Evolution of cooperation
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Evolution of Cooperation. The importance of being suspicious. Do we see cooperation in Nature?. Do we see cooperation in Nature?. United Nations. Big Picture. Do we see cooperation in Nature?. Do we see cooperation in Nature?. Do we see cooperation in Nature?.

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Evolution of Cooperation

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Evolution of cooperation

Evolution of Cooperation

The importance of being suspicious


Do we see cooperation in nature

Do we see cooperation in Nature?


Do we see cooperation in nature1

Do we see cooperation in Nature?

United Nations

Big Picture


Evolution of cooperation

Do we see cooperation in Nature?


Evolution of cooperation

Do we see cooperation in Nature?


Evolution of cooperation

Do we see cooperation in Nature?


Evolution of cooperation

Do we see cooperation in Nature?


Evolution of cooperation

Do we see cooperation in Nature?

If I give you some DNA

will you give me some?

Ya, Sure.

Just promise it won’t get

complicated between us

Small

Picture:

Bacteria Sex


Martin a nowak 2006

Martin A. Nowak (2006):

  • Genes cooperate in genomes.


Martin a nowak 20061

Martin A. Nowak (2006):

  • Genes cooperate in genomes.

  • Chromosomes cooperate in eukaryotic cells.


Martin a nowak 20062

Martin A. Nowak (2006):

  • Genes cooperate in genomes.

  • Chromosomes cooperate in eukaryotic cells.

  • Cells cooperate in multicellular organisms.


Martin a nowak 20063

Martin A. Nowak (2006):

  • Genes cooperate in genomes.

  • Chromosomes cooperate in eukaryotic cells.

  • Cells cooperate in multicellular organisms.

  • There are many examples of cooperation among animals.


Martin a nowak 20064

Martin A. Nowak (2006):

  • Genes cooperate in genomes.

  • Chromosomes cooperate in eukaryotic cells.

  • Cells cooperate in multicellular organisms.

  • There are many examples of cooperation among animals.

  • Humans are the champions of cooperation: From hunter-gatherer societies to nation-states, cooperation is the decisive organizing principle of human society.


Martin a nowak 20065

Martin A. Nowak (2006):

  • Genes cooperate in genomes.

  • Chromosomes cooperate in eukaryotic cells.

  • Cells cooperate in multicellular organisms.

  • There are many examples of cooperation among animals.

  • Humans are the champions of cooperation: From hunter-gatherer societies to nation-states, cooperation is the decisive organizing principle of human society.

  • The question of how natural selection can lead to cooperative behavior has fascinated evolutionary biologists for several decades.


Cooperation as a paradox the tragedy of the commons

Cooperation as a “paradox”:The Tragedy of the Commons

  • Take a fishing lake where there is an upper limit on how much harvest can be taken in a sustainable manner.

  • Above this limit, the fish pop. eventually crashes and everyone is worse off.


Cooperation as a paradox the tragedy of the commons1

Cooperation as a “paradox”:The Tragedy of the Commons

  • And they have to wait for someone to come and give them fish...


Cooperation as a paradox the tragedy of the commons2

Cooperation as a “paradox”:The Tragedy of the Commons

  • And they have to wait for someone to come and give them fish...


Tragedy of the commons what should you do

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.


Tragedy of the commons what should you do1

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.


Tragedy of the commons what should you do2

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.

Pretty bad: Everyone fishes above the limit, and you do too.


Tragedy of the commons what should you do3

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.

Pretty bad: Everyone fishes above the limit, and you do too.

Worst: Everyone fishes above the limit, but you don’t for some reason.


Tragedy of the commons what should you do results

Tragedy of the Commons What should you do? Results.

Lesson: No matter what everyone else is doing, you always do better by cheating.


Tragedy of the commons what should you do results1

Tragedy of the Commons What should you do? Results.

Lesson: No matter what everyone else is doing, you always do better by cheating.

Conclusion: Everyone cheats. Everyone does pretty bad.


Tragedy of the commons assigning score

Tragedy of the Commons Assigning score

(5)Best (T): temptation to cheat

(3)Next best (R): reward for cooperating

(1)Pretty bad (P): punishment for everyone cheating

(0)Worst (S): suckers payoff for cooperating against cheaters

**Scores are arbitrary, while obeying T > R > P > S, and an additional

condition: (T+P)/2 > R. These scores are the convention.


Tragedy of the commons simplified to two people

Tragedy of the Commons Simplified to two people


Tragedy of the commons simplified to two people1

Tragedy of the Commons Simplified to two people

***This is the Prisoner’s Dilemma


The prisoner s dilemma pd

The Prisoner’s Dilemma (PD)

If you are playing a cooperator, you can do best

by defecting


The prisoner s dilemma pd1

The Prisoner’s Dilemma (PD)

If you are playing a cooperator, you can do best

by defecting

If you are playing a defector, you can do best

by defecting


The prisoner s dilemma pd2

The Prisoner’s Dilemma (PD)

  • No matter what type of strategists are in a population, the best response is always to defect.


The prisoner s dilemma pd3

The Prisoner’s Dilemma (PD)

  • No matter what type of strategists are in a population, the best response is always to defect.

  • If we consider score to be a measure of fitness, then we should expect defectors to leave more offspring.


The prisoner s dilemma pd4

The Prisoner’s Dilemma (PD)

  • No matter what type of strategists are in a population, the best response is always to defect.

  • If we consider score to be a measure of fitness, then we should expect defectors to leave more offspring.

  • Defectors take over, and can’t be invaded by a cooperator.


Nice guys finish last

Nice guys finish last...

  • So defection dominates, even though everyone does worse than if everyone cooperated.


Nice guys finish last1

Nice guys finish last...

  • So defection dominates, even though everyone does worse than if everyone cooperated.

  • “Everyone cooperating” is an optimal strategy for the population, but it is unstable. Defectors invade and take over.


Nice guys finish last2

Nice guys finish last...

  • So defection dominates, even though everyone does worse than if everyone cooperated.

  • “Everyone cooperating” is an optimal strategy for the population, but it is unstable. Defectors invade and take over.

  • How can we explain the emergence of cooperation?


Achieving cooperation direct reciprocity

Achieving Cooperation: Direct Reciprocity

  • When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers).


Achieving cooperation direct reciprocity1

Achieving Cooperation: Direct Reciprocity

  • When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers)

  • We could have two agents repeat the game. Call this the Iterated PD (IPD).


Achieving cooperation direct reciprocity2

Achieving Cooperation: Direct Reciprocity

  • When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers)

  • We could have two agents repeat the game. Call this the Iterated PD (IPD).

  • Axelrod (1980a, b) hosted two round-robin tournaments of the IPD. A wide range of complex strategies were submitted...


Achieving cooperation direct reciprocity3

Achieving Cooperation: Direct Reciprocity

  • Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).


Achieving cooperation direct reciprocity4

Achieving Cooperation: Direct Reciprocity

  • Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).

  • TFT cooperates on the first turn then copies its opponent’s previous move.


Achieving cooperation direct reciprocity5

Achieving Cooperation: Direct Reciprocity

  • Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).

  • TFT cooperates on the first turn then copies its opponent’s previous move.

  • TFT can be considered as a special case of a “reactive strategy.”


Reactive strategies for the ipd

Reactive Strategies for the IPD

  • Reactive strategies are given by an ordered triple (y,p,q) that define their behaviour in the IPD.


Reactive strategies for the ipd1

Reactive Strategies for the IPD

  • Reactive strategies are given by an ordered triple (y,p,q) that define their behaviour in the IPD.

    y – probability of C on the 1st turn

    p – probability of C following a C

    q – probability of C following a D


Reactive strategies for the ipd2

Reactive Strategies for the IPD

  • Thus TFT is (1,1,0). Other interesting strategies at the vertices are:

    Always defect AllD = (0,0,0)

    Always cooperate AllC = (1,1,1)


Reactive strategies for the ipd3

Reactive Strategies for the IPD

  • Thus TFT is (1,1,0). Other interesting strategies at the vertices are:

    Always defect AllD = (0,0,0)

    Always cooperate AllC = (1,1,1)

  • (0,1,0) is “Suspicious TFT” since it defects on the first turn (nervous of strangers) then has TFT behaviour.


Evolution of tft in the ipd

Evolution of TFT in the IPD.

  • Many models consider the infinitely iterated version, or a sufficiently long version of the IPD (Nowak & Sigmund, 1992; 1994; Imhof et al., 2005)


Evolution of tft in the ipd1

Evolution of TFT in the IPD.

  • Many models consider the infinitely iterated version, or a sufficiently long version of the IPD (Nowak & Sigmund, 1992; 1994; Imhof et al., 2005)

  • This completely discounts the effects of the first turn, which allows for the reduction of strategy space from (y,p,q) to a strategy square: (p,q).


Is this biologically reasonable

Is this biologically reasonable?

  • At some levels of organization, the assumption of long games may be founded.


Is this biologically reasonable1

Is this biologically reasonable?

  • At some levels of organization, the assumption of long games may be founded.

  • For multi-cellular organisms, this assumption seems hard to justify.


Is this biologically reasonable2

Is this biologically reasonable?

  • At some levels of organization, the assumption of long games may be founded.

  • For multi-cellular organisms, this assumption seems hard to justify.

  • Also, if encounters are infrequent the agents may not recognize each other when they play again (and remember their opponents “last move”). Or end interactions early with defectors.


Let s make a model

Let’s make a model

  • Let ‘N’ individuals play the PD iterated ‘m’ times (m = 10 for results).

  • Let each individual be given by (y,p). ‘y’ matters in short games.

  • Start the population always defecting.

  • Have many generations of: selection, reproduction, mutation, death.


Selection

Selection


Selection pairing

Selection: Pairing


Selection playing

Selection: Playing


Selection first play

Selection: First Play

  • Probability of cooperating on the first turn is defined by each player’s ‘y’ value

Probability y2

Probability 1 - y2

Probability 1 – y4

Probability y4


Selection subsequent plays

Selection: Subsequent Plays

  • Probability of p2 cooperating on round i given that p4 cooperated on round i-1 is p2.

Probability p2

Probability 1 - p2

  • p4 defects in round i if p2 defected in round i - 1


Reproduction mutation death

Reproduction, Mutation, Death

  • Based on their cumulative scores, an individual is selected stochastically for reproduction.

  • Another individual is selected randomly to be replaced.

  • The reproducing individual produces an offspring with the same ‘y’ and ‘p’ value with a small chance of a random mutation.

  • All results are for population size N = 30, number of iterations m = 10, number of populations D = 50, and number of generations = 10000


Results no noise weak selection

Results: no noise, weak selection


Results no noise intermediate selection

Results: no noise, intermediate selection


Results no noise strong selection

Results: no noise,strong selection


Results noise 0 00001 strong selection 10

Results: noise = 0.00001,strong selection (10)


Results noise 0 0001 strong selection 10

Results: noise = 0.0001,strong selection (10)


Results noise 0 0001 very strong selection 30

Results: noise = 0.0001,very strong selection (30)


I have time for discussion

I have time for discussion?

  • Without noise, a population can evolve toward TFT for sufficiently strong selection – even though the game is iterated a short amount

  • With even a modest amount of noise, selection must be increased in strength to see natural selection (as opposed to drift)


I have time for discussion1

I have time for discussion?

  • For high noise (0.1%) A population must be under very strong selection to reach TFT from always defect

  • A population accomplishes this using a trajectory close to STFT.


Thanks

Thanks,

  • Students, organizers, and mentors for your discussions!

  • Special thanks to Alex and Lou for your help and patience.


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