Convergence of Local Dynamics to Balanced Outcomes in Exchange Networks

Bargaining games on exchange networks have been studied by both economists and sociologists. A Balanced Outcome for such a game is an equilibrium concept that combines notions of stability and fairness. In a recent paper, Kleinberg and Tardos introduced balanced outcomes to the computer science community and provided a polynomial-time algorithm to compute the set of such outcomes. Their work left open a pertinent question: are there natural, local dynamics that converge quickly to a balanced outcome? In this paper, we provide a partial answer to this question by showing that simple edge-balancing dynamics converge to a balanced outcome whenever one exists.

[1]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[2]  J. Davenport.  Editor , 1960 .

[3]  L. Shapley,et al.  The assignment game I: The core , 1971 .

[4]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[5]  K. Cook,et al.  Power, Equity and Commitment in Exchange Networks , 1978 .

[6]  Bengt Aspvall,et al.  A Polynomial Time Algorithm for Solving Systems of Linear Inequalities with Two Variables per Inequality , 1980, SIAM J. Comput..

[7]  K. Cook,et al.  The Distribution of Power in Exchange Networks: Theory and Experimental Results , 1983, American Journal of Sociology.

[8]  Sharon C. Rochford,et al.  Symmetrically pairwise-bargained allocations in an assignment market , 1984 .

[9]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[10]  Karen S. Cook,et al.  Power in exchange networks: a power-dependence formulation , 1992 .

[11]  Theo S. H. Driessen.  A note on the inclusion of the kernel in the core of the bilateral assignment game , 1998, Int. J. Game Theory.

[12]  David Willer.  Network Exchange Theory , 1999 .

[13]  S. Griffis.  EDITOR , 1997, Journal of Navigation.

[14]  Margarida Corominas-Bosch,et al.  Bargaining in a network of buyers and sellers , 2004, J. Econ. Theory.

[15]  Devavrat Shah,et al.  Maximum weight matching via max-product belief propagation , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[16]  Steve Chien,et al.  Convergence to approximate Nash equilibria in congestion games , 2007, SODA '07.

[17]  Dmitry M. Malioutov,et al.  Linear programming analysis of loopy belief propagation for weighted matching , 2007, NIPS.

[18]  Yossi Azar,et al.  Fast convergence to nearly optimal solutions in potential games , 2008, EC '08.

[19]  V. Mirrokni,et al.  Uncoordinated two-sided matching markets , 2008, EC '08.

[20]  C. Borgs,et al.  On the exactness of the cavity method for weighted b-matchings on arbitrary graphs and its relation to linear programs , 2008, 0807.3159.

[21]  Éva Tardos,et al.  Balanced outcomes in social exchange networks , 2008, STOC.

[22]  Vahab S. Mirrokni,et al.  Uncoordinated two-sided matching markets , 2009, SECO.

[23]  Dimitri P. Bertsekas,et al.  Auction Algorithms , 2009, Encyclopedia of Optimization.