scholarly journals An axiomatization of the Banzhaf value for cooperative games on antimatroids

2004 ◽  
Vol 59 (1) ◽  
pp. 147-166 ◽  
Author(s):  
E. Algaba ◽  
J. M. Bilbao ◽  
R. van den Brink ◽  
A. Jim�nez-Losada
Keyword(s):  
Cooperative Games ◽  
Banzhaf Value

Interval Banzhaf Value for Cooperative Interval Games on Augmenting Systems

2014 ◽  
Vol 1030-1032 ◽  
pp. 1726-1732
Author(s):  
Zuo Feng Gao ◽  
Chao Han ◽  
Jing Wu
Keyword(s):  
Cooperative Games ◽  
Axiomatic System ◽  
Banzhaf Value ◽  
Real Numbers ◽  
Interval Numbers ◽  
Interval Games

This paper focuses on the Banzhaf value for cooperative games where the set of players is restraint on augmenting systems and the coalition values are compact intervals of real numbers. The interval Banzhaf value for cooperative interval games on augmenting systems is put forward on the basis of corresponding axiomatic system and operations of interval numbers. Moreover, some properties of the interval Banzhaf value are given. Finally, a practical example is offered to illustrate the validity and feasibility of this method on these kinds of cooperative interval games.

scholarly journals On the Banzhaf-like Value for Cooperative Games with Interval Payoffs

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 372 ◽  
Author(s):  
Chunqiao Tan ◽  
Wenrui Feng ◽  
Weibin Han
Keyword(s):  
Cooperative Games ◽  
Total Order ◽  
Banzhaf Value ◽  
Closed Intervals ◽  
Interval Games ◽  
Interval Value

By using Moore’s subtraction operator and a total order on the set of closed intervals, we introduce a new variation of the Banzhaf value for cooperative interval games called the interval Banzhaf-like value which may accommodate the shortcomings of the interval Banzhaf value. We first reveal the relation between this introduced value and the interval Banzhaf value. Then, we present two sets of properties that may be used to determine whether an interval value is median-indifferent to the interval Banzhaf-like value. Finally, in order to overcome the disadvantages of the interval Banzhaf-like value, we propose the contracted interval Banzhaf-like value and give an axiomatization of this proposed value.

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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