Abstract
Different from the multi-choice extension of the equal allocation of nonseparable costs (EANSC) due to Liao (Econ Bull 3:1–8, 2008), this paper proposes an alternative extension of the EANSC on multi-choice transferable-utility (TU) games. It turns out that the EANSC of a multi-choice TU game coincides with the EANSC of a corresponding “replicated” TU game. Further, we introduce an extended reduced game to characterize this extended EANSC by means of related consistency. Based on the reduced games, a dynamic process is also proposed.
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Notes
Formally, the definition of a payoff vector should be as follows. Denote \(M=\{(i,j) | i\in N,j \in M_i \}\). A payoff vector of (N, v) is a function \({x:M \rightarrow \mathbb{R}},\) where, for all \(i\in N\) and \(j\in M_i \backslash \{0\}, x_{ij}\) denotes the increase in payoff to player i corresponding to a change of activity from level j − 1 to level j by this player and x i0 = 0 for all \(i\in N\).
Without loss of generality, we can assume that S(m) = N.
The technique of the proof can be found in Hart and Mas-Colell (1989), p. 599.
λ is a fixed positive number, which reflects the assumption that player i does not ask for full correction (when λ = 1) but only (usually) a fraction of it.
See Moulin (1985).
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The author is grateful to the editor, the associate editor and the anonymous referees for very helpful suggestions and comments.
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Liao, YH. The duplicate extension for the equal allocation of nonseparable costs. Oper Res Int J 13, 385–397 (2013). https://doi.org/10.1007/s12351-012-0127-9
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DOI: https://doi.org/10.1007/s12351-012-0127-9