research-article

A coalitional value for games on convex geometries with a coalition structure

Authors:

Qiang ZhangAuthors Info & Claims

Applied Mathematics and Computation, Volume 266, Issue C

Pages 605 - 614

https://doi.org/10.1016/j.amc.2015.05.110

Published: 01 September 2015 Publication History

Abstract

With respect to games on convex geometries with a coalition structure, a coalitional value named the generalized symmetric coalitional Banzhaf value is defined, which can be seen as an extension of the symmetric coalitional Banzhaf value given by Alonso-Meijide and Fiestrs-Janeiro and the Shapley value for games on convex geometries introduced by Bilbao. Based on the established axiomatic system, the existence and uniqueness of the given coalitional value is shown. Meanwhile, a special case is briefly studied.

References

[1]

Z. Wang, A. Szolnoki, M. Perc, Interdependent network reciprocity in evolutionary games, Sci. Rep., 3 (2013) 1183.

[2]

Z. Wang, A. Szolnoki, M. Perc, Optimal interdependence between networks for the evolution of cooperation, Sci. Rep., 3 (2013) 2470.

[3]

Z. Wang, A. Szolnoki, M. Perc, Rewarding evolutionary fitness with links between populations promotes cooperation, J. Theor. Biol., 349 (2014) 50-56.

[4]

Z. Wang, M. Perc, Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game, Phys. Rev. E, 82 (2010) 021115.

[5]

M. Perc, Z. Wang, Heterogeneous aspirations promote cooperation in the prisoner's dilemma game, Plos One, 5 (2010) e15117.

[6]

A. Szolnoki, Z. Wang, M. Perc, Wisdom of groups promote cooperation in evolutionary social dilemmas, Sci. Rep, 2 (2012) 576.

[7]

S. Boccaletti, G. Bianconi, R. Criado, C.I. Del Genio, J. Gómez-Gardeñes, M. Romance, The structure and dynamics of multilayer networks, Phy. Rep., 544 (2014) 1-122.

[8]

Z. Wang, L. Wang, M. Perc, Degree mixing in multilayer networks impedes the evolution of cooperation, Phys. Rev. E, 89 (2014) 052813.

[9]

Z. Wang, A. Szolnoki, M. Perc, Evolution of public cooperation on interdependent networks: The impact of biased utility functions, EPL-Europhys. Lett., 97 (2012) 48001.

[10]

X. Deng, Z. Wang, Q. Liu, Y. Deng, S. Mahadevan, A belief-based evolutionarily stable strategy, J. Theor. Biol., 361 (2014) 81-86.

[11]

M. Perc, P. Grigolini, Collective behavior and evolutionary games-an introduction, Chaos Soliton Fract., 56 (2013) 1-5.

[12]

M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L.M. Floría, Y. Moreno, Evolutionary dynamics of group interactions on structured populations: a review, J. R. Soc. Interface, 10 (2013) 20120997.

[13]

Z. Wang, A. Szolnoki, M. Perc, Self-organization towards optimally interdependent networks by means of coevolution, New J. Phys., 16 (2014) 033041.

[14]

M. Perc, A. Szolnoki, Coevolutionary games - a mini review, BioSyst., 99 (2010) 109-125.

[15]

R. Aumann, J. Dreze, Cooperative games with a coalition structure, Int. J. Game Theory, 3 (1974) 217-237.

[16]

G. Owen, Values of games with a priori unions, in: Lecture Notes in Economics and Mathematical Systems, Essays in Honor of Oskar Morgenstern, Springer Verlag, Nueva York, 1977.

[17]

G. Owen, Characterization of the Banzhaf-Coleman index, SIAM J. Appl. Math., 35 (1978) 315-327.

[18]

J.M. Alonso-Meijde, M.G. Fiestras-Janeiro, Modification of the Banzhaf value for games with a coalition structure, Ann. Oper. Res., 109 (2002) 213-227.

[19]

M.J. Albizuri, Axiomatizations of the Owen value without efficiency, Math. Soc. Sci., 55 (2008) 78-89.

[20]

G. Hamiache, A new axiomatization of the Owen value for games with a coalition structure, Math. Soc. Sci., 37 (1999) 281-305.

[21]

A.B. Khmelnitskaya, E.B. Yanovskaya, Owen coalitional value without additivity axiom, Math. Meth. Oper. Res., 66 (2007) 255-261.

[22]

R. Amer, F. Carreras, J.M. Gimenez, The modified Banzhaf value for games with coalition structure: an axiomatic characterization, Math. Soc. Sci., 43 (2002) 45-54.

[23]

J.M. Alonso-Meijide, F. Carreras, M.G. Fiestras-Janeiro, G. Owen, A comparative axiomatic characterization of the Banzhaf-Owen coalitional value, Decis. Support Syst., 43 (2007) 701-712.

Digital Library

[24]

M.J. Albizuri, The multichoice coalition value, Ann. Oper. Res., 172 (2009) 363-374.

[25]

F.Y. Meng, Q. Zhang, A coalitional value for multichoice games with a coalition structure, Appl. Math. Inform. Sci., 8 (2014) 193-203.

[26]

F.Y. Meng, C.Q. Tan, Q. Zhang, The generalized symmetric coalitional Banzhaf value for multichoice games with a coalition structure, J. Syst. Sci. Complex., 27 (2014) 1064-1078.

[27]

R.B. Myerson, Graphs and cooperation in games, Meth. Oper. Res., 2 (1977) 225-229.

Digital Library

[28]

U. Faigle, W. Kern, The Shapley value for cooperative games under precedence constraints, Int. J. Game Theory, 21 (1992) 249-266.

[29]

R.P. Gilles, G. Owen, Cooperative games and disjunctive permission structures, Tilburg University, Tilburg The Netherlands, 1999.

[30]

R.P. Gilles, G. Owen, J.R. van den Brink, Games with permission structures: the conjunctive approach, Int. J. Game Theory, 20 (1992) 277-293.

Digital Library

[31]

J.M. Bilbao, Axioms for the Shapley value on convex geometries, Eur. J. Oper. Res., 110 (1998) 368-376.

[32]

J.M. Bilbao, T.S.H. Driessen, A.J. Losada, E. Lebron, The Shapley value for games on matroids: the static model, Math. Meth. Oper. Res., 53 (2001) 333-348.

[33]

J.M. Bilbao, T.S.H. Driessen, A.J. Losada, E. Lebron, The Shapley value for games on matroids: the dynamic model, Math. Meth. Oper. Res., 56 (2002) 287-301.

[34]

E. Algaba, J.M. Bilbao, R. van den Brink, A.J. Losada, Axiomatizations of the Shapley value for cooperative games on antimatroids, Math. Meth. Oper. Res., 57 (2003) 49-65.

[35]

J.M. Bilbao, Cooperative games under augmenting systems, SIAM J. Dis. Math., 17 (2004) 122-133.

Digital Library

[36]

F.Y. Meng, Q. Zhang, Cooperative games on convex geometries with a coalition structure, J. Syst. Sci. Complex., 25 (2012) 909-925.

[37]

J.M. Bilbao, P.H. Edelman, The Shapley value on convex geometries, Dis. Appl. Math., 103 (2000) 33-40.

Digital Library

[38]

J.M. Bilbao, A. Jimenez, J.J. Lopez, The Banzhaf power index on convex geometries, Math. Soc. Sci., 36 (1998) 157-173.

[39]

P.H. Edelman, R.E. Jamison, The theory of convex geometries, Geometriae Dedicata, 19 (1985) 247-270.

Cited By

Tang JLi ZMeng F(2023)Quasi-Owen Value for Games on Augmenting Systems with a Coalition StructureInformatica10.15388/23-INFOR52434:3(635-663)Online publication date: 25-Aug-2023
https://dl.acm.org/doi/10.15388/23-INFOR524
Yu XZhou HZhang XZhang QLiu YPang J(2017)The fuzzy bargaining set of cooperative game with fuzzy coalitionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-16241733:3(1757-1765)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-162417

Recommendations

Impartial achievement games on convex geometries
Abstract
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able ...
Shapley, Owen and Aumann---Dreze values in a patrolling game with coalition structure

This paper considers a simple model of a cooperative patrolling game with coalition structure. It is shown that the Shapley value coincides with the Owen and Aumann---Dreze values under an odd number of defenders.
Uncertain coalition structure game with payoff of belief structure
Abstract
The uncertain coalition structure game with payoff of belief structure (UCS game) is studied based on belief structures of D–S theory. This type of UCS games gives us the uncertainty by assigning the probability to the set composed of ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Applied Mathematics and Computation

Applied Mathematics and Computation Volume 266, Issue C

September 2015

1177 pages

ISSN:0096-3003

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 September 2015

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 27 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Tang JLi ZMeng F(2023)Quasi-Owen Value for Games on Augmenting Systems with a Coalition StructureInformatica10.15388/23-INFOR52434:3(635-663)Online publication date: 25-Aug-2023
https://dl.acm.org/doi/10.15388/23-INFOR524
Yu XZhou HZhang XZhang QLiu YPang J(2017)The fuzzy bargaining set of cooperative game with fuzzy coalitionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-16241733:3(1757-1765)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-162417

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents