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Stability kernel in finite games with perturbed payoffs

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The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.
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Bibliogr. 21 poz.
  • Belarusian State University, Faculty of Mechanics and Mathematics, Nezavisimosti 4, 220030 Minsk, Belarus
  • University of Turku, Department of Mathematics and Statistics, 20014 Turku, Finland
  • Aubin J-P. and Frankowska H. (1990) Set-valued Analysis. Birkhaüser, Basel.
  • Bukhtoyarov, S. and Emelichev, V. (2006) Measure of stability for a finite cooperative game with a parametric optimality principle (from Pareto to Nash). Comput. Math. and Math. Phys., 46, 7, 1193–1199.
  • Emelichev, V., Girlich, E., Nikulin, Yu. and Podkopaev, D. (2002) Stability and regularization of vector problem of integer linear programming. Optimization, 51, 4, 645–676.
  • Emelichev, V. and Karelkina, O. (2021) Postoptimal analysis of a finite cooperative game. Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 1, to appear.
  • Emelichev, V. and Karelkina, O. (2009) Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric. Discrete Mathematics and Applications, 19, 3, 229–236.
  • Emelichev, V., Kotov, V., Kuzmin, K., Lebedeva, N., Semenova, N. and Sergienko, T. (2014) Stability and effective algorithms for solving multiobjective discrete optimization problems with incomplete information. J. of Automation and Inf. Sciences, 46, 2, 27–41.
  • Emelichev, V. and Kuzmin, K. (2006) Stability radius of an efficient solution of a vector problem of integer linear programming in the Hölder metric. Cybernetics and Systems Analysis, 42, 609-614.
  • Emelichev, V. and Nikulin, Yu. (2019) On a quasistability radius for multicriteria integer linear programming problem of finding extremum solutions. Cybernetics and System Analysis. 55, 6, 949–957.
  • Emelichev, V. and Nikulin, Yu. (2020) Finite Games with Perturbed Payoffs. In: N. Olenev, Y. Evtushenko, M. Khachay, V. Malkova, eds., Advances in Optimization and Applications. OPTIMA 2020. Communications in Computer and Information Science, 1340, Springer, Cham 158–185.
  • Hardy, G., Littlewood, J. and Polya, G. (1988) Inequalities. University Press, Cambridge.
  • Lebedeva, T., Semenova, N. and Sergienko, T. (2021) Stability Kernel of a Multicriteria Optimization Problem Under Perturbations of Input Data of the Vector Criterion. Cybernetics and Systems Analysis, 57, 4, 578–583.
  • Miettinen, K. (1999) Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston.
  • Nash, J. (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 1, 48–49.
  • Nash, J. (1951) Non-Cooperative Games. The Annals of Mathematics, 54, 2, 286–295.
  • Nikulin, Yu., Karelkina, O. and M¨akel¨a, M. (2013) On accuracy, robustness and tolerances in vector Boolean optimization. European Journal of Operational Research, 224, 3, 449–457.
  • Noghin, V. (2018) Reduction of the Pareto Set: An Axiomatic Approach. Springer, Cham.
  • Osborne, M. and Rubinstein, A. (1994) A Course in Game Theory. MIT Press.
  • Pareto, V. (1909) Manuel D’Economie Politique. V. Giard & E. Briere, Paris.
  • Sergienko, I. and Shilo, V. (2003) Discrete Optimization Problems. Problems, Methods, Research. Naukova dumka, Kiev.
  • Smale, S. (1974) Global analysis and economics V: Pareto theory with constraints. J. of Mathematical Economics, 1, 3, 213–221.
  • Steuer, R. (1986) Multiple Criteria Optimization: Theory, Computation and Application. John Wiley & Sons, New York.
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