Government versus Opposition: Who Should be Who in the 16th German Bundestag?

2006

SSRN Journal

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Section: Theorem 3 Let α ∈ R Nmentioning

confidence: 95%

mentioning

confidence: 97%

Coalition Formation in Simple Games: The Semistrict Core

Dimitrov

2006

SSRN Journal

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“…Note finally, that the Bundestag game discussed in Dimitrov & Haake (2006) shows that C3 is not a necessary condition for core existence.…”

Section: The Paradox Of Smaller Coalitions and Core Stabilitymentioning

confidence: 96%

“…When the members of S have to agree on how power is shared among them, then the subgame v S naturally should be taken into account, as it reflects possibilities given S has already formed. For example, within a minimal winning coalition, all members should be treated equally, since all have the same possibilities to form other winning coalitions within S (see Dimitrov & Haake (2006) for further details).…”

Section: Simple Games and Solutionsmentioning

confidence: 99%

A note on the paradox of smaller coalitions

Dimitrov

2007

Soc Choice Welfare

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We consider hedonic coalition formation games that are induced by a simple TUgame and a cooperative solution. For such models, Shenoy's (1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy's paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy's paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.

“…Nonetheless, for the current German parliament, this method proposes to form the actual government. Further details are found in Shenoy (1979), Dimitrov and Haake (2006), and Dimitrov and Haake (2008). 5.…”

Section: For S T ∈ W and I ∈ S ∩ T Define S I T If And Only If φ Imentioning

confidence: 98%

Comments on: Transversality of the Shapley value

2008

TOP

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The paper by Stefano Moretti and Fioravante Patrone celebrates the possibly most influential solution concepts from cooperative game theory: the Shapley value. With their excellent collection of applications, in which the Shapley value provides a meaningful solution, the authors in fact not only highlight the importance of this particular solution but also the relevance of cooperative game theory as a "technique" usable in other fields of research.Before discussing the applications, sections three to five introduce, axiomatize, reformulate, and extend the value, giving the reader a brief overview of what came out of Shapley's original work in the past fifty-five years. From the wide spectrum of applications, the authors on the one hand picked economics-related problems such as cost sharing, irrigation problems, or the theory of belief functions. On the other hand, noneconomic models from biology and reliability theory complement the discussion.In the conclusions the authors express their hope that the reader has taken some advantage from their efforts. In my view, I am sure that he did. The authors' selection of topics was motivated by maximizing the diversity of applications. Yet, they manage to introduce into any new topic in as much as it is necessary to get the gist of how cooperative game theory and the value contribute to that field. For example, one needs not be a cardiologist in order to understand that the value can be used to assess and rank certain risk factors for myocardial infarction.My comments on the paper fall into two categories: First, I would like to reemphasize certain aspects. And second, as any selection of examples is subjective, I would like to slightly extend the list by my subjective points of view.This comment refers to the invited paper available at: http://dx.