A Simple Way to Obtain the Sufficient Nonemptiness Conditions for Core of TU Game

Authors

  • Alexandra B. Zinchenko Southern Federal University

Abstract

The system of linear constraints like one that determines the core of TU game is considered. Expressing its basis solutions through characteristic function we obtain a list of sufficient conditions under which the core is nonempty. Some of them are the generalizations of known results.

Keywords:

cooperative TU game, core, balancedness, sufficient conditions

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References

Branzei, R. and S. Tijs (2001). Additivity regions for solutions in cooperative game theory. Libertas Mathematica, 21, 155–167.

Branzei, R. and S. H. Tijs (2001). Cooperative games with a simplical core. Balkan Journal of Geometry and Application, 6, 7–15.

Bondareva, O. N. (1963). Certain applications of the methods of linear programing to the theory of cooperative games. Problemy Kibernetiki, 10, 119–139 (in Russian).

Hamers, H., F. Klijn, T. Solymosi, S. Tijs and J. P. Villar (2002). Assignment games satisfy the CoMa-property. Games and Economic Behavior, 38(2), 231–239.

Gillies, D. B. (1953). Some theorems on n-person games. PhD thesis, University Press Princeton, Princeton, New Jersey.

Granot, D. and Huberman, G. (1981). Minimum Cost Spanning Tree Games. Mathematical Programming, 21, 1–18.

Kuipers, J. (1993). On the Core of Information Graph Games. Int. J. Game Theory, 21, 339–350.

Muto, S., M. Nakayama, J. Potters and S. Tijs (1988). On big boss games. The Economic Studies Quarterly, 39, 303–321.

Potters, J., R. Poos, S. Tijs and S. Muto (1989). Clan games. Games and Economic Behavior, 1, 275–293.

Shapley, L.S. (1967). On balanced sets and cores. Naval Research Logistics Quarterly, 14, 453–460.

Shapley, L.S. (1967). Cores of Convex Games. Int. J. Game Theory, 1, 11–26.

Voorneveld, M. and S. Grahn (2001). A minimal test for convex games and the Shapley value. Working paper series, Department of economics, Uppsala university, 2, 1–8.

van Velzen , B., H. Hamersa and H. Nordea, (2005). A note on permutationally convex games. CentER Discussion Paper 2005-83, Tilburg University, 1–18.

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Published

2022-08-22

How to Cite

Zinchenko, A. B. . (2022). A Simple Way to Obtain the Sufficient Nonemptiness Conditions for Core of TU Game. Contributions to Game Theory and Management, 6. Retrieved from https://gametheory.spbu.ru/article/view/14240

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