Man and Superman

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.


psychologist-physicist collaborations • B. Simple review of the minority game with and



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.





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.



without evolution.• C. Description of the experiments• D. Naive expectations of the outcome of human

MG.• E. Expected limitations (and strengths) of human


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





What do Humans Do?

7±2

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?





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.





• 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

Comparison: Silicon vs. Carbon2/N as a function of time (N=5, 17, 101)






• 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)






Silicon Player Performance as a Function of Strategy Complexity

• In evolutionary computer games, best performing agents have simplest strategies

Human Player Performance as a Function of Strategy Complexity

• 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





• 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





• 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)

Documents

Man and Superman