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This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the ?|N |/2?-core cover. Furthermore, full characteriz ations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided.

This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the b jNj 2 c-core cover. Furthermore, full characterizations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided. ; Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C03

This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the b jNj 2 c-core cover. Furthermore, full characterizations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided. ; Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C03

Why Conservatives Should Stop Opposing the Common Core (Common Core: Yea)by Sol SternIn the past few decades – as progressives gained influence in universities and schools of education – the idea of a coherent, content-rich curriculum has been erased from America's classrooms. Now, for all its faults, the Common Core State Standards represent the best opportunity we have to restore that structure in our schools.In this Broadside, Sol Stern shows how both sides of the education spectrum have misrepresented the Common Core. The left regards the standards as a threat to their ideological hegemony