Distributed Bargaining in Dyadic-Exchange Networks

This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provably correct continuous-time algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having the dynamics for finding stable outcomes feeding into the one for finding balanced ones. Our technical approach to establish convergence and robustness combines notions and tools from optimization, graph theory, nonsmooth analysis, and Lyapunov stability theory and provides a useful framework for further extensions. We illustrate our results in a wireless communication scenario where single-antenna devices have the possibility of working as 2-antenna virtual devices to improve channel capacity.

[1]  Xiang Cheng,et al.  Cooperative MIMO channel models: A survey , 2010, IEEE Communications Magazine.

[2]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[3]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[4]  Yashodhan Kanoria,et al.  Bargaining dynamics in exchange networks , 2010, J. Econ. Theory.

[5]  Dimitri P. Bertsekas,et al.  Network optimization : continuous and discrete models , 1998 .

[6]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[7]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[8]  Jorge Cortés Monforte.  Geometric, control and numerical aspects of nonholonomic systems , 2002 .

[9]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[10]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[11]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[12]  Chinwendu Enyioha,et al.  Optimal Resource Allocation for Network Protection: A Geometric Programming Approach , 2013, ArXiv.

[13]  Chinwendu Enyioha,et al.  Optimal Resource Allocation for Network Protection Against Spreading Processes , 2013, IEEE Transactions on Control of Network Systems.

[14]  Jorge Cortés,et al.  Robust Distributed Linear Programming , 2014, IEEE Transactions on Automatic Control.

[15]  Iven M. Y. Mareels,et al.  Control of Large-Scale Irrigation Networks , 2007, Proceedings of the IEEE.

[16]  Chai-Keong Toh,et al.  Ad hoc mobile wireless networks : protocols and systems , 2002 .

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

[18]  Jorge Cortés,et al.  Optimal leader allocation in UAV formation pairs ensuring cooperation , 2013, Autom..

[19]  Amit K. Roy-Chowdhury,et al.  Distributed Camera Networks , 2011, IEEE Signal Processing Magazine.

[20]  Mohsen Guizani,et al.  A Cooperation Strategy Based on Nash Bargaining Solution in Cooperative Relay Networks , 2008, IEEE Transactions on Vehicular Technology.

[21]  Yuval Peres,et al.  Convergence of Local Dynamics to Balanced Outcomes in Exchange Networks , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[22]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

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

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

[25]  Giuseppe Notarstefano,et al.  A distributed simplex algorithm for degenerate linear programs and multi-agent assignments , 2012, Autom..

[26]  Rakesh Nagi,et al.  Data mining in an engineering design environment: OR applications from graph matching , 2006, Comput. Oper. Res..

[27]  Walid Saad,et al.  Author manuscript, published in "IEEE Transactions on Wireless Communications (2009) Saad-ITransW-2009" A Distributed Coalition Formation Framework for Fair User Cooperation in Wireless Networks , 2022 .

[28]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[29]  Nicole Immorlica,et al.  The Cooperative Game Theory Foundations of Network Bargaining Games , 2010, ICALP.

[30]  Michael Chertkov,et al.  Synchronization in complex oscillator networks and smart grids , 2012, Proceedings of the National Academy of Sciences.

[31]  Jorge Cortés,et al.  Distributed linear programming and bargaining in exchange networks , 2013, 2013 American Control Conference.

[32]  Milos S. Stankovic,et al.  Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks , 2012, IEEE Transactions on Automatic Control.

[33]  Zhu Han,et al.  Coalitional game theory for communication networks , 2009, IEEE Signal Processing Magazine.

[34]  Tanmoy Chakraborty,et al.  A behavioral study of bargaining in social networks , 2010, EC '10.