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 Punishment to selfish could promote the evolution of cooperation. But .... This is a big problem!! punisher a fine Selfish incur a cost to punish a selfish player cooperate each other incur a cost to punish a selfish player benefit Altruist Selfish a fine Altruist-punisher (AP) AP can make up for a cost of punishment

The lattice promotes the evolution of cooperation, but... Iwasa, Nakamaru and Levin (1998) The lattice structured population promotes the evolution of spite damage Spiteful behavior SPITE from the viewpoint of = the payoff incur a cost to reduce others ’ fitness Punishment Nakamaru et al (1997, 1998) The score-dependent viability model also promotes the evolution of spiteful behavior in a lattice. It is suggested that the lattice and the viability model enable punishers to evolve.

Why does lattice promote the evolution of spite, especially in the Viability model? The viability model = “score = survivorship” It dies spite spite If spite succeeds in damage colonizing a new open site, The neighbor ’ s score reduces spite Its survivorship is low spite can increase in number Spite has more chance to get an empty site in the neighborhood of spite.

Strategies following Sigmund et al.(2001) There are four possible strategies: punisher nonpunisher A P A N Altruist altruist-punisher altruist-nonpunisher S P S N Selfish selfish-punisher selfish-nonpunisher paradoxical strategy! Can Selfish Punisher suppress an increase of Pure Selfish and then promote the evolution of cooperation?

Payoff Matrix q = c = 1 b, c, p, q >0 opponent A P A N S P S N AP AN SP SN A P b-c b-c -c-q -c-q AP b-c b-c -c -c A N AN focal player b-p b -q-p -q SP S P b-p b -p 0 SN S N a benefit from a cost of a fine of a cost of cooperation cooperation punishment punishing b -c -p -q An opponent AP or AN SN or SP AP or SP 0 0 0 0 An opponent An opponent AN or SN SN or SP

Spatial structured population complete mixing population lattice structued population AP SN AP AP SN AP AP AN SP SP Each interacts with four Each only interacts with four players chosen randomly nearest neighbors. The score of this “AP” The score of this “AP” = 2E[AP/AP]+E[AP/SN]+E[AP/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)- population complete mixing lattice-structured structure population population Updating rule The lattice Altruist Punisher SN always wins a benefit ( b ) (AP) always wins promotes the score-dependent evolution of fertility model Bistability SN Bistability Altruist-Punisher. always wins a fine p s n Punishment i w SN Bistability s score-dependent Bistability affects the y AP always a w viability model always evolutionary wins l a wins AP N dynamics in S always wins Viability model. How does “Selfish Punisher” play its role in these 4 models?

the Score-dependent fertility model (the Fertility model) “Birth rate” affects the dynamics of evolution. One of 4 neighbors who has a highest score can colonize the It dies randomly empty site with highest probability. score colonization probability

The result of the Fertility model in the complete mixing population AP=0.9, AN=0.03, SP=0.03, SN=0.04 Pure Selfish (SN) wins a benefit from cooperation ( b ) p = c against others Bistability a fine of punishment ( p ) Selfish-Punisher never wins against others.

the evolutionary dynamics in a two- dimensional lattice model of the Fertility model b = 5, p = 1 initial AP = 0.3, initial AN = 0.3, initial SP = 0.3, initial SN = 0.1 time = 0 Altruist- Punisher density AP Pure Altruist AP Pure Selfish Selfish- Punisher time SN time = 200 SN AN

high 0.0/0.5 SP Altruist wins The lattice of the Fertility model 0.1/0.4 SN/SP 0.4/0.1 AN+AP = 0.5 SN+SP = 0.5 0.5/0.0 50x50 lattice SN wins 0.0/0.5 0.2/0.3 0.4/0.1 0.5/0.0 SN & AP only AN/AP high AN

the Score-dependent viability model (the Viability model) “Survivorship” affects the dynamics of evolution. One who obtains a One of 4 neighbors high score dies with colonizes the empty low probability site randomly. score survivorship

The result of the Viability model in the complete mixing model AP=0.03, AN=0.9, SP=0.03, SN=0.04 Selfish-Punisher wins When p > 4 q SP < SN SP > SN SP wins against SN! a benefit from cooperation( b ) b = 3 p - 1 SN wins b = 4 p - 5 SN decreases. against others Altruist AP increases in the b = p - 8 wins bistable region SP > AP AP > SP AP + AN SP wins p wins against against others. others. KEY p = 4 q

a b b a a a b high 0.0/0.5 Altruist a b a b SP a a a b The lattice of the wins a b b a a a a b b b viability model 0.1/0.4 SN/SP 0.4/0.1 AN+AP = 0.5 0.5/0.0 SN+SP = 0.5 SN wins 50x50 lattice 0.0/0.5 0.2/0.3 0.4/0.1 0.5/0.0 SN & AP only AN/AP high AN

Summary The role of Selfish Punishment (SP), a paradoxical strategy The complete mixing population The Viability model The Fertility model -SP encourages the -Basically SP has no evolution of Altruist- effect on the Punisher (AP) evolutionary dynamics -SP itself evolves The lattice population of both models SP encourages the evolution of AP AN discourages the evolution of AP

Another interpretation as the decision-making process models The score-dependent fertility model commonly used A focal player decides to imitate a behavior of a neighbor with a high score (= attractive or socially successful). the behavior of a cooperator tends to spread Take it into account! The score-dependent viability model A focal player with a low score makes a decision to quite his/her behavior and imitate a behavior of a neighbor chosen randomly the spiteful behavior tends to spread