Interval valued bimatrix games

Milan Hladík

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 435-446
  • ISSN: 0023-5954

Abstract

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Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we characterize the set of all possible equilibria by mean of a linear mixed integer system.

How to cite

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Hladík, Milan. "Interval valued bimatrix games." Kybernetika 46.3 (2010): 435-446. <http://eudml.org/doc/196348>.

@article{Hladík2010,
abstract = {Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we characterize the set of all possible equilibria by mean of a linear mixed integer system.},
author = {Hladík, Milan},
journal = {Kybernetika},
keywords = {bimatrix game; interval matrix; interval analysis; bimatrix game; interval matrix},
language = {eng},
number = {3},
pages = {435-446},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Interval valued bimatrix games},
url = {http://eudml.org/doc/196348},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Hladík, Milan
TI - Interval valued bimatrix games
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 435
EP - 446
AB - Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we characterize the set of all possible equilibria by mean of a linear mixed integer system.
LA - eng
KW - bimatrix game; interval matrix; interval analysis; bimatrix game; interval matrix
UR - http://eudml.org/doc/196348
ER -

References

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  10. Rohn, J., Solvability of systems of interval linear equations and inequalities, In: Linear Optimization Problems with Inexact Data (M. Fiedler et al., eds.), Chapter 2, Springer, New York 2006, pp. .35–77. 
  11. Shashikhin, V., 10.1023/B:CASA.0000047877.10921.d0, Cybern. Syst. Anal. 40 (2004), 4, 556–564. Zbl1132.91329MR2136247DOI10.1023/B:CASA.0000047877.10921.d0
  12. Thomas, L. C., Games, Theory and Applications, Reprint of the 1986 edition. Dover Publications, Mineola, NY 2003. Zbl1140.91023MR2025526
  13. Neumann, J. von, Morgenstern, O., Theory of Games and Economic Behavior, With an Introduction by Harold Kuhn and an Afterword by Ariel Rubinstein. Princeton University Press, Princeton, NJ 2007. MR2316805
  14. Stengel, B. von, Computing equilibria for two-person games, In: Handbook of Game Theory with Economic Applications (R. J. Aumann and S. Hart, eds.), Volume 3, Chapter 45, Elsevier, Amsterdam 2002, pp. 1723–1759. 
  15. Yager, R. R., Kreinovich, V., 10.1142/S0218488500000423, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 8 (2000), 5, 611–618. Zbl1113.68542MR1784650DOI10.1142/S0218488500000423

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