Talk:Shapley value

message: One property is missing: If a player is null, it receives zero. A player i is null if v(S\cup \{i\}) = v(S) for all S not containg i. The Shapley value is the only value that satisfies this property, plus 2, 3, and 5.  —Preceding unsigned comment added by 193.147.86.254 (talk) 17:26, 14 September 2007 (UTC)
replies: text: You are right. Just take v(N) and divide it evenly among the players. This is another solution, different from the Shapley value, that satisfies 2, 3, and 5. --Fioravante Patrone en (talk) 01:19, 29 April 2008 (UTC)
thread_title:  Properties 2, 3 and 5 do NOT characterize the Shapley value 

message: I think the article would benefit from an intuitive explanation of the solution concept (while I'm at it, I think it'd be good to avoid the word "fair" in the lede in favor of "cooperative solution"); the fact that each member of the coalition receives share of total surplus equal to their "marginal product" or "marginal contribution", where this is based 'as if' all the members of the coalition arrived randomly. Casting the example in the article in these terms can make this concept more accessible to the lay readers.radek (talk) 08:03, 25 January 2010 (UTC)
thread_title:  a non-technical explanation 

message: v does not necesarily need to be superadditive, see for instance Multiagent Systems  —Preceding unsigned comment added by 186.48.240.86 (talk) 01:46, 23 March 2011 (UTC)
thread_title:  Incorrect v function definition 

message: The references should be linked to the text. As they are, they seem superfluous.Koczy (talk) 10:09, 1 July 2011 (UTC)
thread_title:  References 

message: Comments on terminology:
:Maybe "coalition game" should say "coalition/cooperative game with transferable utility". The Shapley value, for superadditive TU games, is a special case of a solution concept for NTU cooperative games.  
:"Linearity" is more clear, and stronger, than "additivity" IMO.
Suggestions on what could be further included:
:A sketch of the short proof of uniqueness, which uses linearity in an essential way, would be nice.
:Cute and immediate example: a special case of Nash bargaining can be viewed as a TU cooperative game. Shapley value and the Nash solution agree in that case.
:Comparison with the core: how about simple examples where the Shapley value lies and does not lie in the core? The Glove game already shows the latter case. 
Mct mht (talk) 04:01, 17 February 2013 (UTC)
replies: text: I am going to go ahead and change "additivity" to linearity. Saying a value is additive is misleading. The term "additive" is alluding to the fact that a game is a measure-like object (in the finite case, imposing additivity makes the game a measure defined on the discrete sigma algebra). A value is a linear functional on this (Banach) space of measures. Mct mht (talk) 08:23, 17 February 2013 (UTC)
thread_title:  Comments and suggestions 

message: Dr. Dehez has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Dehez has published scholarly research which seems to be relevant to this Wikipedia article:
*Reference : Pierre Dehez & Daniela Tellone, 2009. "Data Games : Sharing public goods with exclusion," Working Papers of BETA 2009-31, Bureau d'Economie Theorique et Appliquee, UDS, Strasbourg.
ExpertIdeasBot (talk) 00:33, 26 May 2015 (UTC)
thread_title:  Dr. Dehez's comment on this article 

message: Dr. Beal has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
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We believe Dr. Beal has expertise on the topic of this article, since he has published relevant scholarly research:
*Reference 1: Sylvain Beal & Andre Casajus & Frank Huettner, 2015. "Efficient extensions of the Myerson value," Working Papers 2015-01, CRESE.
*Reference 2: Beal, Sylvain & Remila, Eric & Solal, Philippe, 2012. "Axioms of invariance for TU-games," MPRA Paper 41530, University Library of Munich, Germany.
ExpertIdeasBot (talk) 15:54, 24 August 2016 (UTC)
thread_title:  Dr. Beal's comment on this article 

message: Dr. Perez-Castrillo has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
\sum _{R}\left[v(P_{i}^{R}\cup \left\{i\right\})-v(P_{i}^{R})\right]\,\!}
Where {\displaystyle R\,\!} R\,\! is an ordering of the players and {\displaystyle P_{i}^{R}\,\!} P_{i}^{R}\,\! is the set of players in {\displaystyle N\,\!} N\,\! which precede {\displaystyle i\,\!} i\,\! in the order {\displaystyle R\,\!} R\,\!"
}}
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Perez-Castrillo has expertise on the topic of this article, since he has published relevant scholarly research:
*Reference 1: Effrosyni Diamantoudi & Ines Macho-Stadler & David Perez-Castrillo & Licun Xue, 2011. "Sharing the surplus in games with externalities within and across issues," UFAE and IAE Working Papers 880.11, Unitat de Fonaments de l'Analisi Economica (UAB) and Institut d'Analisi Economica (CSIC).
*Reference 2: David Perez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," UFAE and IAE Working Papers 647.05, Unitat de Fonaments de l'Analisi Economica (UAB) and Institut d'Analisi Economica (CSIC).
ExpertIdeasBot (talk) 02:39, 6 September 2016 (UTC)
thread_title:  Dr. Perez-Castrillo's comment on this article 

message: I am interested in the generalisation to coalitions stated in the last paragraph. However, the paper cited for this formula does not in fact appear to contain it. So I am stuck - where can I read more about that extension? Nathaniel Virgo (talk) 14:47, 18 July 2018 (UTC)
replies: text: I found myself in exactly the same situation now, and couldn't find the formula or something similar in the referenced paper either. It appears the edit was made by Romanpoet on 04:56, 31 May 2017‎ (if anyone is interested in this information). For the moment, until there is more information, I've marked his citation as irrelevant. And Nathaniel, about where to read more about the topic: I've found another paper which seems to cover this topic, but haven't read it yet. So this might or might not provide useful information. Ception (talk) 14:46, 26 February 2020 (UTC)
thread_title:  Generalisation to coalitions - reference appears not to match content 

message: This is based spin a “note” (not full article) in a perfectly respectable but not top journal. This is not the kind of information that belongs in the lede even if it *may be* pertinent somewhere else. Volunteer Marek  00:02, 20 May 2024 (UTC)
thread_title:  Not in lede