the evolution of cooperation
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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!