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B.1 Convention In this Appendix we shall use the terminology and notation of § 6.2. By ‘CF’ we shall always mean CF of some SVG (rather than a more general cooperative game). We shall attribute various properties of SVGs to their respective CFs. Thus, for example, when we say that a CF is proper we mean that its SVG is proper.1 Similarly, we shall attribute various pieces of furniture of an SVG to its CF. Thus, for example, by the assembly of a CF we mean the assembly of its SVG. We shall always denote a CF and its SVG by corresponding letters, possibly with affixes. So, for example, if we denote a CF by ‘wM ’, the reader should take it for granted that ‘WM ’ denotes its SVG. The characterization Thms. 6.2.14 and 6.2.15 fail if we replace the class of all games (or all superadditive games) on N by the class of CFs (or proper CFs) with assembly N . We shall illustrate this for the case n = 3, although counter-examples can be found for any n > 2. B.2 Example Let G be the class of all CFs with assembly I3 = {1, 2, 3}. Let ξ be any value assignment such that ξa (w) = βa [W] for all w ∈ G. 1 As we noted in Rem. 6.2.2(ii), this amounts to saying that the CF is superadditive. 299 300 B. Axiomatic Characterizations It is easy to see that ξ is iso-invariant, efficient and vanishes for dummies on G (cf....