Capacitated Network Bargaining Games: Stability and Structure (2311.09904v3)
Abstract: Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit-weight instances of this problem (that is, ensure that they admit a stable outcome) via capacity-reduction and edge-removal operations, without decreasing the total value that the players can get. Furthermore, for general weighted instances, we show that computing a minimum amount of vertex-capacity to reduce to make an instance stable is a polynomial-time solvable problem. We then exploit this to give approximation results for the NP-hard problem of stabilizing a graph via edge-removal operations. Our work extends and generalizes previous results in the literature that dealt with a unit-capacity version of the problem, using several new arguments. In particular, while previous results mainly used combinatorial techniques, we here rely on polyhedral arguments and, more specifically, on the notion of circuits of a polytope.
- Stabilizing network bargaining games by blocking players. Mathematical Programming, 172:249–275, 2018.
- A bidirected generalization of network matrices. Networks, 47(4):185–198, 2006.
- The cooperative game theory foundations of network bargaining games, 2010.
- On solution concepts for matching games. In Jan Kratochvíl, Angsheng Li, Jiří Fiala, and Petr Kolman, editors, Theory and Applications of Models of Computation, pages 117–127, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg.
- Finding small stabilizers for unstable graphs. Mathematical Programming, 154:173–196, 2015.
- Karthekeyan Chandrasekaran. Graph Stabilization: A Survey, pages 21–41. Springer Singapore, 2017.
- Additive stabilizers for unstable graphs. Discrete Optimization, 31:56–78, 2019.
- Pivot rules for circuit-augmentation algorithms in linear optimization. SIAM Journal on Optimization, 32(3):2156–2179, 2022.
- Elisabeth Finhold. Circuit diameters and their application to transportation problems. PhD thesis, Technische Universität München, 2014.
- Stabilization of capacitated matching games, 2022. arXiv:2211.12179.
- Corinna Gottschalk. Personal communication, 2018.
- Efficient stabilization of cooperative matching games. Theoretical Computer Science, 677:69–82, 2017.
- Balanced outcomes in social exchange networks. In Proceedings of the 40th STOC, pages 295–304, 2008.
- Stabilizing weighted graphs. Mathematics of Operations Research, 45(4):1318–1341, 2020.
- Network bargaining: Using approximate blocking sets to stabilize unstable instances. In Maria Serna, editor, Algorithmic Game Theory, pages 216–226, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg.
- John F. Nash. The bargaining problem. Econometrica, 18:155–162, 1950.
- Laura Sanità. The diameter of the fractional matching polytope and its hardness implications. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 910–921, 2018.
- Alexander Schrijver. Combinatorial Optimization. Springer, 2003.
- Laura Sanità (28 papers)
- Lucy Verberk (4 papers)