The coevolution of altruism and punishment: role of the selfish - - PowerPoint PPT Presentation

The coevolution of altruism and punishment: role of the selfish punisher

Mayuko Nakamaru Tokyo Institute of Technology

Altruistic punishment

Selfish Altruist Altruist-punisher (AP)

benefit

incur a cost to punish a selfish player a fine cooperate each other

AP can make up for a cost of punishment

Selfish

incur a cost to punish a selfish player a fine

punisher This is a big problem!! Punishment to selfish could promote the evolution of

• cooperation. But ....

The lattice promotes the evolution

• f cooperation, but...

Iwasa, Nakamaru and Levin (1998)

The lattice structured population promotes the evolution of spite Spiteful behavior Punishment incur a cost to reduce others’ fitness

=

damage

SPITE

from the viewpoint of the payoff

It is suggested that the lattice and the viability model enable punishers to evolve. Nakamaru et al (1997, 1998) The score-dependent viability model also promotes the evolution of spiteful behavior in a lattice.

Why does lattice promote the evolution

• f spite, especially in the Viability model?

spite

damage

spite

The neighbor’s score reduces

spite

Its survivorship is low It dies If spite succeeds in colonizing a new

• pen site,

spite can increase in number Spite has more chance to get an empty site in the neighborhood of spite.

The viability model = “score = survivorship”

Strategies following Sigmund et al.(2001)

There are four possible strategies: A punisher Altruist S Selfish nonpunisher P

altruist-punisher selfish-nonpunisher altruist-nonpunisher selfish-punisher

N A P S N paradoxical strategy! Can Selfish Punisher suppress an increase of Pure Selfish and then promote the evolution of cooperation?

Payoff Matrix

AP

b-p

• pponent

focal player

q = c = 1 b, c, p, q >0 AN SN

b-c

SP

• p
• c

AN

b-c b

SN

• c

AP

b-c

• c-q

b-c

• c-q

SP

b-p

• q-p

b

• q

SN or SP

a cost of cooperation a benefit from cooperation

AP or SP AP or AN b

• c

a fine of punishment a cost of punishing

• p
• q

SN or SP AN or SN A P A P A N A N P S P S S N S N An opponent An opponent An opponent

Spatial structured population

AP SP

AP SN

AP lattice structued population complete mixing population

Each interacts with four players chosen randomly Each only interacts with four nearest neighbors.

AP AP SN The score of this “AP” = 2E[AP/AP]+E[AP/SN]+E[AP/AP]

SP AN

The score of this “AP” = 2E[AP/AP]+E[AP/SN]+E[AP/AP] Analyzed by the computer simulation and the ordinary differential equation

Nakamaru & Iwasa (2005)

• Altruist punisher (AP) vs. Pure selfish (SN)-

lattice-structured population score-dependent fertility model score-dependent viability model complete mixing population

Updating rule population structure

SN always wins Bistability SN always wins Altruist Punisher (AP) always wins Bistability

AP always wins

a benefit (b) S N a l w a y s w i n s Bistability SN always wins AP always wins Bistability a fine p

The lattice promotes the evolution of Altruist-Punisher. Punishment affects the evolutionary dynamics in Viability model.

How does “Selfish Punisher” play its role in these 4 models?

the Score-dependent fertility model (the Fertility model)

It dies randomly One of 4 neighbors who has a highest score can colonize the empty site with highest probability.

“Birth rate” affects the dynamics of evolution. score colonization probability

The result of the Fertility model in the complete mixing population

a fine of punishment (p) a benefit from cooperation (b)

Bistability

p = c

Pure Selfish (SN) wins against others

AP=0.9, AN=0.03, SP=0.03, SN=0.04

Selfish-Punisher never wins against others.

the evolutionary dynamics in a two- dimensional lattice model of the Fertility model

Altruist- Punisher Pure Selfish

time density

b = 5, p = 1 initial AP = 0.3, initial AN = 0.3, initial SP = 0.3, initial SN = 0.1

time = 0 time = 200

AP SN

Pure Altruist Selfish- Punisher

AP AN

SN

0.5/0.0 0.4/0.1 0.2/0.3 0.0/0.5

AN/AP SN/SP

0.5/0.0 0.4/0.1 0.1/0.4 0.0/0.5

The lattice of the Fertility model

Altruist wins SN wins

AN+AP = 0.5 SN+SP = 0.5 50x50 lattice

SN & AP only high SP high AN

the Score-dependent viability model (the Viability model)

One who obtains a high score dies with low probability One of 4 neighbors colonizes the empty site randomly.

“Survivorship” affects the dynamics of evolution. score survivorship

The result of the Viability model in the complete mixing model

Altruist wins

SN wins against

• thers

Selfish-Punisher wins

b = 4p - 5 b = p - 8 b = 3p - 1

AP=0.03, AN=0.9, SP=0.03, SN=0.04

SP > SN SP < SN

p = 4q

KEY When p > 4q

p a benefit from cooperation(b)

SP wins against SN! SN decreases. AP increases in the bistable region AP + AN wins against

• thers.

AP > SP SP > AP

SP wins

against others.

The lattice of the viability model

0.5/0.0 0.4/0.1 0.2/0.3 0.0/0.5

AN/AP SN/SP

0.5/0.0 0.4/0.1 0.1/0.4 0.0/0.5

a a a a a a a a a a a a b b b b b b b b b b b a a

Altruist wins SN wins

AN+AP = 0.5 SN+SP = 0.5 50x50 lattice

SN & AP only

high SP high AN

Summary

The role of Selfish Punishment (SP), a paradoxical strategy The complete mixing population The lattice population of both models SP encourages the evolution of AP AN discourages the evolution of AP The Viability model The Fertility model

• SP itself evolves
• SP encourages the

evolution of Altruist- Punisher (AP)

• Basically SP has no

effect on the evolutionary dynamics

Another interpretation as the decision-making process models

The score-dependent fertility model The score-dependent viability model A focal player decides to imitate a behavior of a neighbor with a high score (= attractive or socially successful). A focal player with a low score makes a decision to quite his/her behavior and imitate a behavior

• f a neighbor chosen randomly

the behavior of a cooperator tends to spread the spiteful behavior tends to spread commonly used Take it into account!