Combinatorial optimization games
Abstract
We introduce a general integer programming formulation for a class of combinatorial optimization games, which immediately allows us to improve the algorithmic result for finding amputations in the core (an important solution concept in cooperative game theory) of the network flow game on simple networks by Kalai and Zemel. An interesting result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several interesting problems, and apply them to resolve algorithmic and complexity issues for their cores along the line as put forward in: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation x, test whether x is in the core. We also explore the properties of totally balanced games in this succinct formulation of cooperative games.
- Authors:
-
- York Univ., North York, Ontario (Canada)
- Kyoto Univ. (Japan)
- Publication Date:
- OSTI Identifier:
- 471730
- Report Number(s):
- CONF-970142-
TRN: 97:001377-0080
- Resource Type:
- Conference
- Resource Relation:
- Conference: 8. annual Association for Computing Machinery (ACM)-Society for Industrial and Applied Mathematics (SIAM) symposium on discrete algorithms, New Orleans, LA (United States), 5-7 Jan 1997; Other Information: PBD: 1997; Related Information: Is Part Of Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms; PB: 798 p.
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; GAME THEORY; ALGORITHMS; DIAGRAMS; OPTIMIZATION; NETWORK ANALYSIS
Citation Formats
Deng, X, Ibaraki, Toshihide, and Nagamochi, Hiroshi. Combinatorial optimization games. United States: N. p., 1997.
Web.
Deng, X, Ibaraki, Toshihide, & Nagamochi, Hiroshi. Combinatorial optimization games. United States.
Deng, X, Ibaraki, Toshihide, and Nagamochi, Hiroshi. 1997.
"Combinatorial optimization games". United States.
@article{osti_471730,
title = {Combinatorial optimization games},
author = {Deng, X and Ibaraki, Toshihide and Nagamochi, Hiroshi},
abstractNote = {We introduce a general integer programming formulation for a class of combinatorial optimization games, which immediately allows us to improve the algorithmic result for finding amputations in the core (an important solution concept in cooperative game theory) of the network flow game on simple networks by Kalai and Zemel. An interesting result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several interesting problems, and apply them to resolve algorithmic and complexity issues for their cores along the line as put forward in: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation x, test whether x is in the core. We also explore the properties of totally balanced games in this succinct formulation of cooperative games.},
doi = {},
url = {https://www.osti.gov/biblio/471730},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jun 01 00:00:00 EDT 1997},
month = {Sun Jun 01 00:00:00 EDT 1997}
}