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On Positive Game Matrices and Their Extensions
Author(s) -
Raghavan T. E. S.
Publication year - 1965
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-40.1.467
Subject(s) - mathematics , row , square (algebra) , matrix (chemical analysis) , property (philosophy) , unit (ring theory) , zero (linguistics) , positive definite matrix , square root , pure mathematics , square matrix , strategy , zero sum game , row and column spaces , combinatorics , mathematical economics , game theory , computer science , symmetric matrix , geometry , physics , linguistics , philosophy , materials science , mathematics education , eigenvalues and eigenvectors , epistemology , quantum mechanics , database , composite material
In this paper we study some relations between the optimal strategies, the characteristic roots and the characteristic vectors of a positive square matrix whose rows and columns correspond to the pure strategy spaces of players in a zero‐sum two‐person game. Further we study a property of the game values of positive matrices that commute. The results are extended to infinite games on the unit square, with positive kernels as pay‐off functions.