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Repeated matrix games

Published online by Cambridge University Press:  14 July 2016

Dana B. Kamerud
Dana B. Kamerud*
Affiliation:
St. Louis University
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Abstract

A matrix game is played repeatedly, with the actions taken at each stage determining both a reward paid to Player I and the probability of continuing to the next stage. An infinite history of play determines a sequence (Rn) of such rewards, to which we assign the payoff lim supn (R1 + · ·· + Rn). Using the concept of playable strategies, we slightly generalize the definition of the value of a game. Then we find sufficient conditions for the existence of a value and for the existence of stationary optimal strategies (Theorems 8 and 9). An example shows that the game need not have a value (Example 4).

Keywords

STOCHASTIC GAMEREPEATED GAMERECURSIVE GAMENONDISCOUNTED PAYOFFSTATIONARY STRATEGIESPLAYABLE STRATEGIESOPTIMAL STOPPINGTWO-PERSON ZERO-SUM GAMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 830 - 842
Copyright
Copyright © Applied Probability Trust 1979 

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