Computational Modeling in the Social Sciences Ken Kollman University of Michigan Overview • • • • • • • Modeling in the social sciences Comparisons and definitions Types of computational models Agent-based modeling Achievements Promise Limitations Models • Disciplined story-telling • “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) • A difficult tradeoff Two Levels of Simplicity • Simple models---Prisoner’s Dilemma, Edgeworth box, Supply and Demand • Not so simple, but profound---Arrow’s theorem, Chaos theorems, Nash theorem Goals of Models • • • • Prediction Insight Conceptual clarity Sometimes things “pop out” Some Want Models to • • • • • • Have an equilibrium Have theorems (closed-form solutions) Be rigorous Be deductive Have rational agents Have rational individuals Types of Modeling • • • • • • • • General equilibrium Differential equations (egs., arms race models) Decision theoretic Game theoretic (cooperative, noncooperative) Social choice Adaptive Computational Agent-based Game Theory Currently Dominant • Theory of interdependent decisions • Study of mathematical models of conflict and cooperation among intelligent, rational decisionmakers (Myerson) • Rational---optimizing Bayesians • Intelligent--decision-makers know and understand everything they do and we do (NOT complete information) • Example of non-intelligence--price theory (agents don’t know the model) Great Strides in Economics and other Social Sciences • • • • Rich theory Cumulative Widely applicable Some design successes (eg., auctions) Three Types of Computational Models • Simulations--numerical examples, usually of an equilibrium outcome • Computations--numerical approximations of equilibria that cannot be solved analytically (Judd) • Agent-based models--diverse, interacting, boundedly-rational, adaptive agents, not necessarily an equilibrium Agent-based Models • “Analysis of simulations of complex social systems” (Axelrod) • Purpose? “To aid intuition, ” not to analyze the consequences of assumptions (Axelrod) • Often, but not always, computational • Schelling’s segregation model as an example • Can be reduced form (pick up where modeler left off) or can be platform for artificial world (calculates each agent’s behavior and aggregates) Schelling: Moving Dimes and Nickels Simple Model by Page of Gender in Professions “We keep hiring women scientists but they keep moving to management or leaving the firm.” Page Tipping Model • • • • Two gender types Utility=comfort level + interest + ability Agents can move professions Feedback Reality 100 90 80 70 60 50 40 30 20 10 0 Men Women Nursing Sales Math Education Model: Initial State 60 50 40 Men Women 30 20 10 0 1 2 3 4 Model: End State 100 90 80 70 60 50 40 30 20 10 0 Men Women 1 2 3 4 “If you didn’t grow it you didn’t show it” (Epstein) Kollman, Miller, Page Models of Political Competition • Political parties competing for support • Each voter has a favorite policy position in the space of possible policies • Parties move in the space to win votes • Receive feedback from opinion polls, and adapt according to information • Hill-climb toward higher vote totals Adaptation on Electoral Landscapes Computational Models Can • • • • Equilibrate Cycle Lead to perpetual novelty All three Computational Models Can • • • • • Complement mathematical models Predict Provide insight Offer conceptual clarity Have things “pop out” Complexity Models, Complex Adaptive Systems Models • • • • • • Santa Fe Institute Emergence Adaptation Non-equilibrium Agent-based Feedback From More General to Less • Models • Computational models • Agent-based models Achievements • Segregation (Schelling) • PD games (Axelrod) • Feedback in markets (Epstein and Axtell, Tesfatsion, Arthur et al) • City Formation (Krugman) • Disease transmission (Simon) Achievements (cont’d) • Organizational hierarchies and feedback (March, Harrington) • Political competition (Kollman, Miller, and Page) • Diversity and decision-making (Hong and Page) • Emergence of complex societies (Padgett and Ansell) • Spread of culture or empire (Nowak, Cederman) • Industrial Organization (Harrington) Promise • Answering difficult questions other approaches cannot---multi-layered institutions, diversity, learning, feedback, spontaneous emergence, path dependence • Simulation and prediction • Robustness under bounded-rationality assumptions Limitations • • • • Elusive standards Not always intuitive Undisciplined modeling Agents not smart enough Opposition • Those opposed to modeling • Those opposed to bounded-rationality approaches • Those opposed to non-equilibrium models One Funeral at a Time…..