2012/07/19 by Aleš Kuběna, Kubena, Ales Antonin, Peter Franek +1
Computer Science · #05A15 #20B35 #91A12 #91A46 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1207.4738
openalex publication_date 2012/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≤ Sn. 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).