Social learning and bayesian games in multiagent signal processing: how do local and global decision makers interact?

How do local agents and global decision makers interact in statistical signal processing problems where autonomous decisions need to be made? When individual agents possess limited sensing, computation, and communication capabilities, can a network of agents achieve sophisticated global behavior? Social learning and Bayesian games are natural settings for addressing these questions. This article presents an overview, novel insights, and a discussion of social learning and Bayesian games in adaptive sensing problems when agents communicate over a network. Two highly stylized examples that demonstrate to the reader the ubiquitous nature of the models, algorithms, and analysis in statistical signal processing are discussed in tutorial fashion.

[1]  Leonidas J. Guibas,et al.  Collaborative signal and information processing: an information-directed approach , 2003 .

[2]  Ali H. Sayed,et al.  Signal Processing Theory and Methods [In the Spotlight] , 2011, IEEE Signal Process. Mag..

[3]  Vikram Krishnamurthy,et al.  Opportunistic file transfer over a fading channel: A POMDP search theory formulation with optimal threshold policies , 2006, IEEE Transactions on Wireless Communications.

[4]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[5]  Ness B. Shroff,et al.  Opportunistic transmission scheduling with resource-sharing constraints in wireless networks , 2001, IEEE J. Sel. Areas Commun..

[6]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[7]  H. Vincent Poor,et al.  A Collaborative Training Algorithm for Distributed Learning , 2009, IEEE Transactions on Information Theory.

[8]  Ulrich Rieder,et al.  Structural results for partially observed control models , 1991, ZOR Methods Model. Oper. Res..

[9]  A. Pavan,et al.  Dynamic Global Games of Regime Change: Learning, Multiplicity and Timing of Attacks , 2004 .

[10]  C. Anderson,et al.  Why do dominant personalities attain influence in face-to-face groups? The competence-signaling effects of trait dominance. , 2009, Journal of personality and social psychology.

[11]  P. Sørensen,et al.  Information aggregation in debate: who should speak first? ☆ , 2001 .

[12]  Vikram Krishnamurthy,et al.  Structured Threshold Policies for Dynamic Sensor Scheduling—A Partially Observed Markov Decision Process Approach , 2007, IEEE Transactions on Signal Processing.

[13]  Soummya Kar,et al.  Gossip Algorithms for Distributed Signal Processing , 2010, Proceedings of the IEEE.

[14]  Vikram Krishnamurthy,et al.  Quickest detection of market shocks in agent based models of the order book , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  Andrea Goldsmith,et al.  Principles of Cognitive Radio , 2012 .

[16]  Michael Vitale,et al.  The Wisdom of Crowds , 2015, Cell.

[17]  A. Shiryaev.  On Optimum Methods in Quickest Detection Problems , 1963 .

[18]  Gang George Yin,et al.  Decentralized Adaptive Filtering Algorithms for Sensor Activation in an Unattended Ground Sensor Network , 2008, IEEE Transactions on Signal Processing.

[19]  A. Cassandra,et al.  Exact and approximate algorithms for partially observable markov decision processes , 1998 .

[20]  H. Vincent Poor,et al.  Aggregating Large Sets of Probabilistic Forecasts by Weighted Coherent Adjustment , 2011, Decis. Anal..

[21]  S. Hart,et al.  A simple adaptive procedure leading to correlated equilibrium , 2000 .

[22]  Robert J. Weber,et al.  Distributional Strategies for Games with Incomplete Information , 1985, Math. Oper. Res..

[23]  V. Krishnamurthy.  Decentralized Activation in Dense Sensor Networks via Global Games , 2008, IEEE Transactions on Signal Processing.

[24]  William S. Lovejoy,et al.  Some Monotonicity Results for Partially Observed Markov Decision Processes , 1987, Oper. Res..

[25]  C. Chamley.  Rational Herds: Economic Models of Social Learning , 2003 .

[26]  S. Hart.  Adaptive Heuristics , 2005 .

[27]  S. Karlin,et al.  Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions , 1980 .

[28]  Vikram Krishnamurthy,et al.  Decentralized Activation in a ZigBee-enabled Unattended Ground Sensor Network: A Correlated Equilibrium Game Theoretic Analysis , 2007, 2007 IEEE International Conference on Communications.

[29]  Asuman E. Ozdaglar,et al.  Opinion Dynamics and Learning in Social Networks , 2010, Dyn. Games Appl..

[30]  Vikram Krishnamurthy.  Decentralized Spectrum Access Amongst Cognitive Radios—An Interacting Multivariate Global Game-Theoretic Approach , 2009, IEEE Transactions on Signal Processing.

[31]  Munther A. Dahleh,et al.  Preliminary results on social learning with partial observations , 2007, ValueTools '07.

[32]  S. Athey.  Monotone Comparative Statics under Uncertainty , 2002 .

[33]  Yang Xiao,et al.  A Survey of Energy-Efficient Scheduling Mechanisms in Sensor Networks , 2006, Mob. Networks Appl..

[34]  Vikram Krishnamurthy,et al.  Quickest Detection POMDPs With Social Learning: Interaction of Local and Global Decision Makers , 2010, IEEE Transactions on Information Theory.

[35]  Shashi Phoha,et al.  Self-organizing sensor networks for integrated target surveillance , 2006, IEEE Transactions on Computers.

[36]  M. Avellaneda,et al.  High-frequency trading in a limit order book , 2008 .

[37]  Vikram Krishnamurthy,et al.  Bayesian Sequential Detection With Phase-Distributed Change Time and Nonlinear Penalty—A POMDP Lattice Programming Approach , 2011, IEEE Transactions on Information Theory.

[38]  R. Aumann.  Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[39]  Qing Zhao,et al.  Decentralized dynamic spectrum access for cognitive radios: cooperative design of a non-cooperative game , 2009, IEEE Transactions on Communications.

[40]  Jennifer C. Hou,et al.  Localized fault-tolerant topology control in wireless ad hoc networks , 2006, IEEE Transactions on Parallel and Distributed Systems.

[41]  Stephen B. Wicker,et al.  Game theory and the design of self-configuring, adaptive wireless networks , 2001, IEEE Commun. Mag..

[42]  H. Carlsson,et al.  Global Games and Equilibrium Selection , 1993 .

[43]  S. Hart,et al.  A Reinforcement Procedure Leading to Correlated Equilibrium , 2001 .

[44]  A. Banerjee,et al.  A Simple Model of Herd Behavior , 1992 .

[45]  John N. Tsitsiklis,et al.  On Learning With Finite Memory , 2012, IEEE Transactions on Information Theory.

[46]  S. Morris,et al.  Global Games: Theory and Applications , 2001 .

[47]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[48]  Vikram Krishnamurthy,et al.  Mis-Information Removal in Social Networks: Constrained Estimation on Dynamic Directed Acyclic Graphs , 2013, IEEE Journal of Selected Topics in Signal Processing.