This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

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Abstract:We consider finite state, finite action, stochastic games over an infinite time horizon. We survey algorithms for the computation of minimax optimal stationary strategies in the zerosum case, and of Nash equilibria in stationary strategies in the nonzerosum case. We also survey those theoretical results that pave the way towards future development of algorithms. Zusammenfassung: In dieser Arbeit werden unendlichstufige stochastische Spiele mit endlichenZustands-und Aktionenr~umen untersucht. Es wird ein Uberblick gegeben fiber Algorithmen zur Berechnung von optimalen station/iren Minimax-Strategien in Nullsummen-Spielen und von station~tren Nash-Gleichgewichtsstrategien in Nicht-Nullsummen-Spielen. Einige theoretische Ergebnisse werden vorgestellt, die far die weitere Entwicklung von Algorithmen nOtzlich sind.

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