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Theorem of conflicts for a pair of probability measures

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  • Volodymyr Koshmanenko

Abstract

We develop mathematical tools suitable for the construction of conflict models with non-annihilating adversaries. In a set of probability measures we introduce a non-commutative conflict composition and consider the associated dynamical system. We prove that for each couple of non-identical mutually nonsingular measures, the corresponding trajectory of the dynamical system converges to an invariant point represented by a pair of mutually singular measures. The disjoint supports of the limiting measures determine the final re-distribution of the starting area of conflict as a result of an “infinite war” for existence space (the pure repelling effect). Copyright Springer-Verlag 2004

Suggested Citation

  • Volodymyr Koshmanenko, 2004. "Theorem of conflicts for a pair of probability measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 303-313, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:303-313
    DOI: 10.1007/s001860300330
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    Cited by:

    1. Karataieva, Tatiana & Koshmanenko, Volodymyr & Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2019. "Mean field model of a game for power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 535-547.

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