Geodesic
Postoptimal analysis of a finite cooperative game
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 121-136.

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We consider a finite cooperative game of several players with parameterized concept of equilibrium (optimality principles), when relations between players in coalition are based on the Pareto maximum. Introduction of this optimality principle allows to connect classical notions of the Pareto optimality and Nash equilibrium. Lower and upper bounds are obtained for the strong stability radius of the game under parameters perturbations with the assumption that arbitrary Hölder norms are defined in the space of outcomes and criteria space. Game classes with an infinite radius are defined. 
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Vladimir Emelichev; Olga Karelkina. Postoptimal analysis of a finite cooperative game. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 121-136. https://geodesic-test.mathdoc.fr/item/BASM_2021_1_a7/

[1] Aubin J-P., Frankowska H., Set-valued analysis, Birkhuser, Basel, 1990 | MR | Zbl

[2] Bukhtoyarov S., Emelichev V., Stepanishina Yu., “Stability of discrete vector problems with the parametric principle of optimality”, Cybernetics and Systems Analysis, 39:4 (2003), 604–614 | DOI | MR | Zbl

[3] Emelichev V., Bukhtoyarov S., “Measure of stability for a finite cooperative game with a parametric optimality principle (from Pareto to Nash)”, Computational Mathematics and Mathematical Physics, 46:7 (2006), 1193–1199 | DOI | MR

[4] Emelichev V., Kuzmin K., “Finite cooperative games with a parametric concept of equilibrium under uncertainty conditions”, Journal of Computer and Systems Sciences. International, 45:2 (2006), 276–281 | DOI | MR | Zbl

[5] Emelichev V., Karelkina O., “Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric”, Discrete Math. Appl., 19:3 (2009), 229–236 | DOI | MR | Zbl

[6] Emelichev V. A., Platonov A. A., “Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric”, Buletinul Academiei de Stiinte a Republicii Moldova, Matematica, 57:2 (2008), 58–67 | MR | Zbl

[7] Emelichev V., Nikulin Y., “Finite games with perturbed payoffs”, Advances in Optimization and Applications, OPTIMA 2020, Communications in Computer and Information Science, 1340, eds. Olenev N., Evtushenko Y., Khachay M., Malkova V., Springer, Cham, 2020, 158–169 | DOI | MR

[8] Emelichev V. A., Bukhtoyarov S. E., “On two stability types for a multicriteria integer linear programmin problem”, Buletinul ASM, ser. Mathem., 92:1 (2020), 17–30 | MR | Zbl

[9] Emelichev V. A., Nikulin Y. V., “Post-optimal analysis for multicriteria integer linear programming problem with parametric optimality”, Control and Cybernetics, 49:2 (2020), 163–178 | MR | Zbl

[10] Emelichev V., Girlich E., Nikulin Y., Podkopaev D., “Stability and regularization of vector problem of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl

[11] Emelichev V. A., Kotov V. M., Kuzmin K. G., Lebedeva T. T., Semenova N. V., Sergienko T. I., “Stability and effective algorithms for solving multiobjective discrete optimization problems with incomplete information”, J. of Automation and Inf. Sciences, 46:2 (2014), 27–41 | DOI | MR

[12] Emelichev V., Nikulin Y., “On one type of stability for multiobjective integer linear programming problem with parameterized optimality”, Computer Science Journal of Moldova, 28:3 (2020), 249–268 | MR | Zbl

[13] Nash J., “Equilibrium points in n-person games”, Proceedings of the National Academy of Sciences, 36:1 (1950), 48–49 | DOI | MR | Zbl

[14] Nash J., “Non-cooperative games”, The Annals of Mathematics, 54:2 (1951), 286–295 | DOI | MR | Zbl

[15] Osborne M., Rubinstein A., Course in game theory, MIT Press, 1994 | MR | Zbl

[16] Pareto V., Manuel d'economie politique, V. Giard $\$ E. Briere, Paris, 1909

[17] Sergienko I., Shilo V., Discrete optimization problems. Problems, Methods, Research, Naukova dumka, Kiev, 2003

[18] Noghin V., Reduction of the Pareto set: an axiomatic approach, Springer, Cham, 2018

[19] Moulin H., Game theory for the social sciences, 2nd edition, New York University Press, 1986 | MR

[20] Chernikov S. N., Linear equations, Nauka, M., 1968 (in Russian) | MR

[21] Hardy G. H., Littlewood J. E., Polya G., Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1952 | MR | Zbl