Compensations in the Shapley value and the compensation solutions for graph games

Autor: Philippe Solal, Sylvain Béal, Eric Rémila
Přispěvatelé: Groupe d'analyse et de théorie économique (GATE Lyon Saint-Étienne), École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-École normale supérieure - Lyon (ENS Lyon), Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne (GATE Lyon Saint-Étienne), École normale supérieure de Lyon (ENS de Lyon)-Université Lumière - Lyon 2 (UL2)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Centre de REcherches sur les Stratégies Economiques (EA 3190) (CRESE), Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Beudon, Soledad, Centre de REcherches sur les Stratégies Economiques (UR 3190) (CRESE), Centre de REcherches sur les Stratégies Economiques - UFC ( CRESE ), Université Bourgogne Franche-Comté ( UBFC ) -Université de Franche-Comté ( UFC ), Groupe d'analyse et de théorie économique ( GATE Lyon Saint-Étienne ), École normale supérieure - Lyon ( ENS Lyon ) -Université Lumière - Lyon 2 ( UL2 ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de l'Informatique du Parallélisme ( LIP ), École normale supérieure - Lyon ( ENS Lyon ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS )
Rok vydání: 2011
Předmět:
game theory
Statistics and Probability
Computer Science::Computer Science and Game Theory
Economics and Econometrics
BFS
0211 other engineering and technologies
Compensations
théorie des jeux
02 engineering and technology
DFS
Grand coalition
Relative fairness
Mathematics (miscellaneous)
0502 economics and business
[ SHS.ECO ] Humanities and Social Sciences/Economies and finances
Shapley value
050207 economics
[SHS.ECO] Humanities and Social Sciences/Economics and Finance
ComputingMilieux_MISCELLANEOUS
Axiom
Mathematics
jel:C71
021103 operations research
Spanning tree
05 social sciences
[SHS.ECO]Humanities and Social Sciences/Economics and Finance
Graph
Equal surplus division
JEL: C - Mathematical and Quantitative Methods/C.C7 - Game Theory and Bargaining Theory
Statistics
Probability and Uncertainty
JEL : C - Mathematical and Quantitative Methods/C.C7 - Game Theory and Bargaining Theory
compensations
relative fairness
compensation solution
equal surplus division
Mathematical economics
Compensation solutions
Social Sciences (miscellaneous)
MathematicsofComputing_DISCRETEMATHEMATICS
Zdroj: First International Workshop "Models of Influence and Network theory"
First International Workshop "Models of Influence and Network theory", Feb 2010, Lyon, France
Séminaire CREM-Université de Caen
Séminaire CREM-Université de Caen, Jan 2010, Caen, France
International Journal of Game Theory
International Journal of Game Theory, Springer Verlag, 2012, 41 (1), pp.157-178. ⟨10.1007/s00182-011-0277-7⟩
International Journal of Game Theory, 2012, 41 (1), pp.157-178. ⟨10.1007/s00182-011-0277-7⟩
European Conference on Complex Systems (ECCS)
European Conference on Complex Systems (ECCS), Sep 2010, Lisbonne, Portugal
International Journal of Game Theory, Springer Verlag, 2012, 41 (1), pp.157-178. 〈10.1007/s00182-011-0277-7〉
ISSN: 1432-1270
0020-7276
DOI: 10.1007/s00182-011-0277-7
Popis: We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give a representation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph in order to construct new allocation rules called the compensation solutions. Firstly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees (see Demange, J Political Econ 112:754–778, 2004) instead of orderings of the players by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively. Secondly, we consider cooperative games with a forest (cycle-free graph) and all its rooted spanning trees. The compensation solution is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component in the communication graph.
Databáze: OpenAIRE
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