Alex

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: Generalized Stable Matching in Bipartite Networks

  Ankur Mani, Asuman Ozdaglar, Alex, Pentland
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  ABSTRACT: In this paper we study the generalized version of weighted matching in bipartite networks. Consider a weighted matching in a bipartite network in which the nodes derive value from the split of the matching edge assigned to them if they are matched. The value a node derives from the split depends both on the split as well as the partner the node is matched to. We assume that the value of a split to the node is continuous and strictly increasing in the part of the split assigned to the node. A stable weighted matching is a matching and splits on the edges in the matching such that no two adjacent nodes in the network can split the edge between them so that both of them can derive a higher value than in the matching. We extend the weighted matching problem to this general case and study the existence of a stable weighted matching. We also present an algorithm that converges to a stable weighted matching. The algorithm generalizes the Hungarian algorithm for bipartite matching. Faster algorithms can be made when there is more structure on the value functions.
  11/2010;
• Source

  Available from: ArXiv

  Article: Existence of Stable Exclusive Bilateral Exchanges in Networks

  Ankur Mani, Asuman Ozdaglar, Alex, Pentland
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  ABSTRACT: In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that no individual breaks her partnership and no two neighbors in the network can form a new partnership while breaking other partnerships if any so that at least one of them improves her payoff and the other one does at least as good. We consider a general class of continuous, strictly convex and strongly monotone preferences over bundles of goods for individuals. Thus, this work extends the general equilibrium framework from markets to networks with exclusive exchanges. We present the complete existence proof using the existence of a generalized stable matching in \cite{Generalized-Stable-Matching}. The existence proof can be extended to problems in social games as in \cite{Matching-Equilibrium} and \cite{Social-Games}.
  11/2010;