On the Banzhaf-like Value for Cooperative Games with Interval Payoffs
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 rev...
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doaj-9466e61e15bf49ccb54c226ab5fbf6ea2020-11-25T02:23:48ZengMDPI AGMathematics2227-73902020-03-018337210.3390/math8030372math8030372On the Banzhaf-like Value for Cooperative Games with Interval PayoffsChunqiao Tan0Wenrui Feng1Weibin Han2School of Business, Central South University, Yuelu District, Changsha 410083, ChinaSchool of Business, Central South University, Yuelu District, Changsha 410083, ChinaSchool of Economics and Management, South China Normal University, Guangzhou Higher Education Mega Center, No. 378, Waihuan Xi Road, Guangzhou 510006, ChinaBy 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.https://www.mdpi.com/2227-7390/8/3/372cooperative interval gameinterval banzhaf valueinterval banzhaf-like valuecontracted interval banzhaf-like value |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Chunqiao Tan Wenrui Feng Weibin Han |
spellingShingle |
Chunqiao Tan Wenrui Feng Weibin Han On the Banzhaf-like Value for Cooperative Games with Interval Payoffs Mathematics cooperative interval game interval banzhaf value interval banzhaf-like value contracted interval banzhaf-like value |
author_facet |
Chunqiao Tan Wenrui Feng Weibin Han |
author_sort |
Chunqiao Tan |
title |
On the Banzhaf-like Value for Cooperative Games with Interval Payoffs |
title_short |
On the Banzhaf-like Value for Cooperative Games with Interval Payoffs |
title_full |
On the Banzhaf-like Value for Cooperative Games with Interval Payoffs |
title_fullStr |
On the Banzhaf-like Value for Cooperative Games with Interval Payoffs |
title_full_unstemmed |
On the Banzhaf-like Value for Cooperative Games with Interval Payoffs |
title_sort |
on the banzhaf-like value for cooperative games with interval payoffs |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-03-01 |
description |
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. |
topic |
cooperative interval game interval banzhaf value interval banzhaf-like value contracted interval banzhaf-like value |
url |
https://www.mdpi.com/2227-7390/8/3/372 |
work_keys_str_mv |
AT chunqiaotan onthebanzhaflikevalueforcooperativegameswithintervalpayoffs AT wenruifeng onthebanzhaflikevalueforcooperativegameswithintervalpayoffs AT weibinhan onthebanzhaflikevalueforcooperativegameswithintervalpayoffs |
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1724857177513918464 |