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Evolution of all-or-none strategies in repeated public goods dilemmas.

Pinheiro FL, Vasconcelos VV, Santos FC, Pacheco JM - PLoS Comput. Biol. (2014)

Bottom Line: We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN).AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes.The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

View Article: PubMed Central - PubMed

Affiliation: Centro de Biologia Molecular e Ambiental da Universidade do Minho, Braga, Portugal; INESC-ID & Instituto Superior Técnico, Universidade de Lisboa, Taguspark, Porto Salvo, Portugal; Centro de Física da Universidade do Minho, Braga, Portugal; ATP-group, CMAF, Instituto para a Investigação Interdisciplinar, Lisboa, Portugal.

ABSTRACT
Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games (PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

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Stationary bit distribution as a function of N.Each bit (square) corresponds to the weighted sum of the fraction of time (i.e. the analytically computed stationary distribution) the population spends in strategy configurations in which bq = 1. Blue (red) cells identify those bits that are employed at least ¾ of the time with value bq = 1.0 (bq = 0.0). The analysis provided extends for groups sizes (N) between 2 and 10 (rows). Other model parameters: Z = 100, β = 1.0, F/N = 0.85, w = 0.96, ε = 0.05, μ≪1/Z.
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pcbi-1003945-g001: Stationary bit distribution as a function of N.Each bit (square) corresponds to the weighted sum of the fraction of time (i.e. the analytically computed stationary distribution) the population spends in strategy configurations in which bq = 1. Blue (red) cells identify those bits that are employed at least ¾ of the time with value bq = 1.0 (bq = 0.0). The analysis provided extends for groups sizes (N) between 2 and 10 (rows). Other model parameters: Z = 100, β = 1.0, F/N = 0.85, w = 0.96, ε = 0.05, μ≪1/Z.

Mentions: Figure 1 shows the stationary bit distribution, , for different group sizes. Colored cells highlight those bits (bq) that retain the same value more than 75% of the time, with ≥0.75 (blue) and ≤0.25 (red). For simplicity, we associate this feature with what we call dominant bit.


Evolution of all-or-none strategies in repeated public goods dilemmas.

Pinheiro FL, Vasconcelos VV, Santos FC, Pacheco JM - PLoS Comput. Biol. (2014)

Stationary bit distribution as a function of N.Each bit (square) corresponds to the weighted sum of the fraction of time (i.e. the analytically computed stationary distribution) the population spends in strategy configurations in which bq = 1. Blue (red) cells identify those bits that are employed at least ¾ of the time with value bq = 1.0 (bq = 0.0). The analysis provided extends for groups sizes (N) between 2 and 10 (rows). Other model parameters: Z = 100, β = 1.0, F/N = 0.85, w = 0.96, ε = 0.05, μ≪1/Z.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230726&req=5

pcbi-1003945-g001: Stationary bit distribution as a function of N.Each bit (square) corresponds to the weighted sum of the fraction of time (i.e. the analytically computed stationary distribution) the population spends in strategy configurations in which bq = 1. Blue (red) cells identify those bits that are employed at least ¾ of the time with value bq = 1.0 (bq = 0.0). The analysis provided extends for groups sizes (N) between 2 and 10 (rows). Other model parameters: Z = 100, β = 1.0, F/N = 0.85, w = 0.96, ε = 0.05, μ≪1/Z.
Mentions: Figure 1 shows the stationary bit distribution, , for different group sizes. Colored cells highlight those bits (bq) that retain the same value more than 75% of the time, with ≥0.75 (blue) and ≤0.25 (red). For simplicity, we associate this feature with what we call dominant bit.

Bottom Line: We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN).AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes.The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

View Article: PubMed Central - PubMed

Affiliation: Centro de Biologia Molecular e Ambiental da Universidade do Minho, Braga, Portugal; INESC-ID & Instituto Superior Técnico, Universidade de Lisboa, Taguspark, Porto Salvo, Portugal; Centro de Física da Universidade do Minho, Braga, Portugal; ATP-group, CMAF, Instituto para a Investigação Interdisciplinar, Lisboa, Portugal.

ABSTRACT
Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games (PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

Show MeSH