Have a personal or library account? Click to login
Stability kernel in finite games with perturbed payoffs Cover

Stability kernel in finite games with perturbed payoffs

Open Access
|Aug 2022

References

  1. Aubin J-P. and Frankowska H. (1990) Set-valued Analysis. Birkhaüser, Basel.
  2. 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.
  3. Emelichev, V., Girlich, E., Nikulin, Yu. and Podkopaev, D. (2002) Stability and regularization of vector problem of integer linear programming. Optimization, 51, 4, 645–676.10.1080/0233193021000030760
  4. Emelichev, V. and Karelkina, O. (2021) Postoptimal analysis of a finite cooperative game. Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 1, to appear.
  5. 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, 229–236.10.1515/DMA.2009.013
  6. 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.
  7. 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, 609-614.10.1007/s10559-006-0097-0
  8. 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.
  9. 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 158–185.10.1007/978-3-030-65739-0_12
  10. Hardy, G., Littlewood, J. and Polya, G. (1988) Inequalities. University Press, Cambridge.
  11. 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, 578–583.10.1007/s10559-021-00382-6
  12. Miettinen, K. (1999) Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston.
  13. Nash, J. (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 1, 48–49.10.1073/pnas.36.1.48
  14. Nash, J. (1951) Non-Cooperative Games. The Annals of Mathematics, 54, 2, 286–295.10.2307/1969529
  15. Nikulin, Yu., Karelkina, O. and Mäkelä, M. (2013) On accuracy, robustness and tolerances in vector Boolean optimization. European Journal of Operational Research, 224, 3, 449–457.10.1016/j.ejor.2012.09.018
  16. Noghin, V. (2018) Reduction of the Pareto Set: An Axiomatic Approach. Springer, Cham.10.1007/978-3-319-67873-3
  17. Osborne, M. and Rubinstein, A. (1994) A Course in Game Theory. MIT Press.
  18. Pareto, V. (1909) Manuel D’Economie Politique. V. Giard & E. Briere, Paris.
  19. Sergienko, I. and Shilo, V. (2003) Discrete Optimization Problems. Problems, Methods, Research. Naukova dumka, Kiev.
  20. Smale, S. (1974) Global analysis and economics V: Pareto theory with constraints. J. of Mathematical Economics, 1, 3, 213–221.10.1016/0304-4068(74)90013-5
  21. Steuer, R. (1986) Multiple Criteria Optimization: Theory, Computation and Application. John Wiley & Sons, New York.
DOI: https://doi.org/10.2478/candc-2022-0001 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569
Language: English
Page range: 6 - 20
Submitted on: Sep 1, 2021
Accepted on: Dec 1, 2021
Published on: Aug 12, 2022
Published by: Systems Research Institute Polish Academy of Sciences
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2022 Vladimir Emelichev, Yury Nikulin, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.