Abstract
According to Shapley’s game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with respect to arbitrary permutations of players. We analyze the consequences of weakening the symmetry axioms and study quasi-values that are symmetric with respect to permutations from a group G ≤ S n . We classify all the permutation groups G that are large enough to assure a unique G-symmetric quasi-value, as well as the structure and dimension of the space of all such quasi-values for a general permutation group G.
We show how to construct G-symmetric quasi-values algorithmically by averaging certain basic quasi-values (marginal operators).
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Kubena, A.A., Franek, P. (2013). Symmetries of Quasi-Values. In: Vöcking, B. (eds) Algorithmic Game Theory. SAGT 2013. Lecture Notes in Computer Science, vol 8146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41392-6_14
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DOI: https://doi.org/10.1007/978-3-642-41392-6_14
Publisher Name: Springer, Berlin, Heidelberg
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