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- 1. Complex Systems Models in the Social Sciences (Lecture 8 + 9) daniel martin katz illinois institute of technology chicago kent college of law @computationaldanielmartinkatz.com computationallegalstudies.com
- 2. Part II of This Class Starting on Monday, Part II of this Course Michael Bommarito Will Lead this Effort In This Final Lecture Will: Highlight the Various Forms of Modeling Frameworks* Try to Tie Together a Series of Conceptual Building Blocks *Drawn from Slides by Ken Kollman
- 3. Modeling Frameworks
- 4. What Are Models For? “a precise and economical statement of a set of relationships that are sufﬁcient to produce the phenomena in question” (Schelling). “Complicated enough to explain something not so obvious or trivial, but simple enough to be intuitive once it’s explained” (Schelling) Sometimes it is just Disciplined story- telling - Sometime it can be more
- 5. What Are Models For? Prediction Conceptual clarity about assumptions Insight about why we observe what we do Evaluating Counterfactuals
- 6. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based
- 7. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based Sometimes You Can Build Ensembles of these Frameworks
- 8. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based We have Mostly Focused on these ...
- 9. Game Theory Currently Dominant Study of mathematical models of conﬂict and cooperation among intelligent, rational decision-makers (Myerson) Rational---optimizing Bayesians Intelligent--decision-makers know and understand everything they do and we do (NOT complete information)
- 10. The Primacy of Nash Equilibrium An “upper” solution concept, in Myerson’s terms If not Nash, then not reasonable to predict Problems: Multiple equilibria Importance of out-of-equilibrium beliefs Actually doesn’t predict very well
- 11. http://www.youtube.com/watch?v=p3Uos2fzIJ0
- 12. Extensions Axelrod’s computer tournaments Adaptive party models M. Laver (NYU Pol Sci) recent work Formation of nation-states, empires Social contagion (S.I.R. Models)
- 13. Complexity Models (1) Agents follow simple rules (2) Emergence of macro patterns Flocking Model is a Good Example
- 14. Justification for Complexity Models We can’t solve the models we want to study given current analytical techniques--computer is necessary We believe we are studying agents who adapt, or in some sense are boundedly rational--computer is convenient but in principle not necessary Computational models are better at modeling our contemporary world
- 15. Complexity Models (3) Agents’ actions are interdependent Can Be Modeled In Several Ways Networks Are One Important way
- 16. Rule Encoding is Key Agents Rules are Mixtures of Global rules + Local rules Simple Birth Rates is Completely Global Wolf-Sheep is a Mixture Energy is indexed locally But Each Agent is still following same rules
- 17. Conceptual Building Blocks
- 18. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 19. How Do I Know That I Am On the Highest Peak? Search / Exploration
- 20. Search / Exploration
- 21. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 22. phat-dependent path-dependent vs.
- 23. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 24. Simple Rules Generating Complexity
- 25. Absence of Top Down Control
- 26. Example: The Flocking Model
- 27. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 28. Feedback = the return to the input of a part of the output (can be +, - or 0 )
- 29. negative feedback negative feedback --> negative if the resulting action opposes the condition that triggers it This class of feedback is often described as auto-regulating in so much as deviations from the equilbriua are dragged back
- 30. Positive Feedback positive --> if the resulting action builds upon the condition that triggers it These are the more interesting class of effects Perturbations to the system can generate a novel set of outcomes
- 31. A positive connection: ! ! For Full Example: http://serc.carleton.edu/introgeo/models/ loops.html ! The positive connection for a cooling coffee cup implies that the hotter the coffee is the faster it cools. The variables Tc and Tr are coffee and room temperature respectively.
- 32. a negative connection:! ! the negative connection in the figure below for a cooling coffee cup implies a positive cooling rate makes the coffee temperature drop. ! For Full Example: http://serc.carleton.edu/introgeo/models/ loops.html
- 33. t h e t w o c o n n e c t i o n s are combined yield a ! negative feedback loop ! ! coffee temperature approaches the stable equilibrium of the room temperature.! going around the loop the positive connection times the negative connection gives a negative loop feedback effect. !
- 34. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 35. Lots of Ways to Potentially Model Diffusion
- 36. In General We are Interested in Dynamics Yielding the Spread of Some “Pathogen”
- 37. SIR Model is the Classic Compartmental model from epidemiology
- 38. S (for susceptible) I (for infectious) R (for removed (i.e. immune or dead)
- 39. Lots of Other Variants The SIS model The SEIR model Carrier state http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology The MSIR model
- 40. “Pathogen” could actually be a pathogen OR it could be something else ...
- 41. Fads, Customs, Ideology, etc.
- 42. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
- 43. We Covered this at great length ...
- 44. Networks are “dependency graphs”
- 45. Places to Learn More
- 46. http://www.complexityexplorer.org/online-courses
- 47. http://complexity.stanford.edu/classes
- 48. https://class.coursera.org/nlp/lecture
- 49. http://www.r-bloggers.com/?s=machine+learning

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