Modeling and Analysis of Human Group Dynamics
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Modeling and Analysis of Human Group Dynamics Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Luis Felipe Giraldo Trujillo, B.S., M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2016 Dissertation Committee: Kevin M Passino, Advisor Wei Zhang John D Clapp c Copyright by Luis Felipe Giraldo Trujillo 2016 Abstract In this work we provide mathematical and computational tools that allow us to model the “physics” of human group behavior: how the relationship between the in- dividuals’ characteristics, interaction dynamics, and environmental factors translates into changes in the behavior of the group. We characterize the group dynamics for four specific situations, and show the importance of these models to improve the per- formance of task-solving groups in organizational management, to design strategies that prevent high-risk behaviors, and to motivate collective action and cooperation in situations that lead to social dilemmas. ii To my family iii Acknowledgments First, I thank God for give me the strength to complete my doctoral studies and the opportunity of having an experience not only at the intelectual level but also social and cultural. I give thanks to my parents and brother for their unconditional love and support. Also, I give special thanks to my advisor and friend Kevin M. Passino. His guidance, willingness to discuss ideas, and kindness make him a great model of an advisor. Also, I want to thank John Clapp for his collaboration and insights, my colleagues Hugo Gonzalez, Isa Fernandez, and Veronica Badescu for their helpful discussions, and the department of Electrical and Computer Engineering for providing funds to support the last years of my studies. iv Vita October 11, 1984 ...........................Ibagu´e, Colombia June, 2006 ..................................B.S. Electrical Engineering, Universi- dad Nacional de Colombia June, 2008 ..................................M.S. Electrical Engineering, Universi- dad de Los Andes, Colombia Publications Research Publications LF Giraldo and KM Passino “Dynamic Task Performance, Cohesion, and Communi- cation in Human groups,” IEEE Transactions on Cybernetics, To be published. LF Giraldo, KM Passino, and JD Clapp “Modeling and Analysis of Group Dynamics in Alcohol-Consumption Enviornments,” IEEE Transactions on Cybernetics, To be published. LF Giraldo and F Lozano and N Quijano “Foraging Theory for Dimensionality Re- duction of Clustered Data,” Machine Learning, 82(1):71–90, Jan. 2011. Fields of Study Major Field: Electrical and Computer Engineering v Table of Contents Page Abstract....................................... ii Dedication...................................... iii Acknowledgments.................................. iv Vita......................................... v ListofTables.................................... ix ListofFigures ................................... x Chapters 1 1. Introduction.................................. 1 2. Dynamic Task Performance, Cohesion, and Communication in Human Groups..................................... 3 2.1 MathematicalModel .......................... 8 2.1.1 ModelFormulation....................... 9 2.1.2 Optimization Point of View for the Model . 13 2.2 ConditionsforCohesiveBehavioroftheGroup . 15 2.3 Dynamics of the Group in Complex Task Environments . 26 2.3.1 Trajectories and Attraction Patterns in the Group . 28 2.3.2 Topology of the Communication Network . 31 2.3.3 Density of the Communication Network . 34 2.3.4 Group Dynamics in a Task Environment Represented by a Plane .............................. 35 vi 2.4 Discussion................................ 36 3. Dynamics of Metabolism and Decision Making during Alcohol-Consumption: ModelingandAnalysis ............................ 39 3.1 ModelFormulation........................... 43 3.1.1 Metabolism........................... 44 3.1.2 Decision Making . 51 3.1.3 Combining the Metabolism and Decision-Making Processes 54 3.2 Estimation from Field Data . 60 3.3 Conclusion ............................... 67 4. Modeling and Analysis of Group Dynamics in Alcohol-Consumption En- vironments .................................. 70 4.1 ConstructionofTheModel . .. .. 76 4.1.1 Individual Influences on Behavior . 76 4.1.2 Adding Social and Environmental Influences . 82 4.2 Simulation Results . 85 4.2.1 Group Dynamics Under Different Conditions on The Per- sonal Preferences and Influence Networks . 86 4.2.2 Estimation of Group Dynamics From Field Data . 87 4.3 MathematicalAnalysisofTheGroupDynamics . 92 4.3.1 No Social and Environmental Pressures . 92 4.3.2 Influence of The Environment and Social Interactions on the GroupDynamics ........................ 94 4.4 Conclusion ............................... 102 4.4.1 FutureDirections. .. .. 103 5. Dynamics of Cooperation in The Task Completion Social Dilemma . 104 5.1 FormulationoftheModel . 109 5.1.1 Task Completion Dynamics . 109 5.1.2 Potential Benefits and Participation Costs . 114 5.1.3 Communication and Relative Reputation . 116 5.2 Collective Action . 118 5.3 Analysis of Participation Dynamics . 126 5.3.1 Participation Patterns in the Community . 126 5.3.2 Monte Carlo Simulations . 130 5.4 Conclusion ............................... 133 6. SummaryandFutureWork . .. .. 136 vii 6.1 SummaryandContributions. 136 6.2 FutureWork .............................. 142 Appendices 145 A. ProofsandImplementationDetailsChapter3 . 145 A.1 Proofs Section 3.1.1: Metabolism . 145 A.2 Proof Section 3.1.3: Combined Metabolism and Decision-Making . 147 A.3 Implementation Details of Simulations in Section 3.1.1 . 151 A.4 Implementation Details of Simulations in Section 3.2 . 152 B. ImplementationDetailsChapter4. 153 B.1 Personal Preference Function For Different Categories of The Desired EffectofTheBACLevel. 153 B.2 Implementation Details of Simulations in Section 4.2.1 . 154 B.3 Implementation Details of Simulations in Section 4.2.2 . 154 C. ProofsChapter5 ............................... 157 C.1 ProofTheorem6 ............................ 157 C.2 ProofCorollary6.1........................... 158 C.3 ProofTheorem7 ............................ 158 C.4 ProofTheorem8 ............................ 159 Bibliography .................................... 161 viii List of Tables Table Page A.1 Functions associated with the category of intended level of intoxication. ..... 152 B.1 Functions associated with the preferred effect of the BAC level. ......... 153 B.2 Functions associated with the environments that are protective against (Environ- e e ment 1, f1 ) and promote (Environment 2, f2 ) high BAC levels. ......... 155 ix List of Figures Figure Page 2.1 (a) Contour of the cost function f(x) and trajectory of the members of the group (black solid lines), where symbol ’o’ indicates the initial position, and the arrows represent the direction of their trajectory. (b) Contour of the performance function and communication network in the group, where the arrows indicate the flow of the information, the thickness of the line indicates the strength in attraction between members, and the symbol ’o’ marks the location of the individual at time step 150. (c) Cohesion γ(t) and performance J(t) of the group. .............. 29 2.2 Mean (solid line) and standard deviation (shaded region) of group cohesion γ(t) and group performance J(t) estimated using Monte Carlo simulations for a group with 10 members under (a,d,g) wheel, (b,e,h) ring, and (c,f,i) line communication networks. Simulations are performed in three different scenarios: (a,b,c) dynamics on the attraction and performance weights, (d,e,f) constant and equal attraction weights, where the attraction term has a predominance in the behavior of the individuals, and (g,h,i) constant and equal attraction weights, where both the at- traction term and gradient of the cost function affect the behavior of the individuals. 33 2.3 Mean (solid line) and standard deviation (shaded region) of group cohesion γ(t) and group performance J(t) estimated using Monte Carlo simulations for commu- nication networks in groups with 50 members (a) with a ring-type topology where each node has 25 neighbors, and (b) fully connected topology. ......... 35 2.4 Mean and standard deviation of group cohesion in (a) position and (b) velocity, and (c) performance of the group for different communication topologies and when the performance function is characterized by a plane. The solid line and the shaded region correspond to the mean and standard deviation estimated using Monte Carlo simulations. ................................. 37 3.1 Block diagram of an intervention strategy that seeks to minimize high-risk drinking behaviors. The network in the diagram represents the drinking group where each individual (small circles) interacts with other individual’s behaviors. ...... 42 x 3.2 Block diagram of the system that results of the interconnection between the drinker’s decision-making process and metabolic process for alcohol. .......... 44 3.3 Causal-loop diagram of the dynamical system that characterizes the metabolic process of alcohol in Equation (3.1). ..................... 46 ∗ ∗ 3.4 (a) Time (t ) and (b) amplitude (xδ (t )) of the maximum value that the BAC reaches during the metabolic process for different values of the parameters ζ and β when the input alcohol intake rate corresponds to an impulse. ........ 49 3.5 Average of BAC samples measured on 12 individuals when a dose of 0.8 g ethanol/kg of weight was administered