Evolution of Justice: Robustness versus Parameter Variation in Agent-Based Models

Model Robustness versus Parameter Evolution Mark H. Goadrich University of Wisconsin – Madison October 2nd, 2003 presented at Agent 2003, Chicago, IL

Issues in Agent-Based Modeling • More details = more parameters Anasazi Village Heatbugs Sugarscape Abstract Realistic Retirement Timing Prisoner’s Dilemma Agent 2003, Chicago, IL

Robustness versus Evolution • How to handle parameters? • Test each one for robustness • Assumes all parameter values equally likely • Tedious, grows exponentially • Use knowledge of likely parameters • Known a priori from data • Learn parameter values using another model • Explore this approach on bargaining game Agent 2003, Chicago, IL

Outline • Evolutionary Divide the Cake • Assortative Correlations • Schelling Segregation Model • Social Network Model • Conclusions Agent 2003, Chicago, IL

Evolution of Justice (Skyrms ’98) Referee Player 2 Player 1 Cake • 50 / 50 split seems fair, but why not 70 / 30? • http://www.nytimes.com/2003/09/18/science/18MONK.html Agent 2003, Chicago, IL

Evolution of Justice • Use Evolutionary Game Theory • 1000 players with preset strategies • Randomly without replacement pair players for games • Fitness is amount of cake received • Reproduce asexually, repeat until stable population • Three strategies, 1/3 (modest), 1/2 (fair), and 2/3 (greedy) • Fair split evolved from 74% of initial populations • How can we rid ourselves of polymorphisms? Agent 2003, Chicago, IL

Skyrms and Correlations • Change random to correlated pairings • Skyrms proposes “like plays with like” • Fair split evolves from 100% of populations • But correlation is now a parameter • D’Arms et. al. introduce “anti-correlation” • greedy players prefer anyone but themselves • Fair split evolves from 56% of populations! • Model is not robust across correlations… Agent 2003, Chicago, IL

Assortative Correlations • Maybe not all correlations equally likely… • Learn parameter values • Schelling Segregation • Dynamic Social Network Creation Skyrms (100%) D’Arms, et. al. (56%) Barrett, et. al. (90%) Agent 2003, Chicago, IL

Schelling Segregation Model • Changes to basic game • Now nine strategies (0.1, 0.2, etc.) • Add spatial dimension • Players have a happiness threshold andmove when unhappy • Assort for 20 time-steps • We can infer preferences from the resulting neighborhood clusters Agent 2003, Chicago, IL

Schelling Assortment After 20 rounds Initial Locations Agent 2003, Chicago, IL

Player Satisfaction Agent 2003, Chicago, IL

Schelling Correlation Matrix Agent 2003, Chicago, IL

Change in Fitness from Assortment Agent 2003, Chicago, IL

Tolerance Threshold Variation Agent 2003, Chicago, IL

Conclusions • Shift in focus from broad applicability to grounded models introduces complexity • When possible, concentrate on likely parameter values instead of robustness • Concentrate debate on models grounded in experience Agent 2003, Chicago, IL

Acknowledgements • Elliott Sober • Brian Skyrms • Laura Goadrich • Matt Jadud • NLM training grant 1T15LM007359-01 Agent 2003, Chicago, IL

Thank you! • http://www.cs.wisc.edu/~richm/ • richm@cs.wisc.edu Agent 2003, Chicago, IL

Social Network Algorithm • Let players associate during generations • Dynamically update preferences • for each player strategy • choose opponent according to preferences • if successful game, increase opponent preference • repeat 1000 times • Players should associate withfavorable opponents Agent 2003, Chicago, IL

Network Correlation Matrix Agent 2003, Chicago, IL

Social Network Fairness Agent 2003, Chicago, IL

Evolution of Justice: Robustness versus Parameter Variation in Agent-Based Models