An algorithm for finding the nucleolus of assignment games
International Journal of Game Theory
The Geometry of Fractional Stable Matchings and its Applications
Mathematics of Operations Research
Core and monotonic allocation methods
International Journal of Game Theory
The nucleolus is not aggregate-monotonic on the domain of convex games
International Journal of Game Theory
Solving convex programs by random walks
Journal of the ACM (JACM)
Approximating the centroid is hard
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Balanced outcomes in social exchange networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The cooperative game theory foundations of network bargaining games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Local dynamics in bargaining networks via random-turn games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Optimizing social welfare for network bargaining games in the face of unstability, greed and spite
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Bargaining for revenue shares on tree trading networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We study bargaining networks, discussed in a recent paper of Kleinberg and Tardos [KT08], from the perspective of cooperative game theory. In particular we examine three solution concepts, the nucleolus, the core center and the core median. All solution concepts define unique solutions, so they provide testable predictions. We define a new monotonicity property that is a natural axiom of any bargaining game solution, and we prove that all three of them satisfy this monotonicity property. This is actually in contrast to the conventional wisdom for general cooperative games that monotonicity and the core condition (which is a basic property that all three of them satisfy) are incompatible with each other. Our proofs are based on a primal-dual argument (for the nucleolus) and on the FKG inequality (for the core center and the core median). We further observe some qualitative differences between the solution concepts. In particular, there are cases where a strict version of our monotonicity property is a natural axiom, but only the core center and the core median satisfy it. On the other hand, the nucleolus is easy to compute, whereas computing the core center or the core median is #P-hard (yet it can be approximated in polynomial time).