Modeling Individual Agents and InstitutionsScott E PageUniversity of MichiganSanta Fe Institute
Outline • Who am I? • Goals for the week • The week in context • Four levels of models • Mechanism Design view of institutions • Complex Adaptive Systems • Outline for the week
The Game Show Introduction • Trained as mathematical economist • Michigan • complex systems • political science • economics • IDEAS-IGERT PI • Project Diversity • Santa Fe Institute • run economics summer school • MacArthur Foundation • inequality/peer effect working group
Goals For The Week • Introduce basic theoretical structure of complex adaptive systems • networks • learning/adaptation • interaction • heterogeneity • Teach some core technical tools • genetic algorithms • simulated annealing • learning models • network theory • Link complex adaptive systems to empirical study of institutions • Make political science more exciting
The Week In Context • Week 1: Foundations • games/models • equilibrium/equilibria • Week 2: A Model in Depth • spatial models • ideal point estimation • Week 4: A Question in Depth • judicial decision making
The Week In Context - 1 • Week 3: The third way • equilibrium? • institutions as rules of game? • getting there versus being there • the information sun or a web of information? • interactions • culture • diversity and feedbacks
The Week In Context - 2 • Week 3: New Tools and Ideas • edge of chaos • emergence • learning models • network theory • toolbox theories • game ensembles • simulated annealing
The Week In Context - 3 Almost all important social problems: War, Terrorism, Economic Inequality, Educational Performance, Crime, Drug use, Political Stability, Environmental Sustainability, Culture and Institutional Performance, Economic Growth, International Relations, Health and Behavior, Nature vs Nurture, and Happiness. are COMPLEX (in a way I’ll formally define)
The Week In Context - 4 Standard way of doing social science is to construct an equilibrium model, to develop hypotheses from that model and to test those hypotheses. But, we can also develop hypotheses from non equilibrium models and from models that describe the path or paths to equilibrium. If you had one word to describe the political arena (or the economic arena) would you choose equilibrium or complex.
Why we model • Understand phenomena • Predict other phenomena • Design institutions • Construct interventions • Amass Tools • Think Different
How we use models • Thinking tools • To find equilibria • Fit data • Hypothesis test • Calibrate • Extrapolate • Construct Scenarios • Seek out counterfactuals
Four Levels of Models • Rule Aggregation • Evolutionary Selection • Intelligent Adaptation • Complete and Perfect Anticipation • equilibrium
An Aside • Lecture demands combining political intuitions with models from other disciplines. • Cleanest empirical examples come from other disciplines. • Bank failure/forest fire model
Example: Bank Failure Model • Banks connected in a line • Banks choose to make a risky loan each period with probability p • Risk loans fail with probability q • Risky loans pay a higher yield • Failures spread to neighboring banks only if those banks have a risky loan outstanding
Example Period 1: 00R00R000RR0R Period 2: R0R00R00RRRRR
Example Period 1: 00R00R000RR0R Period 2: R0R00R00RRRRR Period 3: R0R00R00FFFFFF Period 4: R0R00R00000000
Level 1: Rule Aggregation • Watch what happens in the model • Threshold effect: yield increases in p up to a point and then falls off rather dramatically. • Empirical test of model: ??
Level 2: Evolutionary Selection • Suppose that the rate of risky loans, p, is evolved. • Scenario 1: globally • Scenario 2: bank by bank
Level 2: Scenario 1 • The global p should be the one that gives the highest yield which is poised at the edge of this threshold. • Empirical test of model:??
Level 2: Scenario 2 • If each bank evolves its own p, then we should see the emergence of firewalls 1110110111011100111 • Empirical test of model:??
Level 3: Intelligent Adaptation • Banks should learn that firewalls are important and they should quickly move to create firewalls. 1110110111011100111 • Empirical test of model:?? • Test versus evolutionary selection model:??
Level 4: Equilibrium • Immediate selection from among efficient configurations • Empirical test of model:?? • Test versus intelligent adaptation:??
An Historical View • Level 1: Behavioral voting • Level 4: Game theory, rational choice theory • Level 2: Evolutionary game theory • Level 3: Learning and adaptation
Generative Social Science We now use Level 2 and Level 3 arguments to underpin Level 4 analyses. We either say, evolutionary pressures lead to equilibrium, or that people learn it. Level 2 and Level 3 models force an emphasis on how the system gets to and maintains an equilibrium.
Within Lecture Quiz • Choose a political question • Give models at each of the four levels • What are the empirical implications of each?
Mechanism Design View of Institutions - Reiter • Agents • Endowments/Information • Message Space • Payoff Function • Equilibrium • Mechanism Equilibrium = SWF Outcome
Mount Reiter Diagram SWF Env Outcome Rule Payoff Message
Why Not Equilibrium? • Big Space: 2nd Law of Thermodynamics • New Players • New Strategies • Linked to other games • Game too hard to solve • Unstable dynamics • Might not be one • convex, upper semi continuous, closed, bounded.
Complex Adaptive Systems • Agents • Space: social, virtual, geographic • Adaptation • Dynamics • Diversity
The Barn Mutation/Adaptation Network Big Area Real Novelty Interaction Diversity
Background Complex adaptive systems consist of adaptive agents who dynamically interact in structures or spaces. The payoff or fitness to any one agent depends upon the actions of the other agents with whom it interacts.
Background Complex adaptive systems can settle into equilibria, they can create patterns, or they can produce novelty. In many cases, the same system produces more than one of these phenomena simultaneously.
More Background Complex adaptive systems scholars distinguish between Stability: returning to an equilibrium Robustness: functional maintenance
History Scholars of complex adaptive systems began with lots of simple models and metaphors (“edge of chaos” “the evolution of evolvability”,etc..). In the past decade or so, there has been an attempt to create a “science of complex systems.”
The Tao of John Miller Water which is too pure has no fish – Ts’a T’an You cannot catch running water in a bucket - Lao Tsu
Methodology Complex systems scholars construct mathematical models and computer models. To investigate a given phenomenon they often construct both. The starker mathematics and the more flexible agent based models are complements.
The Barn Mutation Network Big Area Real Novelty Interaction Diversity
Exploration versus Exploitation To search for solutions to difficult problems or to evolve strategies in complex environments, involves a tradeoff between explore and exploit. - James March
Exploration versus Exploitation Genetic Algorithm: if the mutation rate and crossover probabilities are too high, no structure gets exploited. Alternatively, if the selection operator is too severe, the initial best is over exploited.
Exploration versus Exploitation value of solution exploit explore
The Evolution of Evolvability Bedau and Packard and others have shown that if you allow the mutation rate to evolve, then it will settle into a region in which evolution can be successful.
The Evolution of Evolvability value of solution mutation rate
Chaos takes a Q The tent map creates chaos x(t+1) = 2x(t) if x < 0.5 x(t+1) = 2 – 2x(t) else
Chaos takes a Q Q-learning x(t+1) = q x(t) + (1-q) Tent map
Q-learning 2/3 cycles chaos q
The Barn Mutation Network Big Area Real Novelty Interaction Diversity
The Edge of Chaos There are three versions of the “edge of chaos” 1. Langton’s lambda model 2. Kaufman’s NK model 3. The metaphor All require slight modification
The Metaphor The “edge of chaos” metaphor states that if you have just the right amount of randomness (or interaction) to support life and or complexity then if you increase the randomness (or the interactions) you fall into “chaos”.
The Edge of Chaos value of solution mutation rate/interactions
The Long Mesa value of solution mutation rate/interactions