0398169 20240103203203.620140314235959.9 84892936168 000333972500014 10.1007/978-3-642-41392-6_14 12 s. P cav_un_epca*0398534978-3-642-41391-90302-9743159-170BerlinSpringer2013 Cooperative game Shapley value Group theory Equity Symmetry Quasi value cav_un_auth*0264564 Kuběna Aleš Antonín Ekonometrie Department of Econometrics E E UTIA-B Department of Econometrics Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0045564 Franek P. CZ http://library.utia.cas.cz/separaty/2013/E/kubena-0398169.pdf OC10048 GA MŠk cav_un_auth*0263621 GBP402/12/G097 GA ČR CZ cav_un_auth*0281000 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). cav_un_auth*0295562 Symposium of Algorithmic Game Theory Aachen 21.10.2013-25.10.2013 DE 2014 BA 2 PR BD RVO:67985556 http://hdl.handle.net/11104/0226009 cav_un_auth*0300911 ČVUT České vysoké učení technické v Praze, Fakulta informačních technologií CZ S 100 0.325 16.75 0.51 Q2 Q3 2013 84892936168 SCOPUS 000333972500014 WOS cav_un_epca*0398534 Algorithmic Game Theory - 6th International Symposium, SAGT 2013 978-3-642-41391-9 0302-9743 159 170 Berlin Springer 2013 Lecture Notes in Computer Science 8146