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The Linear Complementarity Problem in Static and Dynamic Games

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Advances in Dynamic Games and Applications

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 5))

Abstract

It is known that the linear complementarity problem (LCP) and matrix game theory problems have interesting connections. Raghavan derived a number of LCP results using Kaplansky’s theorem. We supplement this by demonstrating more connections between LCP and matrix games. A new result is obtained in which it is shown that if a matrix game is completely mixed with value 0 and if the payoff matrix is a U-matrix, then all the proper principal minors of the payoff matrix are positive. A cursory mention is made regarding the applications of LCP in solving stochastic games.

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, Habsiguda, Hyderabad, India

    G. S. R. Murthy

  2. Indian Statistical Institute, New Delhi, India

    T. Parthasarathy & B. Sriparna

Authors
  1. G. S. R. Murthy
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  2. T. Parthasarathy
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  3. B. Sriparna
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Editor information

Editors and Affiliations

  1. Centre for Industrial and Applicable Mathematics School of Mathematics, University of South Australia, 5000, Adelaide, SA, Australia

    Jerzy A. Filar

  2. School of Mathematics, University of South Australia, 5000, Adelaide, SA, Australia

    Vladimir Gaitsgory

  3. Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, 1-7-1, Kagamiyama, 739-8521, Higashi-Hiroshima City, Japan

    Koichi Mizukami

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© 2000 Springer Science+Business Media New York

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Murthy, G.S.R., Parthasarathy, T., Sriparna, B. (2000). The Linear Complementarity Problem in Static and Dynamic Games. In: Filar, J.A., Gaitsgory, V., Mizukami, K. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 5. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1336-9_16

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  • DOI: https://doi.org/10.1007/978-1-4612-1336-9_16

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7100-0

  • Online ISBN: 978-1-4612-1336-9

  • eBook Packages: Springer Book Archive

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