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Man and Superman
Human Limitations, innovation and
emergence in resource competitionRobert Savit
University of Michigan
Collaborators
Katia Koelle, Biology, University of Michigan
Wendy Treynor, Psychology, UM
Richard Gonzalez, Department of Psychology, UM
Thanks to Yi Li, Physics, UM
Introduction
• Theme of workshop is the design, prediction and control of collectives
• Generally we understand the collectives to be composed of silicon agents, or at least related thereto.
• But, many situations in which collectives may be involve carbon-based agents.
Introduction (2.)
• In particular, may be interested in collectives of humans, or collectives some of whose agents are human and some silicon.
• Examples: – Markets and their regulation. – Systems in which humans exercise judgement or
intervene in systems that are basically collectives of silicon agents. Eg. Logistics supply networks or networks of sensors and actuators which can be overridden by human controllers.
Introduction (3)
• Many ways in which human agents different from silicon ones
• lessons we learn from the study of collectives of silicon agents may have to be modified when we try to design, predict and control collectives of humans, or mixed collectives
Introduction (4)
• Will report on preliminary controlled experiments with humans playing the minority game.
• Indications of interesting new phenomena which may be important in design and control of human collectives
Outline• A. epistemological considerations: A story of
psychologist-physicist collaboration • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
Epistemological Considerations
• Never underestimate the naïveté of a psychologist nor the ignorance of a physicist
• OR
• Never underestimate the ignorance of a psychologist nor the naïveté of a physicist.
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
B. The Minority Game (a.k.a. El Farol Bar Problem)
• At each time step
each player picks a resource
each player on minority resource gets one point.
Players in the majority group get nothing.
• Objective: Each player wants to maximize his total points.
Players
Resources
Resource 0 Resource 1
How do the players make their choices?
t 1 2 3 4 5 6 7 8 9
Minority Resource 0 1 1 0 1 0 1 0 0
History of Minority
Resources
Window of last m minorities
m=3
Strategy
Next step, choose 0
•EEach player has several (two) randomly generated strategies of
window (memory) m.•AAt each step, the player uses the strategy that would have maximized
its gains over the entire history.
An example of an m=3 strategy
Recent History Predicted next minority group
000 0
001 1
010 1
011 0
100 0
101 0
110 1
111 1
The population of group 1 as a function of time (N=101)
44
45
46
47
48
49
50
51
52
53
54
high standard deviationPoor use of the resource
Low standard deviationGood use of the resource
Maladaptive behavior—
poor system-wide
performance
Emergent coordination of agent
choice
Degrading performance---too much information
Phase transition
The Minority Game with Evolution
• Agents can change their strategies
• Different rules– fixed m – variable m.
The Minority Game with Evolution--Results
The σ2/N of two evolution games (all after 300 generations). The normal minority games have higher σ2/N. For comparison σ2/N for standard MG at dip .07.
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human
MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
Description of the Experiments
• N participants, each at a computer terminal• Each participant paid a flat sum plus $.05 each
time he is in the minority group (generally)• See the history of minority groups• See a running total of their winnings• No other information• 5 seconds to make each decision• Game runs for 400 time steps
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
What do Humans Do?
• Therefore, expect best performance at Nc19. Actually, finite size effects indicate a better value is Nc 15.
• But maybe this is too naïve (or ignorant)…
What do Humans Do?
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
Human Limitations and Strengths
• Boredom• Memory limitations• Processing limitations
– Biases– Systematic error in processing. Eg.overestimates of
probabilities based on recent events– Random errors in processing– Emotions– Fallacies of causal inference—I.e. limitations in
understanding about the way the system works
Human Limitations and Strengths (cont.)
• Possibility for great creativity– Possible source for response to non-stationarity
or non-autonomy– Also possible weakness.
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
• 2/N as a function of time
2/N as a function of N
• player performance as a function of strategy complexity
What Really Happens?
• 2/N as a function of time
2/N as a function of N
• player performance as a function of strategy complexity
What Really Happens?
• 2/N as a function of time
2/N as a function of N
• player performance as a function of strategy complexity
What Really Happens?
• Note good performance (relative to RCG) for all N
• Note oscillations
• Need more data to determine 2/N vs. N quantitatively (will come back to this)
2/N as a function of N
• 2/N as a function of time
2/N as a function of N
• player performance as a function of strategy complexity
What Really Happens?
Silicon Player Performance as a Function of Strategy Complexity
• In evolutionary computer games, best performing agents have simplest strategies
• Horizontal axis a measure of determinism of agent’s strategy, assuming m3.
• In fact, best performance is for m=0 strategies!!• Next best are m=1 strategies.
• 72 implies Nc 15
• But, humans’ strategies seem to evolve. So,
• Maybe log2mt 72
• In which case, 2/N will be small for all N<N* 30 or so.
Back to 2/N as a function of N
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
• Why??– Appropriately clever (but not too clever) and
insightful agents?– Boredom?
• Is boredom an evolutionarily selected for adaptive strategy??– an adaptive mechanism which we evolved in
order to limit our cleverness.
Player Performance as a Function of Strategy Complexity
Outline• A. epistemological considerations: A story of
psychologist-physicist collaborations • B. Simple review of the minority game with and
without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human MG.• E. Expected limitations (and strengths) of human
agents vis-à-vis silicon agents • F. What really happens • G. Why???• H. Directions for future work.
• Need continued close collaboration between social and natural scientists to bridge the gulf created by mutual ignorance and naïveté.
• Need to develop thereby a richer epistemology of social dynamics than is now afforded either by social psychology/sociology or by econophysics.
Future Work
• Methods must include well designed and controlled experiments to better determine what the important underlying dynamics and principles are.
• Examples– Need to understand what is the operative dynamics
underlying simple strategy selection by humans– Top-down vs. emergent coordination—experiments in
progress
Future Work (2)