the evolution of cooperation

The evolution of cooperation

Altruism and the selfish gene

Altruism: benefit b to recipient at cost -c to the donor

Altruism and the selfish gene

Altruism: benefit b to recipient at cost -c to the donor

`get the altruism out of altruism...´ (Trivers)

Altruism and the selfish gene

Altruism: benefit b to recipient at cost -c to the donor

`get the altruism out of altruism...´ (Trivers)

kin selection Hamilton´s rule: c< b.r

Altruism and the selfish gene

Altruism: benefit b to recipient at cost -c to the donor

`get the altruism out of altruism...´ (Trivers)

kin selection Hamilton´s rule: c< b.r in humans co-operation among non-relatives

Darwin:

The small strength and speed of man, his want of natural weapons, etc., are more than counterbalanced ... by his social qualities, which led him to give and receive aid from his fellow men.

Cooperation among non-relatives

Direct reciprocation and the Prisoner´s Dilemma

Indirect reciprocation Public Goods

Consequently, theories of evolution which, in accordance with the philosophies inspiring them, consider the mind as emerging from the forces of living matter, or as a mere epiphenomenon of this matter, are incompatible with the truth about man. Nor are they able to ground the dignity of the person.

Reciprocity

Reciprocal altruism...the trading of altruistic acts in which benefit is larger than cost, so that over a period of time both parties enjoy a net gain.

(Trivers)

The Prisoner´s Dilemma game

To cooperate or to defect

(example: cooperate means to give a gift of value b at cost -c)

Prisoner´s Dilemma

015defectsJohnny

5-10cooperatesJohnny

defects cooperates

Oskar Oskar

Prisoner´s Dilemma

Chicken) (like Game Snowdrift if

Dilemma sPrisoner' also if

and

Sucker ,Punishment ,Temptation Reward,

matrix Payoff

defect) and (cooperate D and C Strategies

PS

SPRTSP

RTPR

SPTR

PT

SR

The iterated Prisoner´s Dilemma

probability w for another round

(for instance, toss a coin, stop game if 6)

shadow of the future (Axelrod)

The iterated Prisoner´s Dilemma

015defect always

5-60TatFor Tit

defect alwaysTatFor Tit

The iterated Prisoner´s Dilemma

)( if Bistable

11AllD

11TatFor Tit

AllDTatFor Tit

b

c

PT

RTw

w

P

w

PwT

w

PwS

w

R

The iterated Prisoner´s Dilemma

errors! assume

TatFor Tit is (1,0)

AllD is (0,0)

D splayer'-coafter Cplay toprob q

C splayer'-coafter Cplay prob.to

strategies),(

p

qp

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

Generous Tit For Tat p close to 1 q sizeable two zones

The iterated Prisoner´s Dilemma

Bully is (0,0,0,1)

Fairbut Firm is (1,0,1,1)

TFT is (1,0,1,0)

AllD is (0,0,0,0)

AllC is )1,1,1,1(

outcomeafter Cplay toprob where

),,,(

strategies onememory

op

pppp

o

PTSR

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

Heteroclinic network A = Tit or Tat B = Firm But Fair C = Bully D = AllD

The iterated Prisoner´s Dilemma

The iterated Prisoner´s Dilemma

Pavlov

Cooperate if other player used same move as yourself in previous round

reinforcement principle: repeat former move after high payoff

Pavlov is error-correcting Pavlov is stable Pavlov cannot invade population of defectors

Pavlov

:shift-lose stay,-win

move same usedplayer -co iff cooperates

Pavlov ),,,()1,0,0,1(

CDDC

PTSRD

D

C

D

D

C

C

C

pppp PSR T

Pavlov

... C D C D C C ... C C C

... D C D C D C ... C C C

TFTagainst TFT If

C C D C C...C C C

C C D D C...C C C

Pavlovagainst Pavlov If

correcting-error is Pavlov

Pavlov

AllD invadecannot Pavlov

)2

(i.e. 2 if stable Pavlov

2 gets

2 roundper payoff

D... DD D D D D

... C D C D C D C

AllDagainst

simpleton'' a is Pavlov

bcRPT

PTAllD

SP

Pavlov

Simple learning rule

stable, error-correcting

but needs retaliator to prepare the ground

Indirect reciprocity

few rounds, as donor or receiver never with the same partner twice

Indirect reciprocity

R. Alexander: Indirect reciprocity .. involves reputation

and status, and results in everyone in the group continually being assessed and reassessed.

Indirect reciprocity

R. Alexander: Indirect reciprocity .. involves reputation and

status, and results in everyone in the group continually being assessed and reassessed.

Cooperation channelled towards cooperative members

Indirect reciprocity

score: increases by 1 if help is given, decreases by 1 if help is withheld

score 0 at birth

Indirect reciprocity

score: increases by 1 if help is given, decreases by 1 if help is withheld

score 0 at birth

strategy k: give only if recipient has score at least k

k>5: always defect k<-5: always help

Indirect reciprocity

Indirect reciprocity

Indirect reciprocity

cooperation based on discrimination but not stable (can occasionally break

down)

Indirect reciprocity

Indirect Reciprocity

William D. Hamilton

The theory of many-person games may seem to stand to that of two-person games in the relation of sea-sickness to a head-ache!