Abstract
We focus on generalized mixed modified semivalues, a family of coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is also provided and an application to the Catalan Parliament (legislature 2012–2016) is shown.
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Notes
The term “multilinear” means that, for each \(i\in N\), the function is linear in \(x_i\), that is, of the form \(f_v(x_1,x_2,\ldots ,x_n)=g_i(x_1,x_2,\ldots ,\overset{\wedge }{x_i},\ldots ,x_n)x_i + h_i(x_1,x_2,\ldots ,\overset{\wedge }{x_i},\ldots ,x_n)\).
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The authors wish to thank the two anonymous reviewers for their helpful suggestions which have been incorporated to the text.
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Research supported by Grant SGR 2009–01029 of the Catalonia Government (Generalitat de Catalunya) and Grant MTM 2012-34426 of the Economy and Competitiveness Spanish Ministry.
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Giménez, J.M., Puente, M.A. A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012–2016). TOP 23, 669–684 (2015). https://doi.org/10.1007/s11750-014-0356-6
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DOI: https://doi.org/10.1007/s11750-014-0356-6