How did cooperation emerge?

Jared Moore and David Gottlieb

How can group benefit change the benefit for an individual?

Our aim: Develop an intuitive sense of cooperative and evolutionary game theory.

Divide the grade point

We will break half of you up into pairs.
The other half will also be paired, but anonymously.

You are dividing up one grade (extra credit) point with another player.
Each of you must place a decimal demand between 0 and 1 inclusive.
You will get as many points as you bet so long as (your bet + their bet) <= 1.
- Otherwise you get no points.
We will go around the class collecting your bets and administering the points.
- For those of you with partners, your partner will learn what bet you placed.

Why so nice?

Evolutionary game theory tries to provide the math to explain why we are nice to each other.

Evolution

Natural Selection

If […] organic beings vary at all in the several parts of their organisation, and I think this cannot be disputed; if there be, owing to the high geometrical powers of increase of each species, at some age, season, or year, a severe struggle for life, and this certainly cannot be disputed; then, considering the infinite complexity of the relations of all organic beings to each other and to their conditions of existence, causing an infinite diversity in structure, constitution, and habits, to be advantageous to them, I think it would be a most extraordinary fact if no variation ever had occurred useful to each being’s own welfare, in the same way as so many variations have occurred useful to man. But if variations useful to any organic being do occur, assuredly individuals thus characterised will have the best chance of being preserved in the struggle for life; and from the strong principle of inheritance they will tend to produce offspring similarly characterised. This principle of preservation, I have called, for the sake of brevity, Natural Selection. (Darwin 1859)

Nutshell

variation
differential fitness
inheritance

Genetic Evolution

Cultural Evolution

What’s another example of something that could or has evolved culturally?

[…] kayaks are clearly adaptations. These peoples’ subsistence was based on hunting seals (and sometimes caribou) in Arctic waters. A fast boat was required to get close enough to these large animals to reliably hit and kill them with an atlatl dart.24 Kayaks are a superb solution to this adaptive problem. Their slim, efficient hull design allowed sustained paddling at up to seven knots. They were extremely light (sometimes less than fifteen kilo- grams), yet strong and seaworthy enough to safely navigate rough, frigid northern seas.25 They were also “reliably developing”—every successful hunter built or acquired one—until firearms allowed hunting from slower, but more stable and more widely useful umiaks. For at least eighty gener- ations, people born into these societies acquired the skills and knowledge necessary to construct these boats from available materials—bone, drift- wood, animal skin, and sinew. Certainly, no evolved “kayak module” lurks in the recesses of the hu- man brain. People have to acquire the knowledge necessary to construct a kayak using the same evolved psychology that people use in other envi- ronments to master other crucial technologies. No doubt, learning any craft requires an evolved “guidance system.” People must be able to evaluate alternatives, to know that boats that don’t sink and are easy to paddle are better than leaky, awkward designs. They have to be able to judge, to some significant degree, whose boats are best, and when and how to combine in- formation from different sources. (boyd_not_2005?)

behave as though they had rationally chosen to maximize their tness. [binmore]

Game theory

Driving game

You wake up in a deserted (viz. lacking signs) landscape in a foreign country in the driver’s seat of a motorcycle. You are thirsty and decide to drive to find a source of water.

Which side of the road do you drive on?

Driving game

You live in a world where everone

Equilibria qua minima

An example of a local and global minimum meant to explain equilibria

What are the equilibria?

	cooperate	defect
cooperate	2	0
defect	3	1

What are the equilibria?

	cooperate	defect
cooperate	4	0
defect	3	1

Haystack

	cooperate	defect
cooperate	2	0
defect	3	1

Founders Activity

	cooperate	defect
cooperate	4	0
defect	3	1

Equilibrium dyanmics

In the stag hunt randomly perturbing the population may eventually move the replicators to a different strategy, but it takes awhile. Such a gif is pictured.

Location

Bacteria poisoning in a stirred medium goes down.

Chao and Levin (1981)

Bacteria poisoning in a still medium goes up.

Chao and Levin (1981)

Divide-10, 10x10

NB: These time steps changes may be off.

blue is demand-4; red: is demand-5; white is demand-6

Within five generations, demand five goes to fixation.

Divide-10, 100x100

blue is demand-4; red: is demand-5; white is demand-6

Within six generations, demand five goes to fixation.

Diagonal

SSSSSS
HHHSSS
HHHSSS
HHHSSS

SSSSSS
HHSSSS
HHHSSS
HHHSSS

SSSSSS
HSSSSS
HHSSSS
HHHSSS

SSSSSS
SSSSSS
HSSSSS
HHSSSS

Signaling

Signaling games

	Act I	Act 2	Act 3
S1	1,1	0,0	0,0
S2	0,0	1,1	0,0
S3	0,0	0,0	1,1

Sender’s Strategy

S1 -> M1

S2 -> M2

S3 -> M3

Receiver’s Strategy

M1 -> A1

M2 -> A2

M3 -> A3

What’s the point of signaling?

	split	steal
split	6.8, 6.8	0, 13.6
steal	13.6, 0	0

The only message you should send is that you’re going to split, but because it is the only message to send it’s “meaningless.”

golden balls - 1

golden balls - 2

Next class – how to explain this?

What do we need to model “morality”?

Repeated (iterated) games (reproduction)
Randomness of strategy
Location or proximity
Signaling (more next class)
- Including punishments (reinforcement learning)

What else?

How sure can we be that our models are ‘seeing what we see’?

Project work time

Creative groups in the front left.

Video essays in the front right.

Philosophical essays in the back left.

Coding projects in the back right.

Exit ticket

What (if anything) are you going to change about your project?

References

Chao, L, and B R Levin. 1981. “Structured Habitats and the Evolution of Anticompetitor Toxins in Bacteria.” Proceedings of the National Academy of Sciences 78 (10): 6324–28. https://doi.org/10.1073/pnas.78.10.6324.

Darwin, Charles. 1859. On the Origin of Species By Means of Natural Selection Or, the Preservation of Favoured Races in the Struggle for Life. First. https://www.gutenberg.org/ebooks/1228.