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
Anasazi
Village
Heatbugs
Sugarscape
Abstract
Prisoner’s
Dilemma

Realistic
Retirement
Timing
More details = more parameters
October 2nd, 2003
Agent 2003, Chicago, IL
2
Robustness versus Evolution

How to handle parameters?

Test each one for robustness



Use knowledge of likely parameters



Assumes all parameter values equally likely
Tedious, grows exponentially
Known a priori from data
Learn parameter values using another model
Explore this approach on bargaining game
October 2nd, 2003
Agent 2003, Chicago, IL
3
Outline





Evolutionary Divide the Cake
Assortative Correlations
Schelling Segregation Model
Social Network Model
Conclusions
October 2nd, 2003
Agent 2003, Chicago, IL
4
Evolution of Justice (Skyrms ’98)
Referee
Player 2
Player 1
Cake


Player 1
Player 2
Win /
Lose
35%
55%
W
70%
60%
L
50%
50%
W
70%
30%
W
50 / 50 split seems fair, but why not 70 / 30?
http://www.nytimes.com/2003/09/18/science/18MONK.html
October 2nd, 2003
Agent 2003, Chicago, IL
5
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?
October 2nd, 2003
Agent 2003, Chicago, IL
6
Skyrms and Correlations

Change random to correlated pairings



But correlation is now a parameter




Skyrms proposes “like plays with like”
Fair split evolves from 100% of populations
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…
October 2nd, 2003
Agent 2003, Chicago, IL
7
Assortative Correlations
M
F
G
M
F
G
M
0.8
0.1
0.1
F
0.1
0.8
G
0.1
0.1
M
0.3
0.3
0.3
0.1
F
0.1
0.8
0.8
G
0.4
0.4
Skyrms (100%)


M
F
G
M
0.3
0.3
0.3
0.1
F
0.4
0.4
0.1
0.1
G
0.8
0.1
0.1
D’Arms, et. al. (56%)
Barrett, et. al. (90%)
Maybe not all correlations equally likely…
Learn parameter values


Schelling Segregation
Dynamic Social Network Creation
October 2nd, 2003
Agent 2003, Chicago, IL
8
Schelling Segregation Model

Changes to basic game





Now nine strategies (0.1, 0.2, etc.)
Add spatial dimension
Players have a happiness threshold and
move when unhappy
Assort for 20 time-steps
We can infer preferences from the resulting
neighborhood clusters
October 2nd, 2003
Agent 2003, Chicago, IL
9
Schelling Assortment
After 20 rounds
Initial Locations
October 2nd, 2003
Agent 2003, Chicago, IL
10
Player Satisfaction
50
# Unhappy
40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Time steps
October 2nd, 2003
Agent 2003, Chicago, IL
11
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
October 2nd, 2003
Agent 2003, Chicago, IL
12
Change in Fitness from Assortment
Fitness increase due to assortment
3
2.5
Fitness
2
1.5
1
0.5
0
0.1
0.2
0.3
0.4
0.5
Strategy
initial
October 2nd, 2003
0.6
0.7
0.8
0.9
assorted
Agent 2003, Chicago, IL
13
Tolerance Threshold Variation
Evolution of Fairness when varying tolerance threshold
1
0.9
0.8
0.7
Fairness
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45 0.5 0.55 0.6
Tolerance Threshold
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
mean fairness
October 2nd, 2003
Agent 2003, Chicago, IL
14
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
October 2nd, 2003
Agent 2003, Chicago, IL
15
Acknowledgements





Elliott Sober
Brian Skyrms
Laura Goadrich
Matt Jadud
NLM training grant 1T15LM007359-01
October 2nd, 2003
Agent 2003, Chicago, IL
16
Thank you!


http://www.cs.wisc.edu/~richm/
[email protected]
October 2nd, 2003
Agent 2003, Chicago, IL
17
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 with
favorable opponents
October 2nd, 2003
Agent 2003, Chicago, IL
18
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
October 2nd, 2003
Agent 2003, Chicago, IL
19
Social Network Fairness
October 2nd, 2003
Agent 2003, Chicago, IL
20