A dynamic axiomatization for the semivalues on classic cooperative games
Each semivalue, as a solution concept defined on cooperative games with a finite set of players, is univocally determined by weighting coefficients that apply to players’ marginal contributions. Taking into account that a semivalue induces semivalues on lower cardinalities, we prove that its weighting coefficients can be reconstructed from the last weighting coefficients of its induced semivalues. Moreover, we provide the conditions of a sequence of numbers in order to be the family of the last coefficients of any induced semivalues. As a consequence of this fact, we give two characterizations of each semivalue defined on cooperative games with a finite set of players: one, among all semivalues; another, among all solution concepts on cooperative games.
Palabras clave / Keywords: semivalue weighting coefficient induced semivalue unanimity game axiomatization
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