A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

Document Type : Research Paper

Authors

1 Yildiz Technical University,, Education Faculty,, Department of Mathematics Education,, Istanbul-Turkey

2 Yildiz Technical University,, Art-Science Faculty,, Department of Mathematics,, Istanbul-Turkey

Abstract

In this paper, we deal with games with fuzzy payoffs. We proved that players
who are playing a zero-sum game with fuzzy payoffs against Nature are able
to increase their joint payoff, and hence their individual payoffs by
cooperating. It is shown that, a cooperative game with the fuzzy
characteristic function can be constructed via the optimal game values of
the zero-sum games with fuzzy payoffs against Nature at which players'
combine their strategies and act like a single player. It is also proven
that, the fuzzy characteristic function that is constructed in this way
satisfies the superadditivity condition. Thus we considered a transition
from two-person zero-sum games with fuzzy payoffs to cooperative games with
fuzzy payoffs. The fair allocation of the maximum payoff (game value) of
this cooperative game among players is done using the Shapley vector.

Keywords

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Iranian Journal of Fuzzy Systems
Volume 15, Issue 7
September and October 2018
Pages 121-131

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