  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 heart of our
results uses a linear-programming formulation to establish a novel connection
between well-studied cooperative game theory concepts (such as core and
prekernel) and the solution concepts of stable and balanced 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 [29] and also 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.
