Two solution concepts for TU games with cycle-free directed cooperation structures

A. Khmelnitskaya, A.J.J. Talman

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of this player together with his successors minus what these successors receive. It implies that every coalition of players consisting of one of the players with all his successors receives precisely its worth. Additionally their efficiency and stability are studied. Simple recursive algorithms to calculate the values are also provided. The application to the water distribution problem of a river with multiple sources, a delta and possibly islands is considered.
Original languageEnglish
Title of host publicationProceedings of the 4th International Conference Game Theory and Management
EditorsL.A. Petrosyan, N.A. Zenkevich
Place of PublicationSt Petersburg
PublisherGraduate School of Management, SPbU
Pages241-265
VolumeIV
ISBN (Print)9785992400694
Publication statusPublished - 2011

Publication series

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VolumeIV

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Directed graphs
Rivers
Water

Cite this

Khmelnitskaya, A., & Talman, A. J. J. (2011). Two solution concepts for TU games with cycle-free directed cooperation structures. In L. A. Petrosyan, & N. A. Zenkevich (Eds.), Proceedings of the 4th International Conference Game Theory and Management (Vol. IV, pp. 241-265). St Petersburg: Graduate School of Management, SPbU.
Khmelnitskaya, A. ; Talman, A.J.J. / Two solution concepts for TU games with cycle-free directed cooperation structures. Proceedings of the 4th International Conference Game Theory and Management. editor / L.A. Petrosyan ; N.A. Zenkevich. Vol. IV St Petersburg : Graduate School of Management, SPbU, 2011. pp. 241-265
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Khmelnitskaya, A & Talman, AJJ 2011, Two solution concepts for TU games with cycle-free directed cooperation structures. in LA Petrosyan & NA Zenkevich (eds), Proceedings of the 4th International Conference Game Theory and Management. vol. IV, Graduate School of Management, SPbU, St Petersburg, pp. 241-265.

Two solution concepts for TU games with cycle-free directed cooperation structures. / Khmelnitskaya, A.; Talman, A.J.J.

Proceedings of the 4th International Conference Game Theory and Management. ed. / L.A. Petrosyan; N.A. Zenkevich. Vol. IV St Petersburg : Graduate School of Management, SPbU, 2011. p. 241-265.

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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AB - For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of this player together with his successors minus what these successors receive. It implies that every coalition of players consisting of one of the players with all his successors receives precisely its worth. Additionally their efficiency and stability are studied. Simple recursive algorithms to calculate the values are also provided. The application to the water distribution problem of a river with multiple sources, a delta and possibly islands is considered.

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Khmelnitskaya A, Talman AJJ. Two solution concepts for TU games with cycle-free directed cooperation structures. In Petrosyan LA, Zenkevich NA, editors, Proceedings of the 4th International Conference Game Theory and Management. Vol. IV. St Petersburg: Graduate School of Management, SPbU. 2011. p. 241-265