Abstract
We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus are represented by weighted edges in our bipartite network. Each agent in the market is additionally limited by a capacity representing the number of contracts which he or she may undertake. When all agents are limited to just one contract each, prior research applied natural generalizations of the Nash bargaining solution to the networked setting, defined the new solution concepts of stable and balanced, and characterized the resulting bargaining outcomes. We simplify and generalize these results to a setting in which participants in only one side of the market are limited to one contract each. The core of our results uses a linear-programming formulation to establish a novel connection between well-studied cooperative game theory concepts and the solution concepts of core and prekernel defined for the bargaining games. This immediately implies one can take advantage of the results and algorithms in cooperative game theory to reproduce results such as those of Azar et al. [1] and Kleinberg and Tardos [28] and generalize them to our setting. The cooperative-game-theoretic connection also inspires us to refine our solution space using standard solution concepts from that literature such as nucleolus and lexicographic kernel. The nucleolus is particularly attractive as it is unique, always exists, and is supported by experimental data in the network bargaining literature. Guided by algorithms from cooperative game theory, we show how to compute the nucleolus by pruning and iteratively solving a natural linear-programming formulation.
The full version of this extended abstract is available as [3], which contains all the missing proofs as well as more discussion about the results.
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Bateni, M., Hajiaghayi, M., Immorlica, N., Mahini, H. (2010). The Cooperative Game Theory Foundations of Network Bargaining Games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_7
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