Limits...
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.

Show MeSH

Related in: MedlinePlus

Left: Level of cooperation as a function of average number of rounds.m for three different values of the enhancement value F (4, 3 and 2) with N = 5 and in the absence of behavioral errors. Right: Gradients of Selection [5] for the evolutionary game between ALLD and AoN (b−1 = 0, N = 5, w = 0.96 or m = 25; other model parameters: Z = 100 and β = 1.0).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4230726&req=5

pcbi-1003945-g003: Left: Level of cooperation as a function of average number of rounds.m for three different values of the enhancement value F (4, 3 and 2) with N = 5 and in the absence of behavioral errors. Right: Gradients of Selection [5] for the evolutionary game between ALLD and AoN (b−1 = 0, N = 5, w = 0.96 or m = 25; other model parameters: Z = 100 and β = 1.0).

Mentions: In the following we investigate the relevant issue of asserting whether the introduction of this strategy can efficiently promote the average fraction of cooperative actions. The level of cooperation, η, may be defined as the average number of contributions per round divided by the maximum number of contributions possible. Denoting by Ci the average number of contributions per round associated with strategy Si, η reads , where τi is the fraction of time the population spends in the configuration Si and N is the group size. As shown in Figure 3, the overall levels of cooperation remain high as long as the average number of rounds is sizeable (left panel, for different values of the PGG enhancement factor F).


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

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

Left: Level of cooperation as a function of average number of rounds.m for three different values of the enhancement value F (4, 3 and 2) with N = 5 and in the absence of behavioral errors. Right: Gradients of Selection [5] for the evolutionary game between ALLD and AoN (b−1 = 0, N = 5, w = 0.96 or m = 25; other model parameters: Z = 100 and β = 1.0).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003945-g003: Left: Level of cooperation as a function of average number of rounds.m for three different values of the enhancement value F (4, 3 and 2) with N = 5 and in the absence of behavioral errors. Right: Gradients of Selection [5] for the evolutionary game between ALLD and AoN (b−1 = 0, N = 5, w = 0.96 or m = 25; other model parameters: Z = 100 and β = 1.0).
Mentions: In the following we investigate the relevant issue of asserting whether the introduction of this strategy can efficiently promote the average fraction of cooperative actions. The level of cooperation, η, may be defined as the average number of contributions per round divided by the maximum number of contributions possible. Denoting by Ci the average number of contributions per round associated with strategy Si, η reads , where τi is the fraction of time the population spends in the configuration Si and N is the group size. As shown in Figure 3, the overall levels of cooperation remain high as long as the average number of rounds is sizeable (left panel, for different values of the PGG enhancement factor F).

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
Related in: MedlinePlus