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Aurangzeb Uta 2502D 12124.Pdf INTERNAL STRUCTURE AND DYNAMIC DECISIONS FOR COALITIONS ON GRAPHS by MUHAMMAD AURANGZEB Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT ARLINGTON May 2013 Copyright © by Muhammad Aurangzeb 2013 All Rights Reserved ii Acknowledgements First of all I want to thank my adorable family for their patience and support without which it was not possible to happen. I want to thank my supervisor Dr. F. L. Lewis who invited me to join his great research group and gave the unique opportunity to work in this ideal environment at University of Texas at Arlington Research Institute (UTARI). During all my stay here at UTA and UTARI, Dr. Lewis put his one to one efforts to teach me how to organize my thoughts and how to put them together in a presentable form. I am very thankful to my parents, all my teachers over the years, and friends to give me zeal, knowledge and courage to pursue this work. I also want to acknowledge the grants supported this work: AFOSR grant FA9550-09-1- 0278, NSF grant ECCS-1128050, ARO grant W91NF-05-1-0314, and China NNSF grant 61120106011. A detailed account of acknowledgement is mentioned in Appendix F at the end. Last but not the least; I want to thank all the honorable dissertation committee members: Dr. F. L. Lewis (Chair), Dr. S. Das, Dr. W. E. Dillon, Dr. M. Huber, and Dr. D. Popa, for their profound presence in the committee and to give their valuable inputs to improve this work. May 10, 2013 iii Abstract INTERNAL STRUCTURE AND DYNAMIC DECISIONS FOR COALITIONS ON GRAPHS Muhammad Aurangzeb The University of Texas at Arlington, 2013 Supervising Professor: Frank L. Lewis The notions of collaboration, advantage, cost and impact are investigated in this dissertation, following are the details. Contribution to Cooperation between Agents for Routing in an Unknown Graph Using Reinforcement Learning First of all this work investigates the cooperation between agents to achieve a common goal. The problem of steering a swarm of autonomous agents out of an unknown maze to some goal located at an unknown location is discussed in this context. The routing algorithm given here provides a mechanism for storing data based on the experiences of previous agents visiting a node that results in routing decisions that improve with time. Contribution to Coalitional Advantage in Agents and Structure in Coalitions on Graphs Next a certain graphical coalitional game is introduced, where the internal topology of the coalition depends on a prescribed communication graph structure among the agents. Three measures of the contributions of agents to a coalition are introduced: marginal contribution, competitive contribution, and altruistic contribution. Results are established regarding the dependence of these three types of contributions on the graph topology, and changes in these contributions due to changes in graph topology. Based on these different contributions, three iv online sequential decision games are defined on top of the graphical coalitional game. The stable graphs under each of these sequential decision games are studied. Contribution to Coalitional Cost and Advantage in Agents and Structure in Coalitions on Graphs Here a Positional Cost is also introduced. Based on the advantage and cost, a notion of Net Payoff or Allocation is defined; this notion is used to further define three measures of net advantages. Taking maximization of these measures of net advantages as the objective functions of agents, three online sequential decision games are defined. A threshold of cost is reached above which no agent is interested to stay in a coalition irrespective of their motives. Contribution to Coalitional Advantage in Agents and Structure in Coalitions on Digraphs Novel digraph structures, are defined. The marginal contribution made by an agent in a digraph is introduced. Results are established regarding the dependence of marginal contributions on the graph topology, and changes in these contributions due to changes in graph topology. Based on marginal contributions, and by varying the rules of the game, three online sequential decision games are defined on top of the graphical coalitional game. The stable graphs under each of these sequential decision games are studied, and give the structures of the coalitions that form in each sequential game. Contribution to Coalitional Impact of Agents on Other Agents Finally the notion of impact of one agent in the coalition upon the other agents is investigated, and a complete impact propagation framework is proposed. The analogy of impact propagation is use to present a comprehensive, and integrated framework to compute the impact made by a scientific work, a scientist, an institution, and a scientific journal. v Table of Contents Acknowledgements ................................................................................................................ iii Abstract .................................................................................................................................. iv List of Illustrations ............................................................................................................... viii List of Tables ......................................................................................................................... ix Chapter 1 Introduction ............................................................................................................. 1 Chapter 2 Cooperation between Agents for Routing in an Unknown Graph .......................... 9 Chapter 3 Positional Advantage in Coalitions and Structure in Coalitions on Graphs ......... 40 Chapter 4 Positional Cost and Advantage in Coalitions on Graphs ...................................... 79 Chapter 5 Internal Structure of Coalitions in Digraphs ....................................................... 133 Chapter 6 Impact Propagation Framework, the End of the Number Game ......................... 167 Chapter 7 Future Work ........................................................................................................ 204 Appendix A Technical Lemmas for Chapter 3 .................................................................... 210 Appendix B Proofs of Lemmas in Chapter 3 ....................................................................... 214 Appendix C Proofs of Lemmas in Chapter 4 ....................................................................... 219 Appendix D Proofs of Lemmas in Chapter 5 ...................................................................... 225 Appendix E Proofs of Results in Chapter 6 ......................................................................... 240 Appendix F Detailed Acknowledgements ........................................................................... 246 vi References ............................................................................................................................ 250 Biographical Information ..................................................................................................... 270 vii List of Illustrations Figure 2.1: Visualization of maze as d systems ............................................................................ 18 Figure 2.2: Visual illustration of the points in the Table I ............................................................ 30 Figure 2.3: A Maze of size 10 10 ............................................................................................... 34 Figure 2.4: Simulation results of Maze Exploration ..................................................................... 36 Figure 2.5: Performance Measure (PM) ....................................................................................... 38 Figure 3.1. Two simple graphs ..................................................................................................... 51 Figure 3.2. Communication graph ................................................................................................ 53 Figure 3.3. Evolution of graph in MMC ....................................................................................... 76 Figure 3.4. Evolution of graph in MCC ........................................................................................ 76 Figure 3.5. Evolution of graph in MAC ........................................................................................ 77 Figure 4.1. Two simple graphs ..................................................................................................... 96 Figure 5.1: Evolution of digraphs in online sequential decision games. ................................... 165 Figure 6.1: System of Works ...................................................................................................... 182 Figure 6.2: A segment of System of Works with Direct Impact Factors shown. ....................... 183 Figure 6.3: Impact Factor Propagation. ...................................................................................... 187 Figure 6.4: A section of the systems of works. ........................................................................... 199 Figure 6.5: Scientific Impacts of various simulated objects ....................................................... 200 viii List of Tables Table 2.1: Rules’ Centroids .......................................................................................................... 29 ix Chapter 1 Introduction This chapter provides an outline
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