Talk:Core (game theory)

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game with no core is not very clear

The example of a game with no core is not very clear. I think it would be a good idea to spell out why there is no solution for 3 miners which cannot be improved for some coalition. Something along the lines of "If there are 3 miners, A, B, and C, and A and B choose to split all the gold between them, then C could offer A a split that is not 50/50. In order for this to be an improvement, C would be getting some non-zero amount and A would be getting the rest, meaning that B could always team up with C to split 50/50 again. So since any payout besides (1/2, 1/2, 0) leaves 2 miners that are getting less than 1/2 (and would thus benefit from a 50/50 split), and the payout of (1/2, 1/2, 0) can be improved by the miner getting 0 offering a non-50/50 split to one of the others, no payout is core." Leusebi 10:52, 15 March 2007 (UTC)[reply]

Thank you for your suggestion! When you feel an article needs improvement, please feel free to make those changes. Wikipedia is a wiki, so anyone can edit almost any article by simply following the Edit this page link at the top. You don't even need to log in (although there are many reasons why you might want to). The Wikipedia community encourages you to be bold in updating pages. Don't worry too much about making honest mistakes — they're likely to be found and corrected quickly. If you're not sure how editing works, check out how to edit a page, or use the sandbox to try out your editing skills. New contributors are always welcome. --best, kevin [kzollman][talk] 22:22, 15 March 2007 (UTC)[reply]

Economics or game theory?

I consider core a game theoretic concept so I am a bit puzzled by the lack of game theory on this page. After a quick survey among colleagues I am rather sure that although core-related results existed in the literature prior to Gillies, these have been rediscovered and labelled as "core" later. If no-one objects I will update the page accordingly.Koczy 17:52, 3 August 2007 (UTC)[reply]

incomplete definition

The definition currently ends with "When the core exists and is not empty, it is the set of imputations that are not dominated." a) What's meant by "exists" here? It always exists; it can be empty, but if that's what's meant, this is redundant with "is not empty" and should be deleted. b) I don't understand why the qualification is necessary at all – can there be dominated imputations if the core is empty? a) The "definition" is circular, as this is the only time it actually mentions the word "core" and it doesn't say how to determine whether it exists and is non-empty.

Dr. Echenique's comment on this article

Dr. Echenique has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The article only talks formally about the core of TU games (and the discussion isn't very useful, omitting for example the balancedness condition for nonemptyness of the core; there's also a typo in the definition of a blocking coalition, the inequality for sum y_i \geq v(C) should be strict.
The discussion of the core of exchange economies and voting theory is very incomplete.
I would suggest having two subsections. One about the core of TU games (which would at least mention the Bondareva Shapley thm) and one about the core of NTU games, which should ref to Scarf's thm, but also to exchange economies (and core convergence) and to stable matching theory.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Echenique has published scholarly research which seems to be relevant to this Wikipedia article:

Reference : Federico Echenique & Mehmet B. Yenmez, 2005. "A Solution to Matching with Preferences over Colleagues," Working Papers 2005.120, Fondazione Eni Enrico Mattei.

ExpertIdeasBot (talk) 02:48, 28 May 2016 (UTC)[reply]

Dr. Volij's comment on this article

Dr. Volij has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The definition of a coalition improving upon a feasible allocation is poorly written. Needs a major improvement. The zero-sum games mentioned in the section Origin, do not belong to the class of games for which the core is defined.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Volij has expertise on the topic of this article, since he has published relevant scholarly research:

Reference : Roberto Serrano & Rajiv Vohra & Oscar Volij, 1999. "On the Failure of Core Convergence in Economies with Asymmetric Information," Economic theory and game theory 011, Oscar Volij.

ExpertIdeasBot (talk) 20:32, 1 July 2016 (UTC)[reply]