Symmetries of Quasi-Values

0398169 - ÚTIA 2014 RIV DE eng C - Conference Paper (international conference)
Kuběna, Aleš Antonín - Franek, P.
Symmetries of Quasi-Values.
Algorithmic Game Theory - 6th International Symposium, SAGT 2013. Berlin: Springer, 2013, s. 159-170. Lecture Notes in Computer Science, 8146. ISBN 978-3-642-41391-9. ISSN 0302-9743.
[Symposium of Algorithmic Game Theory. Aachen (DE), 21.10.2013-25.10.2013]
R&D Projects: GA MŠMT OC10048; GA ČR(CZ) GBP402/12/G097
Institutional support: RVO:67985556
Keywords : Cooperative game * Shapley value * Group theory * Equity * Symmetry * Quasi value
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2013/E/kubena-0398169.pdf

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).
Permanent Link: http://hdl.handle.net/11104/0226009