Model Robustness versus Parameter Evolution

1
Model Robustness versus Parameter Evolution

• Mark H. Goadrich
• University of Wisconsin Madison
• October 2nd, 2003
• presented at Agent 2003, Chicago, IL

2
Issues in Agent-Based Modeling
Anasazi Village
Heatbugs
Sugarscape
Abstract
Realistic
Retirement Timing
Prisoners Dilemma

• More details more parameters

3
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

4
Outline

• Evolutionary Divide the Cake
• Assortative Correlations
• Schelling Segregation Model
• Social Network Model
• Conclusions

5
Evolution of Justice (Skyrms 98)
Referee
Player 1 Player 2 Win / Lose
35 55 W
70 60 L
50 50 W
70 30 W
Player 2
Player 1
Cake

• 50 / 50 split seems fair, but why not 70 / 30?
• http//www.nytimes.com/2003/09/18/science/18MONK.h
  tml

6
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?

7
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
• DArms et. al. introduce anti-correlation
• greedy players prefer anyone but themselves
• Fair split evolves from 56 of populations!
• Model is not robust across correlations

8
Assortative Correlations
M F G
M 0.8 0.1 0.1
F 0.1 0.8 0.1
G 0.1 0.1 0.8
M F G
M 0.3 0.3 0.3
F 0.4 0.4 0.1
G 0.8 0.1 0.1
M F G
M 0.3 0.3 0.3
F 0.1 0.8 0.1
G 0.4 0.4 0.1
Barrett, et. al. (90)
DArms, et. al. (56)
Skyrms (100)

• Maybe not all correlations equally likely
• Learn parameter values
• Schelling Segregation
• Dynamic Social Network Creation

9
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

10
Schelling Assortment
After 20 rounds
Initial Locations
11
Player Satisfaction
12
Schelling Correlation Matrix
Strategy i pref(i,0.1) pref(i,0.2) pref(i,0.3) pref(i,0.4) pref(i,0.5) pref(i,0.6) pref(i,0.7) pref(i,0.8) pref(i,0.9)
0.1 0.10 0.17 0.14 0.12 0.13 0.12 0.07 0.06 0.07
0.2 0.13 0.18 0.16 0.13 0.13 0.12 0.08 0.03 0.02
0.3 0.10 0.16 0.12 0.18 0.13 0.18 0.06 0.04 0.02
0.4 0.09 0.12 0.17 0.26 0.13 0.17 0.02 0.01 0.03
0.5 0.11 0.14 0.15 0.15 0.23 0.02 0.05 0.07 0.07
0.6 0.11 0.14 0.21 0.21 0.02 0.12 0.05 0.07 0.07
0.7 0.10 0.14 0.11 0.04 0.07 0.07 0.14 0.22 0.11
0.8 0.09 0.06 0.07 0.02 0.11 0.11 0.23 0.13 0.18
0.9 0.09 0.03 0.04 0.05 0.11 0.11 0.11 0.17 0.28
13
Change in Fitness from Assortment
14
Tolerance Threshold Variation
15
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

16
Acknowledgements

• Elliott Sober
• Brian Skyrms
• Laura Goadrich
• Matt Jadud
• NLM training grant 1T15LM007359-01

17
Thank you!

• http//www.cs.wisc.edu/richm/
• richm_at_cs.wisc.edu

18
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

19
Network Correlation Matrix
Strategy i pref(i,0.1) pref(i,0.2) pref(i,0.3) pref(i,0.4) pref(i,0.5) pref(i,0.6) pref(i,0.7) pref(i,0.8) pref(i,0.9)
0.1 0.08 0.17 0.02 0.12 0.06 0.21 0.14 0.13 0.07
0.2 0.12 0.00 0.07 0.07 0.15 0.24 0.08 0.27 0.00
0.3 0.06 0.03 0.02 0.44 0.41 0.03 0.01 0.01 0.00
0.4 0.55 0.07 0.11 0.07 0.13 0.04 0.00 0.01 0.01
0.5 0.19 0.16 0.18 0.25 0.21 0.00 0.00 0.01 0.01
0.6 0.39 0.03 0.41 0.15 0.00 0.00 0.01 0.00 0.01
0.7 0.01 0.84 0.13 0.00 0.01 0.01 0.00 0.00 0.00
0.8 0.58 0.40 0.00 0.00 0.00 0.00 0.00 0.01 0.00
0.9 0.94 0.00 0.01 0.00 0.01 0.01 0.00 0.01 0.00
20
Social Network Fairness