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Short versus long term benefits and the evolution of cooperation in the prisoner's dilemma game.

Brede M - PLoS ONE (2013)

Bottom Line: In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators.For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons.Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations.

View Article: PubMed Central - PubMed

Affiliation: Department of Electronics and Computer Science, University of Southampton, Southampton, Hampshire, United Kingdom.

ABSTRACT
In this paper I investigate the evolution of cooperation in the prisoner's dilemma when individuals change their strategies subject to performance evaluation of their neighbours over variable time horizons. In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators. For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons. Moreover, considering the continuous spectrum in between enhanced and discounted weights of past performance, cooperation is optimally supported when cooperators neither give enhanced weight to past nor more recent events, but simply average payoffs. Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations.

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Dependence of cooperation on the dilemma strength when strategies and perspectives co-evolve.(left) Dependence of the fraction of cooperators on the dilemma strength  for various values of  (see legend) for  and  on a  square lattice. Notice, that the optimal perspective for cooperation is no longer the largest possible value of  as in Fig. 3, but cooperation is maximized near . (right) Phase diagram depicting the extinction threshold of cooperation depending on the largest timescale of payoff evaluation  (while ) for a square lattice with . Error bars are smaller than the size of the symbols.
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pone-0056016-g008: Dependence of cooperation on the dilemma strength when strategies and perspectives co-evolve.(left) Dependence of the fraction of cooperators on the dilemma strength for various values of (see legend) for and on a square lattice. Notice, that the optimal perspective for cooperation is no longer the largest possible value of as in Fig. 3, but cooperation is maximized near . (right) Phase diagram depicting the extinction threshold of cooperation depending on the largest timescale of payoff evaluation (while ) for a square lattice with . Error bars are smaller than the size of the symbols.

Mentions: Figure 8 gives data for the phase boundaries between cooperation and defection for the two perspective scenario. The first panel gives the dependence of equilibrium concentrations of cooperators on the dilemma strength for various choices of . In no case can cooperators dominate the population (in contrast to the monochrome setting discussed previously), but coexistence equilibria of cooperators and defectors are still possible even for rather tough dilemma situations. The data clearly demonstrate that the support for cooperation is maximized very close to , i.e. the perspective that averages payoff. This finding is reinforced by an analysis of the extinction threshold for the mixed phase given in the bottom panel of Fig. 8. The extinction thresholds have a sharp peak around . Exaggerating recent or past events in payoff histories strongly reduces support for cooperation and for the extinction thresholds quickly approach the known phase boundary for spatial lattices with von Neumann neighbourhoods [6].


Short versus long term benefits and the evolution of cooperation in the prisoner's dilemma game.

Brede M - PLoS ONE (2013)

Dependence of cooperation on the dilemma strength when strategies and perspectives co-evolve.(left) Dependence of the fraction of cooperators on the dilemma strength  for various values of  (see legend) for  and  on a  square lattice. Notice, that the optimal perspective for cooperation is no longer the largest possible value of  as in Fig. 3, but cooperation is maximized near . (right) Phase diagram depicting the extinction threshold of cooperation depending on the largest timescale of payoff evaluation  (while ) for a square lattice with . Error bars are smaller than the size of the symbols.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3569424&req=5

pone-0056016-g008: Dependence of cooperation on the dilemma strength when strategies and perspectives co-evolve.(left) Dependence of the fraction of cooperators on the dilemma strength for various values of (see legend) for and on a square lattice. Notice, that the optimal perspective for cooperation is no longer the largest possible value of as in Fig. 3, but cooperation is maximized near . (right) Phase diagram depicting the extinction threshold of cooperation depending on the largest timescale of payoff evaluation (while ) for a square lattice with . Error bars are smaller than the size of the symbols.
Mentions: Figure 8 gives data for the phase boundaries between cooperation and defection for the two perspective scenario. The first panel gives the dependence of equilibrium concentrations of cooperators on the dilemma strength for various choices of . In no case can cooperators dominate the population (in contrast to the monochrome setting discussed previously), but coexistence equilibria of cooperators and defectors are still possible even for rather tough dilemma situations. The data clearly demonstrate that the support for cooperation is maximized very close to , i.e. the perspective that averages payoff. This finding is reinforced by an analysis of the extinction threshold for the mixed phase given in the bottom panel of Fig. 8. The extinction thresholds have a sharp peak around . Exaggerating recent or past events in payoff histories strongly reduces support for cooperation and for the extinction thresholds quickly approach the known phase boundary for spatial lattices with von Neumann neighbourhoods [6].

Bottom Line: In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators.For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons.Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations.

View Article: PubMed Central - PubMed

Affiliation: Department of Electronics and Computer Science, University of Southampton, Southampton, Hampshire, United Kingdom.

ABSTRACT
In this paper I investigate the evolution of cooperation in the prisoner's dilemma when individuals change their strategies subject to performance evaluation of their neighbours over variable time horizons. In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators. For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons. Moreover, considering the continuous spectrum in between enhanced and discounted weights of past performance, cooperation is optimally supported when cooperators neither give enhanced weight to past nor more recent events, but simply average payoffs. Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations.

Show MeSH
Related in: MedlinePlus