three-player game,” European Journal of Law and Economics, vol. 56, pp. 497–532, Oct. 2023. https://doi.org/10.1007/s10657-023-09782-9 Search in Google Scholar

[12] A. Bharadwaj, V. H. Devaiah, and I. Gupta, “Comparative analysis of policy developments,” in: Locating Legal Certainty in Patent Licensing. Singapore, Springer, 2023, pp. 1–50. https://doi.org/10.1007/978-981-15-0181-4_1 Search in Google Scholar

[13] U. Weiss and J. Agassi, “Game Theory and Social Science,” in Games to Play and Games not to Play. Studies in Systems, Decision and Control, vol. 469. Cham, Springer, pp. 61–83, May 2023. https://doi.org/10.1007/978-3-031-27601-9_5 Search in Google Scholar

[14] G. J. Mailath and L. Samuelson, Repeated Games and Reputations: Long-Run Relationships. Oxford University Press, 2006. https://doi.org/10.1093/acprof:oso/9780195300796.001.0001 Search in Google Scholar

[15] V. V. Romanuke, “Environment guard model as dyadic three-person game with the generalized fine for the reservoir pollution,” Ecological Safety and Nature Management, vol. 6, pp. 77–94, 2010. Search in Google Scholar

[16] J. F. Mignot, “Strategic behavior in road cycling competitions,” in The Economics of Professional Road Cycling. Sports Economics, Management and Policy, D. Van Reeth, Ed., vol. 19. Cham, Springer, 2022, pp. 227–251. https://doi.org/10.1007/978-3-031-11258-4_10 Search in Google Scholar

[17] S. Phani Praveen, M. H. Ali, M. A., Jarwar, C. Prakash, C. Ravi Kishore Reddy, L. Malliga, and C. Chandru Vignesh, “6G assisted federated learning for continuous monitoring in wireless sensor network using game theory,” Wireless Networks, vol. 30, pp. 5211–5237, Feb. 2024. https://doi.org/10.1007/s11276-023-03249-0 Search in Google Scholar

[18] D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA, MIT Press, 1991. Search in Google Scholar

[19] V. V. Romanuke, “Refinement of acyclic-and-asymmetric payoff aggregates of pure strategy efficient Nash equilibria in finite noncooperative games by maximultimin and superoptimality,” Decision Making: Applications in Management and Engineering, vol. 4, no. 2, pp. 178–199, Dec. 2021. https://doi.org/10.31181/dmame210402178r Search in Google Scholar

[20] P. Prokopovych and N. C. Yannelis, “On the existence of mixed strategy Nash equilibria,” Journal of Mathematical Economics, vol. 52, pp. 87–97, May 2014. https://doi.org/10.1016/j.jmateco.2014.04.002 Search in Google Scholar

[21] V. V. Romanuke, “Adaptive finite approximation of continuous noncooperative games,” Journal of Automation and Information Sciences, vol. 52, no. 10, pp. 31–41, 2020. https://doi.org/10.1615/JAutomatInfScien.v52.i10.20 Search in Google Scholar

[22] C. E. Lemke and J. T. Howson, “Equilibrium points of bimatrix games,” SIAM Journal on Applied Mathematics, vol. 12, no. 2, pp. 413–423, 1964. https://doi.org/10.1137/0112033 Search in Google Scholar

[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, no. 17, pp. 1599–1606, Apr. 2009. https://doi.org/10.1016/j.tcs.2008.12.033 Search in Google Scholar

[24] P. Bernhard and J. Shinar, “On finite approximation of a game solution with mixed strategies,” Applied Mathematics Letters, vol. 3, no. 1, pp. 1–4, 1990. https://doi.org/10.1016/0893-9659(90)90054-F Search in Google Scholar

[25] V. V. Romanuke, “Convergence and estimation of the process of computer implementation of the optimality principle in matrix games with apparent play horizon,” Journal of Automation and Information Sciences, vol. 45, no. 10, pp. 49–56, 2013. https://doi.org/10.1615/JAutomatInfScien.v45.i10.70 Search in Google Scholar

[26] S. Yilmaz and S. Sen, “Chapter 2 – Metaheuristic approaches for solving multiobjective optimization problems,” in Comprehensive Metaheuristics, S. Mirjalili and A. H. Gandomi, Eds. Academic Press, 2023, pp. 21–48. https://doi.org/10.1016/B978-0-323-91781-0.00002-8 Search in Google Scholar

[27] H. Huang and Z. Hao, “Chapter 4 – Application of multiobjective optimization intelligence algorithms,” in Intelligent Algorithms, H. Huang and Z. Hao, Eds. Elsevier, 2024, pp. 143–195. https://doi.org/10.1016/B978-0-443-21758-6.00004-8 Search in Google Scholar