Consistency for the additive efficient normalization of semivalues
► The B-reduced game is defined and extension of Sobolev’s reduced game. ► B-reduced and path-independent linear reduced game only coincide on Sobolev’s case. ► The additive efficient normalization of semivalues is characterized by B-consistency. ► The ESE-value is characterized by path-independentl...
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| Veröffentlicht in: | European journal of operational research 2013-02, Vol.224 (3), p.566-571 |
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| container_title | European journal of operational research |
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| creator | Xu, Genjiu Driessen, Theo S.H. Sun, Hao Su, Jun |
| description | ► The B-reduced game is defined and extension of Sobolev’s reduced game. ► B-reduced and path-independent linear reduced game only coincide on Sobolev’s case. ► The additive efficient normalization of semivalues is characterized by B-consistency. ► The ESE-value is characterized by path-independently linear consistency. ► The relationship between ESE-values and the least square values is derived.
This paper contributes to consistency for the additive efficient normalization of semivalues. Motivated from the additive efficient normalization of a semivalue being a B-revision of the Shapley value, we introduce the B-reduced game which is an extension of Sobolev’s reduced game. Then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance, symmetry, and B-consistency. Furthermore, by means of the path-independently linear consistency together with the standardness for two-person games, the additive efficient normalization of semivalues is also characterized. Accessorily, the additive efficient normalization of semivalues is directly verified as the linear consistent least square values (see Ruiz et al., 1998). |
| doi_str_mv | 10.1016/j.ejor.2012.08.018 |
| format | Article |
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This paper contributes to consistency for the additive efficient normalization of semivalues. Motivated from the additive efficient normalization of a semivalue being a B-revision of the Shapley value, we introduce the B-reduced game which is an extension of Sobolev’s reduced game. Then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance, symmetry, and B-consistency. Furthermore, by means of the path-independently linear consistency together with the standardness for two-person games, the additive efficient normalization of semivalues is also characterized. Accessorily, the additive efficient normalization of semivalues is directly verified as the linear consistent least square values (see Ruiz et al., 1998).</description><identifier>ISSN: 0377-2217</identifier><identifier>EISSN: 1872-6860</identifier><identifier>DOI: 10.1016/j.ejor.2012.08.018</identifier><identifier>CODEN: EJORDT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>[formula omitted]-consistency ; Additive efficient normalization of semivalues ; Game theory ; Linear consistency ; Mathematical functions ; Shapley value ; Studies ; Symmetry</subject><ispartof>European journal of operational research, 2013-02, Vol.224 (3), p.566-571</ispartof><rights>2012 Elsevier B.V.</rights><rights>Copyright Elsevier Sequoia S.A. Feb 1, 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-33581b308e2e0c8f7c3ac5771aa97dedb20d88759d27b863c7c8a4857a81a14f3</citedby><cites>FETCH-LOGICAL-c382t-33581b308e2e0c8f7c3ac5771aa97dedb20d88759d27b863c7c8a4857a81a14f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ejor.2012.08.018$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,778,782,3539,27911,27912,45982</link.rule.ids></links><search><creatorcontrib>Xu, Genjiu</creatorcontrib><creatorcontrib>Driessen, Theo S.H.</creatorcontrib><creatorcontrib>Sun, Hao</creatorcontrib><creatorcontrib>Su, Jun</creatorcontrib><title>Consistency for the additive efficient normalization of semivalues</title><title>European journal of operational research</title><description>► The B-reduced game is defined and extension of Sobolev’s reduced game. ► B-reduced and path-independent linear reduced game only coincide on Sobolev’s case. ► The additive efficient normalization of semivalues is characterized by B-consistency. ► The ESE-value is characterized by path-independently linear consistency. ► The relationship between ESE-values and the least square values is derived.
This paper contributes to consistency for the additive efficient normalization of semivalues. Motivated from the additive efficient normalization of a semivalue being a B-revision of the Shapley value, we introduce the B-reduced game which is an extension of Sobolev’s reduced game. Then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance, symmetry, and B-consistency. Furthermore, by means of the path-independently linear consistency together with the standardness for two-person games, the additive efficient normalization of semivalues is also characterized. Accessorily, the additive efficient normalization of semivalues is directly verified as the linear consistent least square values (see Ruiz et al., 1998).</description><subject>[formula omitted]-consistency</subject><subject>Additive efficient normalization of semivalues</subject><subject>Game theory</subject><subject>Linear consistency</subject><subject>Mathematical functions</subject><subject>Shapley value</subject><subject>Studies</subject><subject>Symmetry</subject><issn>0377-2217</issn><issn>1872-6860</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWD_-gKcFz7tmkmYzBS9a_IKCFz2HNDvBLO2mJmmh_nq31LOnubzPvDMPYzfAG-DQ3vUN9TE1goNoODYc8IRNALWoW2z5KZtwqXUtBOhzdpFzzzkHBWrCHudxyCEXGty-8jFV5Ysq23WhhB1V5H1wgYZSDTGt7Sr82BLiUEVfZVqHnV1tKV-xM29Xma7_5iX7fH76mL_Wi_eXt_nDonYSRamlVAhLyZEEcYdeO2md0hqsnemOuqXgHaJWs07oJbbSaYd2ikpbBAtTLy_Z7XHvJsXvsbeYPm7TMFYaAFASFW_FmBLHlEsx50TebFJY27Q3wM3BlenNwZU5uDIczehqhO6PEI337wIlkw9vO-pCIldMF8N_-C8Iu3KM</recordid><startdate>20130201</startdate><enddate>20130201</enddate><creator>Xu, Genjiu</creator><creator>Driessen, Theo S.H.</creator><creator>Sun, Hao</creator><creator>Su, Jun</creator><general>Elsevier B.V</general><general>Elsevier Sequoia S.A</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130201</creationdate><title>Consistency for the additive efficient normalization of semivalues</title><author>Xu, Genjiu ; Driessen, Theo S.H. ; Sun, Hao ; Su, Jun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-33581b308e2e0c8f7c3ac5771aa97dedb20d88759d27b863c7c8a4857a81a14f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>[formula omitted]-consistency</topic><topic>Additive efficient normalization of semivalues</topic><topic>Game theory</topic><topic>Linear consistency</topic><topic>Mathematical functions</topic><topic>Shapley value</topic><topic>Studies</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, Genjiu</creatorcontrib><creatorcontrib>Driessen, Theo S.H.</creatorcontrib><creatorcontrib>Sun, Hao</creatorcontrib><creatorcontrib>Su, Jun</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>European journal of operational research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xu, Genjiu</au><au>Driessen, Theo S.H.</au><au>Sun, Hao</au><au>Su, Jun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Consistency for the additive efficient normalization of semivalues</atitle><jtitle>European journal of operational research</jtitle><date>2013-02-01</date><risdate>2013</risdate><volume>224</volume><issue>3</issue><spage>566</spage><epage>571</epage><pages>566-571</pages><issn>0377-2217</issn><eissn>1872-6860</eissn><coden>EJORDT</coden><abstract>► The B-reduced game is defined and extension of Sobolev’s reduced game. ► B-reduced and path-independent linear reduced game only coincide on Sobolev’s case. ► The additive efficient normalization of semivalues is characterized by B-consistency. ► The ESE-value is characterized by path-independently linear consistency. ► The relationship between ESE-values and the least square values is derived.
This paper contributes to consistency for the additive efficient normalization of semivalues. Motivated from the additive efficient normalization of a semivalue being a B-revision of the Shapley value, we introduce the B-reduced game which is an extension of Sobolev’s reduced game. Then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance, symmetry, and B-consistency. Furthermore, by means of the path-independently linear consistency together with the standardness for two-person games, the additive efficient normalization of semivalues is also characterized. Accessorily, the additive efficient normalization of semivalues is directly verified as the linear consistent least square values (see Ruiz et al., 1998).</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ejor.2012.08.018</doi><tpages>6</tpages></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | [formula omitted]-consistency Additive efficient normalization of semivalues Game theory Linear consistency Mathematical functions Shapley value Studies Symmetry |
| title | Consistency for the additive efficient normalization of semivalues |
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