The paper studies linear, symmetric and efficient (LSE) solutions or values for games in partition function form. The family of such solutions is rather broad and includes the Shapley value, the Consensus value and the Myerson value just to mention some.

Yet, the authors derive a linear formula that all LSE solutions can be uniquely expressed by. The formula contains parameters

of two of the coalitions with the grand coalition, – where such pair does not exist – treated separately. When the appropriate partition function form generalisation of the null player property is added, the four properties uniquely define an extension of the Solidarity value [Nowak and Radzik, 1994 – not cited]. This characterisation is different from that of Nowak and Radzik’s solidarity value, but whether it could be applied to games in characteristic function form, or whether the new value is actually a generalisation, is not discussed.(Written for

L. Hernández-Lamoneda, J. Sánchez-Pérez and F. Sáchez-Sáchez, The class of efficient linear symmetric values for games in partition function form, Internat. Game Theory Review, 11(2009), 369-382.

A. S. Nowak and T. Radzik, A solidarity value for n-person transferable utility games, Internat. J. Game Theory 23 (1994), no. 1, 43–48.

Yet, the authors derive a linear formula that all LSE solutions can be uniquely expressed by. The formula contains parameters

*β*(*λ,s,t*) that only depends on the list of coalition sizes*λ*embedded in a partition as well as the sizes*s*and tof two of the coalitions with the grand coalition, – where such pair does not exist – treated separately. When the appropriate partition function form generalisation of the null player property is added, the four properties uniquely define an extension of the Solidarity value [Nowak and Radzik, 1994 – not cited]. This characterisation is different from that of Nowak and Radzik’s solidarity value, but whether it could be applied to games in characteristic function form, or whether the new value is actually a generalisation, is not discussed.(Written for

*Mathematical Reviews*)**References**L. Hernández-Lamoneda, J. Sánchez-Pérez and F. Sáchez-Sáchez, The class of efficient linear symmetric values for games in partition function form, Internat. Game Theory Review, 11(2009), 369-382.

A. S. Nowak and T. Radzik, A solidarity value for n-person transferable utility games, Internat. J. Game Theory 23 (1994), no. 1, 43–48.

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