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

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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Main Authors: Chunqiao Tan, Wenrui Feng, Weibin Han
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Mathematics
Subjects:
cooperative interval game
interval banzhaf value
interval banzhaf-like value
contracted interval banzhaf-like value
Online Access:https://www.mdpi.com/2227-7390/8/3/372
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spelling 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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