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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 evolved memory lengths of cooperators, discount factors of cooperators, and density of cooperators on costs per unit of memory.The setup is the same as for the previous figure, but . Timescales are bounded by an upper limit of , and simulations were performed on a  torus using .
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pone-0056016-g005: Dependence of evolved memory lengths of cooperators, discount factors of cooperators, and density of cooperators on costs per unit of memory.The setup is the same as for the previous figure, but . Timescales are bounded by an upper limit of , and simulations were performed on a torus using .

Mentions: It is instructive to investigate a further extension of the model and allow memory lengths to co-evolve with strategies and perspectives. Since defectors make little use of past information, memory lengths of defectors are subject to random drift while memory lengths of cooperators keep increasing until the marginal benefit of further increases is counteracted by the noise level in strategy propagation. In real-world situations memory is often associated with a cost. Including such a cost per unit of time in memory, memory lengths of defectors quickly converge to zero. In contrast, memory lengths of cooperators reach an equilibrium at which the costs of memory balance the advantages for strategy spread. Figure 5 illustrates data gleaned from simulation experiments with co-evolving memory lengths, perspectives, and game strategies. The first panel gives the dependence of stationary memory length of cooperators on costs, the second the corresponding stationary perspectives and the third the stationary densities of cooperators. In all shown cases a coexistence equilibrium of cooperators and defectors could be reached. This becomes impossible above some cost threshold, at which memory becomes too costly for cooperators to allow for meaningful long-term evaluation.


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

Brede M - PLoS ONE (2013)

Dependence of evolved memory lengths of cooperators, discount factors of cooperators, and density of cooperators on costs per unit of memory.The setup is the same as for the previous figure, but . Timescales are bounded by an upper limit of , and simulations were performed on a  torus using .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0056016-g005: Dependence of evolved memory lengths of cooperators, discount factors of cooperators, and density of cooperators on costs per unit of memory.The setup is the same as for the previous figure, but . Timescales are bounded by an upper limit of , and simulations were performed on a torus using .
Mentions: It is instructive to investigate a further extension of the model and allow memory lengths to co-evolve with strategies and perspectives. Since defectors make little use of past information, memory lengths of defectors are subject to random drift while memory lengths of cooperators keep increasing until the marginal benefit of further increases is counteracted by the noise level in strategy propagation. In real-world situations memory is often associated with a cost. Including such a cost per unit of time in memory, memory lengths of defectors quickly converge to zero. In contrast, memory lengths of cooperators reach an equilibrium at which the costs of memory balance the advantages for strategy spread. Figure 5 illustrates data gleaned from simulation experiments with co-evolving memory lengths, perspectives, and game strategies. The first panel gives the dependence of stationary memory length of cooperators on costs, the second the corresponding stationary perspectives and the third the stationary densities of cooperators. In all shown cases a coexistence equilibrium of cooperators and defectors could be reached. This becomes impossible above some cost threshold, at which memory becomes too costly for cooperators to allow for meaningful long-term evaluation.

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