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Partially symmetric values. (English) Zbl 1073.91509
Summary: We consider spaces of differentiable nonatomic and mixed vector measure games, \(pNA\) and \(pM\), with finitely or countably many types of players. Type-symmetric values on these spaces of games are investigated (all Aumann and Shapley conditions except symmetry are assumed, the latter being replaced by a weaker assumption of covariance under automorphisms of the space of players that preserve each type). We show that if the types are uncountable, then type-symmetric values are random path values. In particular, the symmetric values on \(pM\) are characterized as mixtures of values defined in Hart (1973).

91A12 Cooperative games
91A06 \(n\)-person games, \(n>2\)
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