Marginalism, egalitarianism and efficiency in multi-choice games

Cost allocation in energy distribution networks

“…In addition, a strategic approach to distribution problems could be interesting. For instance, Lowing and Techer (2022) demonstrate that the multi-choice Shapley value is related to the Serial cost sharing mechanism proposed by Moulin and Shenker (1992) for cost sharing problems. Consequently, the Connection rule is also related to this mechanism.…”

“…□ 6.5. Proof of Theorem 7 Lowing and Techer (2022) show that the multi-choice Shapley value belongs to the Core of sub-modular (cost) games. Therefore, it suffices to show that distribution games are submodular games to prove Theorem 7.…”

“…The worth of a coalition corresponds to the total cost of the network in which each link meets its peak capacity. The Connection rule applied to a distribution problem corresponds to the multi-choice Shapley value, introduced by Lowing and Techer (2022), of the corresponding distribution game. Similarly, the Uniform rule corresponds to the multi-choice Equal division value and the Mixed rules to the multi-choice Egalitarian Shapley values.…”

“…Similarly, the Uniform rule corresponds to the multi-choice Equal division value and the Mixed rules to the multi-choice Egalitarian Shapley values. Both values are introduced by Lowing and Techer (2022). Moreover, for each distribution problem, the multi-choice Shapley value of the corresponding distribution game is in its Core (in the sense of Grabisch and Xie, 2007).…”

“…This section presents several solution concepts for multi-choice games and compare them with the rules of Section 3. First, we present the multi-choice Shapley value as introduced by Lowing and Techer (2022) for multi-choice games. To that end, we must present a certain coalition formation process.…”