Fuzzy Bi-cooperative games in multilinear extension form

2015 ◽  
Vol 259 ◽  
pp. 44-55 ◽  
Author(s):  
Surajit Borkotokey ◽  
Pankaj Hazarika ◽  
Radko Mesiar
Keyword(s):  
Cooperative Games ◽  
Multilinear Extension

CHOQUET EXTENSION OF COOPERATIVE GAMES

2013 ◽  
Vol 30 (04) ◽  
pp. 1350005 ◽  
Author(s):  
CHUNQIAO TAN ◽  
ZHONG-ZHONG JIANG ◽  
XIAOHONG CHEN
Keyword(s):  
Explicit Formula ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Extension Method ◽  
Equivalent Definition ◽  
Multilinear Extension ◽  
Shapley Function ◽  
Definition Of

A multilinear extension of the n-person cooperative game was introduced by Owen in 1972, and a new extension method is proposed in this paper. For n-person cooperative games, any coalition can equivalently be represented by its characteristic vectors. By means of the Choquet integral, a new fuzzy extension, called the Choquet extension, is developed. Furthermore, a Shapley function in this class of fuzzy cooperative games with the Choquet extension form is defined. Axioms of the Shapley function are proposed, and an explicit formula for the Shapley function is given. Finally, an equivalent definition of this Shapley function is discussed.

Some Characterizations of k-Monotonicity Through the Bipolar Möbius Transform in Bi-Capacities

2005 ◽  
Vol 9 (5) ◽  
pp. 484-495 ◽  
Author(s):  
Katsushige Fujimoto ◽  
◽  
Toshiaki Murofushi ◽  
Keyword(s):  
Boolean Function ◽  
Cooperative Games ◽  
Möbius Transform ◽  
Partial Derivatives ◽  
Multilinear Extension ◽  
Möbius Transforms ◽  
Derivatives Of

This paper first proposes the bipolar Möbius transform as an extension of dividends of cooperative games to that of bi-cooperative games (bi-capacities) defined on 3N, which is different from the Möbius transform defined by Grabisch and Labreuche. The k-monotonicity of bi-capacities is characterized through each of the following notions: the bipolar and ordinary Möbius transforms, discrete derivatives, and partial derivatives of the piecewise multilinear extension of the ternary pseudo-Boolean function corresponding to the bi-capacities.

A multilinear extension of a class of fuzzy bi-cooperative games

2015 ◽  
Vol 28 (2) ◽  
pp. 681-691 ◽  
Author(s):  
Surajit Borkotokey ◽  
Pankaj Hazarika ◽  
Radko Mesiar
Keyword(s):  
Cooperative Games ◽  
Multilinear Extension

Share-out in Cooperative Games under Uncertainty

1999 ◽  
Vol 31 (11) ◽  
pp. 10-14
Author(s):  
Vladislav I. Zhukovskiy ◽  
E. N. Opletayeva
Keyword(s):  
Cooperative Games

A stochastic approach to approximate values in cooperative games

2019 ◽  
Vol 279 (1) ◽  
pp. 93-106 ◽  
Author(s):  
Stefano Benati ◽  
Fernando López-Blázquez ◽  
Justo Puerto
Keyword(s):  
Cooperative Games ◽  
Stochastic Approach

scholarly journals Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 127-134
Author(s):  
Konstantin Kudryavtsev ◽  
Ustav Malkov
Keyword(s):  
Cooperative Games ◽  
Hippocratic Oath ◽  
The Other ◽  
Mixed Strategies ◽  
Finite Games ◽  
Moral Basis ◽  
Other Hand ◽  
Berge Equilibrium ◽  
Do No Harm ◽  
Non Cooperative Games

AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

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