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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 the frequency of cooperation on the dilemma strength.(left) Dependence of  on  for various values of  (see legend) for  on a  square lattice. (right) Phase diagram depicting the extinction threshold of cooperation () and the extinction threshold of defection () depending on the timescale of payoff evaluation  for a square lattice with . Error bars are smaller than the size of the symbols. Notice, that cooperation can always dominate if  is slightly larger than one.
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pone-0056016-g003: Dependence of the frequency of cooperation on the dilemma strength.(left) Dependence of on for various values of (see legend) for on a square lattice. (right) Phase diagram depicting the extinction threshold of cooperation () and the extinction threshold of defection () depending on the timescale of payoff evaluation for a square lattice with . Error bars are smaller than the size of the symbols. Notice, that cooperation can always dominate if is slightly larger than one.

Mentions: By presenting a more thorough investigation of phase boundaries, the panels of figure 3 reinforce this point. The data illustrate that the support for cooperation grows systematically, when more and more emphasis is placed on the evaluation of past payoffs. A more detailed analysis of the phase transitions where cooperation or defection die out is given in the bottom panel of the figure. For cooperation dies out and defection dominates, for cooperation dominates and in between for mixed equilibria of cooperators and defectors are possible (cf. the regions labelled “C”, “D”, and “C+D” in Fig. 3). The detailed analysis of the phase transitions reveals that for choices of slightly greater than one, cooperation can even dominate over the entire range of dilemma strength, thus resolving the dilemma in any situation!


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

Brede M - PLoS ONE (2013)

Dependence of the frequency of cooperation on the dilemma strength.(left) Dependence of  on  for various values of  (see legend) for  on a  square lattice. (right) Phase diagram depicting the extinction threshold of cooperation () and the extinction threshold of defection () depending on the timescale of payoff evaluation  for a square lattice with . Error bars are smaller than the size of the symbols. Notice, that cooperation can always dominate if  is slightly larger than one.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0056016-g003: Dependence of the frequency of cooperation on the dilemma strength.(left) Dependence of on for various values of (see legend) for on a square lattice. (right) Phase diagram depicting the extinction threshold of cooperation () and the extinction threshold of defection () depending on the timescale of payoff evaluation for a square lattice with . Error bars are smaller than the size of the symbols. Notice, that cooperation can always dominate if is slightly larger than one.
Mentions: By presenting a more thorough investigation of phase boundaries, the panels of figure 3 reinforce this point. The data illustrate that the support for cooperation grows systematically, when more and more emphasis is placed on the evaluation of past payoffs. A more detailed analysis of the phase transitions where cooperation or defection die out is given in the bottom panel of the figure. For cooperation dies out and defection dominates, for cooperation dominates and in between for mixed equilibria of cooperators and defectors are possible (cf. the regions labelled “C”, “D”, and “C+D” in Fig. 3). The detailed analysis of the phase transitions reveals that for choices of slightly greater than one, cooperation can even dominate over the entire range of dilemma strength, thus resolving the dilemma in any situation!

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