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 decision- makers (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

Model: Initial State

Model: End State

“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…..