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This paper provides results in the area of the analytical derivation of the efficient set of a mean-variance portfolio selection problem that has more than three criteria. By "analytical" we mean derived by formula as opposed to being computed by algorithm. By "more than three criteria", we mean that beyond the mean and variance of regular portfolio selection, the problems addressed have two or more additional linear objectives. The additional objectives might include sustainability, dividend yield, liquidity, and R&D as extra objectives like these are being seen with greater frequency. While not all multiple criteria portfolio selection problems lend themselves to an analytical derivation, a certain class does and the problems in this class are covered by the mathematics of this paper. [ABSTRACT FROM AUTHOR]

We introduce the concepts of the components' second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components' second-order payoffs for one-point solutions for CS games as generalizations of the players' second-order productivities in TU games and of the players' second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212–219, 2021). The players' second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player's marginal contributions to coalitions containing neither of them by entering these coalitions. The players' second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components' second-order productivities are conceptualized as their second-order productivities in the game between components; the components' second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players' and the components' second-order productivities in terms of their second-order payoffs. [ABSTRACT FROM AUTHOR]