A solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution and the center-of-gravity of the imputation-set value. The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value. We provide characterizations of the two classes of (...) solutions using either population solidarity or a reduced game consistency in addition to other standard properties. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed (...) player set. Specifications of several properties characterize specific solutions in this class. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed (...) player set. Specifications of several properties characterize specific solutions in this class. (shrink)

We introduce a family of proportional surplus division values for TU-games. Each value first assigns to each player a compromise between her stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value (...) in this family. (shrink)

In sub-Sect. 3.3, the terms “one-person” and “-person” were incorrectly updated by mistake during the correction stage in the online published article.

In cooperative game theory with transferable utilities, there are two well-established ways of redistributing Shapley value payoffs: using egalitarian Shapley values, and using consensus values. We present parallel characterizations of these classes of solutions. Together with the axioms that characterize the original Shapley value, those that specify the redistribution methods characterize the two classes of values. For the class of egalitarian Shapley values, we focus on redistributions in one-person unanimity games from two perspectives: allowing the worth of coalitions to vary, (...) while keeping the player set fixed; and allowing the player set to change, while keeping the worth of coalitions fixed. This class of values is characterized by efficiency, the balanced contributions property for equal contributors, weak covariance, a proportionately decreasing redistribution in one-person unanimity games, desirability, and null players in unanimity games. For the class of consensus values, we concentrate on redistributions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}-person unanimity games from the same two perspectives. This class of values is characterized by efficiency, the balanced contributions property for equal contributors to social surplus, complement weak covariance, a proportionately decreasing redistribution in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}-person unanimity games, desirability, and null players in unanimity games. (shrink)