Gilbert Roberts - Academia.edu (original) (raw)
Papers by Gilbert Roberts
Proceedings of the Royal Society B: Biological Sciences, 1998
Abstract Current work on cooperation is focused on the theory of reciprocal altruism. However, re... more Abstract Current work on cooperation is focused on the theory of reciprocal altruism. However, reciprocity is just one way of getting a return on an investment in altruism and is difficult to apply to many examples. Reciprocity theory addresses how animals respond dynamically to others so as to cooperate without being exploited. I discuss how introducing differences in individual generosity together with partner choice into models of reciprocity can lead to an escalation in altruistic behaviour. Individuals may compete for the most ...
PLoS ONE, 2013
Explaining cooperation in groups remains a key problem because reciprocity breaks down between mo... more Explaining cooperation in groups remains a key problem because reciprocity breaks down between more than two. Punishing individuals who contribute little provides a potential answer but changes the dilemma to why pay the costs of punishing which, like cooperation itself, provides a public good. Nevertheless, people are observed to punish others in behavioural economic games, posing a problem for existing theory which highlights the difficulty in explaining the spread and persistence of punishment. Here, I consider the apparent mismatch between theory and evidence and show by means of instructive analysis and simulation how much of the experimental evidence for punishment comes from scenarios in which punishers may expect to obtain a net benefit from punishing free-riders. In repeated games within groups, punishment works by imposing costs on defectors so that it pays them to switch to cooperating. Both punishers and non-punishers then benefit from the resulting increase in cooperation, hence investing in punishment can constitute a social dilemma. However, I show the conditions in which the benefits of increased cooperation are so great that they more than offset the costs of punishing, thereby removing the temptation to free-ride on others' investments and making punishment explicable in terms of direct self-interest. Crucially, this is because of the leveraging effect imposed in typical studies whereby people can pay a small cost to inflict a heavy loss on a punished individual. In contrast to previous models suggesting punishment is disadvantaged when rare, I show it can invade until it comes into a producer-scrounger equilibrium with non-punishers. I conclude that adding punishment to an iterated public goods game can solve the problem of achieving cooperation by removing the social dilemma.
PLOS ONE, 2015
Indirect reciprocity potentially provides an important means for generating cooperation based on ... more Indirect reciprocity potentially provides an important means for generating cooperation based on helping those who help others. However, the use of 'image scores' to summarize individuals' past behaviour presents a dilemma: individuals withholding help from those of low image score harm their own reputation, yet giving to defectors erodes cooperation. Explaining how indirect reciprocity could evolve has therefore remained problematic. In all previous treatments of indirect reciprocity, individuals are assigned potential recipients and decide whether to cooperate or defect based on their reputation. A second way of achieving discrimination is through partner choice, which should enable individuals to avoid defectors. Here, I develop a model in which individuals choose to donate to anyone within their group, or to none. Whereas image scoring with random pairing produces cycles of cooperation and defection, with partner choice there is almost maximal cooperation. In contrast to image scoring with random pairing, partner choice results in almost perfect contingency, producing the correlation between giving and receiving required for cooperation. In this way, partner choice facilitates much higher and more stable levels of cooperation through image scoring than previously reported and provides a simple mechanism through which systems of helping those who help others can work.
Proceedings of the Royal Society B: Biological Sciences, 2008
Indirect reciprocity (IR) occurs when individuals help those who help others. It is important as ... more Indirect reciprocity (IR) occurs when individuals help those who help others. It is important as a potential explanation for why people might develop cooperative reputations. However, previous models of IR are based on the assumption that individuals never meet again. Yet humans and other animals often interact repeatedly within groups, thereby violating the fundamental basis of these models. Whenever re-meeting can occur, discriminating reciprocators can decide whether to help those who helped others (IR) or those who helped them (direct reciprocity, DR). Here I used simulation models to investigate the conditions in which we can expect the different forms of reciprocity to predominate. I show that IR through image scoring becomes unstable with respect to DR by experience scoring as the probability of re-meeting increases. However, using the standing strategy, which takes into account the context of observed defections, IR can be stable with respect to DR even when individuals interact with few partners many times. The findings are important in showing that IR cannot explain a concern for reputation in typical societies unless reputations provide as reliable a guide to cooperative behaviour as does experience.
Journal of Theoretical Biology, 1998
In this paper we present a resource-explicit Donor-Receiver model for reciprocally altruistic int... more In this paper we present a resource-explicit Donor-Receiver model for reciprocally altruistic interactions that obeys the defining inequalities of the Prisoner's Dilemma. In our model, individuals vary in the quantity of resource they invest when cooperating (termed "generosity") and they have the freedom to opt out of interactions with potential partners on the basis of their past experiences with these players (termed "choosiness"). Dynamic optimal solutions were found using a genetic algorithm in which the decision rules (cooperate or defect), generosity when cooperating, and choosiness exhibited by individuals when deciding to opt out, were all coded on genes held on two separate chromosomes. Through this genetic algorithm, individuals that had alleles which resulted in greatest success at playing our modified Prisoner's Dilemma left more offspring. When the benefit of receiving a unit resource exceeded the cost of giving, then generous cooperative behaviour tended to emerge within the population, even when the alleles of all the individuals in the starting population were set to defect. When the probability of individuals re-encountering one another was increased, individuals not only cooperated more, but they developed greater generosity. However, as the ratio of the benefits received to costs expended increased above 1, individuals in this model remained highly cooperative but their median generosity decreased significantly. In contrast to earlier studies using genetic algorithms, the extra potential for cheating afforded by asymmetrical degrees of generosity meant that genuinely cooperative behaviour did not emerge in the equivalent round-robin tournament in which individuals were not able to exercise partner preference.
Journal of Theoretical Biology, 1999
The iterated Prisoner's Dilemma re#ects the essence of repeated cooperative interactions with sel... more The iterated Prisoner's Dilemma re#ects the essence of repeated cooperative interactions with sel"sh incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice di!erent degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in bene"ting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identi"ed using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial &&strategy soup''. Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-de"ned strategy of &&Raise-the-Stakes'', the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike &&Raisethe-Stakes'', they began trading relations at intermediate levels and, when the bene"t-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost e!ectiveness of cooperative trade.
Current Biology, 2015
An analysis of online charity donations reveals that, when males make large donations to attracti... more An analysis of online charity donations reveals that, when males make large donations to attractive female fundraisers, other males respond in kind, providing field evidence for 'competitive altruism' in which helpful acts are used as a display to attract partners.
Journal of Theoretical Biology, 2002
In this paper, we attempt to reconcile the results of several studies which have investigated the... more In this paper, we attempt to reconcile the results of several studies which have investigated the evolution of cooperation between non-relatives in systems where investment in partners can vary. In contrast to previous proposals, we show for the first time that variable-investment cooperation can be readily maintained in inter-species mutualistic relationships even in the absence of spatial structure, but that the stability of this interaction is dependent on the particular investment-response rule that is employed. By allowing the evolution of investment-response parameters in both inter- and intra-specific versions of the continuous variable-investment Prisoners' Dilemma we show that, in the absence of further factors, the raise-the stakes (RTS) strategy is likely to evolve into a simpler, variable investment form of Give-as-Good-as-you-Get that initially offers a high fixed amount and subsequently matches its partner's investment. Nevertheless, we demonstrate that genuine RTS-like strategies will still be selected if two intuitively reasonable conditions hold: if individuals are limited in terms of the total they can invest in cooperative actions over their lifetimes, and if there are always some individuals in a population that cannot cooperate.
Behavioural Processes, 2007
highlight the paradox that despite cooperative breeding being one of the prime examples of animal... more highlight the paradox that despite cooperative breeding being one of the prime examples of animal cooperation, there is surprisingly little interplay between those working on cooperative breeding and those working on cooperation more generally. We agree with their observation, and suggest that if we can understand the reasons for this then it may help to overcome the barriers. We suggest the following may be contributory factors.
Behavioural Processes, 2003
A reduction in individual vigilance with an increase in group size is one of the most frequently ... more A reduction in individual vigilance with an increase in group size is one of the most frequently reported relationships in animal behaviour, yet the reasons for it remain unclear. A key issue is whether the group-size effect is better explained by the detection (or 'many eyes') hypothesis, modelled by influential paper, or by risk dilution . This question was the focus of an earlier review . However, in this review, Beauchamp questions whether the group-size effect is due to predation-related factors at all, and whether it might instead be a consequence of foraging-related effects, particularly scramble competition. This may be seen as echoing concern that factors such as foraging effects might confound any relationship between group size and vigilance. Yet there have been a number of theoretical developments concerning the inter-relationships between group size, foraging and vigilance that make an updated review timely.
Behavioural Processes, Nov 1, 2007
highlight the paradox that despite cooperative breeding being one of the prime examples of animal... more highlight the paradox that despite cooperative breeding being one of the prime examples of animal cooperation, there is surprisingly little interplay between those working on cooperative breeding and those working on cooperation more generally. We agree with their observation, and suggest that if we can understand the reasons for this then it may help to overcome the barriers. We suggest the following may be contributory factors.
Behavioral Ecology, 2001
Abstract At any one time, a population is likely to contain individuals that are either permanent... more Abstract At any one time, a population is likely to contain individuals that are either permanently incapable of cooperating or temporarily lack the time, energy, or resources to allow them to act altruistically. These individuals have been called “phenotypic defectors.” We show that, rather than prevent cooperation from emerging, these individuals are extremely important to the stability of reciprocal altruism because they prevent the drift toward increasing naivete that is generally associated with highly cooperative ...
Nature, Aug 5, 1999
Sherratt and Roberts reply—Killingback and Doebeli argue that our cooperative strategy 'rais... more Sherratt and Roberts reply—Killingback and Doebeli argue that our cooperative strategy 'raise the stakes'1 (RTS) can be continually undermined by selection for less generous strategies. They suggest that the “lack of robustness of RTS” arises from our use of a discontinuous strategy. However, this cannot be the case because the instability they report was in their reformulation of our model in continuous terms. Whether a continuous model is “essential” is debatable. Discontinuous strategies can be more realistic, ...
Behaviour, 1993
Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water... more Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water's edge on a sandy beach. Studies of the responses of birds to disturbances have concentrated on the relationship between group size and the distance from the cause of the disturbance at which members of the group take flight (the flight reaction distance). The study of responses to disturbance is extended to consider the frequencies with which birds took flight; their flight directions (whether towards the approacher and then in behind or ...
Behaviour, 1993
Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water... more Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water's edge on a sandy beach. Studies of the responses of birds to disturbances have concentrated on the relationship between group size and the distance from the cause of the disturbance at which members of the group take flight (the flight reaction distance). The study of responses to disturbance is extended to consider the frequencies with which birds took flight; their flight directions (whether towards the approacher and then in behind or ...
Proceedings of the Royal Society B: Biological Sciences, 1998
Abstract Current work on cooperation is focused on the theory of reciprocal altruism. However, re... more Abstract Current work on cooperation is focused on the theory of reciprocal altruism. However, reciprocity is just one way of getting a return on an investment in altruism and is difficult to apply to many examples. Reciprocity theory addresses how animals respond dynamically to others so as to cooperate without being exploited. I discuss how introducing differences in individual generosity together with partner choice into models of reciprocity can lead to an escalation in altruistic behaviour. Individuals may compete for the most ...
PLoS ONE, 2013
Explaining cooperation in groups remains a key problem because reciprocity breaks down between mo... more Explaining cooperation in groups remains a key problem because reciprocity breaks down between more than two. Punishing individuals who contribute little provides a potential answer but changes the dilemma to why pay the costs of punishing which, like cooperation itself, provides a public good. Nevertheless, people are observed to punish others in behavioural economic games, posing a problem for existing theory which highlights the difficulty in explaining the spread and persistence of punishment. Here, I consider the apparent mismatch between theory and evidence and show by means of instructive analysis and simulation how much of the experimental evidence for punishment comes from scenarios in which punishers may expect to obtain a net benefit from punishing free-riders. In repeated games within groups, punishment works by imposing costs on defectors so that it pays them to switch to cooperating. Both punishers and non-punishers then benefit from the resulting increase in cooperation, hence investing in punishment can constitute a social dilemma. However, I show the conditions in which the benefits of increased cooperation are so great that they more than offset the costs of punishing, thereby removing the temptation to free-ride on others' investments and making punishment explicable in terms of direct self-interest. Crucially, this is because of the leveraging effect imposed in typical studies whereby people can pay a small cost to inflict a heavy loss on a punished individual. In contrast to previous models suggesting punishment is disadvantaged when rare, I show it can invade until it comes into a producer-scrounger equilibrium with non-punishers. I conclude that adding punishment to an iterated public goods game can solve the problem of achieving cooperation by removing the social dilemma.
PLOS ONE, 2015
Indirect reciprocity potentially provides an important means for generating cooperation based on ... more Indirect reciprocity potentially provides an important means for generating cooperation based on helping those who help others. However, the use of 'image scores' to summarize individuals' past behaviour presents a dilemma: individuals withholding help from those of low image score harm their own reputation, yet giving to defectors erodes cooperation. Explaining how indirect reciprocity could evolve has therefore remained problematic. In all previous treatments of indirect reciprocity, individuals are assigned potential recipients and decide whether to cooperate or defect based on their reputation. A second way of achieving discrimination is through partner choice, which should enable individuals to avoid defectors. Here, I develop a model in which individuals choose to donate to anyone within their group, or to none. Whereas image scoring with random pairing produces cycles of cooperation and defection, with partner choice there is almost maximal cooperation. In contrast to image scoring with random pairing, partner choice results in almost perfect contingency, producing the correlation between giving and receiving required for cooperation. In this way, partner choice facilitates much higher and more stable levels of cooperation through image scoring than previously reported and provides a simple mechanism through which systems of helping those who help others can work.
Proceedings of the Royal Society B: Biological Sciences, 2008
Indirect reciprocity (IR) occurs when individuals help those who help others. It is important as ... more Indirect reciprocity (IR) occurs when individuals help those who help others. It is important as a potential explanation for why people might develop cooperative reputations. However, previous models of IR are based on the assumption that individuals never meet again. Yet humans and other animals often interact repeatedly within groups, thereby violating the fundamental basis of these models. Whenever re-meeting can occur, discriminating reciprocators can decide whether to help those who helped others (IR) or those who helped them (direct reciprocity, DR). Here I used simulation models to investigate the conditions in which we can expect the different forms of reciprocity to predominate. I show that IR through image scoring becomes unstable with respect to DR by experience scoring as the probability of re-meeting increases. However, using the standing strategy, which takes into account the context of observed defections, IR can be stable with respect to DR even when individuals interact with few partners many times. The findings are important in showing that IR cannot explain a concern for reputation in typical societies unless reputations provide as reliable a guide to cooperative behaviour as does experience.
Journal of Theoretical Biology, 1998
In this paper we present a resource-explicit Donor-Receiver model for reciprocally altruistic int... more In this paper we present a resource-explicit Donor-Receiver model for reciprocally altruistic interactions that obeys the defining inequalities of the Prisoner's Dilemma. In our model, individuals vary in the quantity of resource they invest when cooperating (termed "generosity") and they have the freedom to opt out of interactions with potential partners on the basis of their past experiences with these players (termed "choosiness"). Dynamic optimal solutions were found using a genetic algorithm in which the decision rules (cooperate or defect), generosity when cooperating, and choosiness exhibited by individuals when deciding to opt out, were all coded on genes held on two separate chromosomes. Through this genetic algorithm, individuals that had alleles which resulted in greatest success at playing our modified Prisoner's Dilemma left more offspring. When the benefit of receiving a unit resource exceeded the cost of giving, then generous cooperative behaviour tended to emerge within the population, even when the alleles of all the individuals in the starting population were set to defect. When the probability of individuals re-encountering one another was increased, individuals not only cooperated more, but they developed greater generosity. However, as the ratio of the benefits received to costs expended increased above 1, individuals in this model remained highly cooperative but their median generosity decreased significantly. In contrast to earlier studies using genetic algorithms, the extra potential for cheating afforded by asymmetrical degrees of generosity meant that genuinely cooperative behaviour did not emerge in the equivalent round-robin tournament in which individuals were not able to exercise partner preference.
Journal of Theoretical Biology, 1999
The iterated Prisoner's Dilemma re#ects the essence of repeated cooperative interactions with sel... more The iterated Prisoner's Dilemma re#ects the essence of repeated cooperative interactions with sel"sh incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice di!erent degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in bene"ting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identi"ed using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial &&strategy soup''. Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-de"ned strategy of &&Raise-the-Stakes'', the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike &&Raisethe-Stakes'', they began trading relations at intermediate levels and, when the bene"t-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost e!ectiveness of cooperative trade.
Current Biology, 2015
An analysis of online charity donations reveals that, when males make large donations to attracti... more An analysis of online charity donations reveals that, when males make large donations to attractive female fundraisers, other males respond in kind, providing field evidence for 'competitive altruism' in which helpful acts are used as a display to attract partners.
Journal of Theoretical Biology, 2002
In this paper, we attempt to reconcile the results of several studies which have investigated the... more In this paper, we attempt to reconcile the results of several studies which have investigated the evolution of cooperation between non-relatives in systems where investment in partners can vary. In contrast to previous proposals, we show for the first time that variable-investment cooperation can be readily maintained in inter-species mutualistic relationships even in the absence of spatial structure, but that the stability of this interaction is dependent on the particular investment-response rule that is employed. By allowing the evolution of investment-response parameters in both inter- and intra-specific versions of the continuous variable-investment Prisoners' Dilemma we show that, in the absence of further factors, the raise-the stakes (RTS) strategy is likely to evolve into a simpler, variable investment form of Give-as-Good-as-you-Get that initially offers a high fixed amount and subsequently matches its partner's investment. Nevertheless, we demonstrate that genuine RTS-like strategies will still be selected if two intuitively reasonable conditions hold: if individuals are limited in terms of the total they can invest in cooperative actions over their lifetimes, and if there are always some individuals in a population that cannot cooperate.
Behavioural Processes, 2007
highlight the paradox that despite cooperative breeding being one of the prime examples of animal... more highlight the paradox that despite cooperative breeding being one of the prime examples of animal cooperation, there is surprisingly little interplay between those working on cooperative breeding and those working on cooperation more generally. We agree with their observation, and suggest that if we can understand the reasons for this then it may help to overcome the barriers. We suggest the following may be contributory factors.
Behavioural Processes, 2003
A reduction in individual vigilance with an increase in group size is one of the most frequently ... more A reduction in individual vigilance with an increase in group size is one of the most frequently reported relationships in animal behaviour, yet the reasons for it remain unclear. A key issue is whether the group-size effect is better explained by the detection (or 'many eyes') hypothesis, modelled by influential paper, or by risk dilution . This question was the focus of an earlier review . However, in this review, Beauchamp questions whether the group-size effect is due to predation-related factors at all, and whether it might instead be a consequence of foraging-related effects, particularly scramble competition. This may be seen as echoing concern that factors such as foraging effects might confound any relationship between group size and vigilance. Yet there have been a number of theoretical developments concerning the inter-relationships between group size, foraging and vigilance that make an updated review timely.
Behavioural Processes, Nov 1, 2007
highlight the paradox that despite cooperative breeding being one of the prime examples of animal... more highlight the paradox that despite cooperative breeding being one of the prime examples of animal cooperation, there is surprisingly little interplay between those working on cooperative breeding and those working on cooperation more generally. We agree with their observation, and suggest that if we can understand the reasons for this then it may help to overcome the barriers. We suggest the following may be contributory factors.
Behavioral Ecology, 2001
Abstract At any one time, a population is likely to contain individuals that are either permanent... more Abstract At any one time, a population is likely to contain individuals that are either permanently incapable of cooperating or temporarily lack the time, energy, or resources to allow them to act altruistically. These individuals have been called “phenotypic defectors.” We show that, rather than prevent cooperation from emerging, these individuals are extremely important to the stability of reciprocal altruism because they prevent the drift toward increasing naivete that is generally associated with highly cooperative ...
Nature, Aug 5, 1999
Sherratt and Roberts reply—Killingback and Doebeli argue that our cooperative strategy 'rais... more Sherratt and Roberts reply—Killingback and Doebeli argue that our cooperative strategy 'raise the stakes'1 (RTS) can be continually undermined by selection for less generous strategies. They suggest that the “lack of robustness of RTS” arises from our use of a discontinuous strategy. However, this cannot be the case because the instability they report was in their reformulation of our model in continuous terms. Whether a continuous model is “essential” is debatable. Discontinuous strategies can be more realistic, ...
Behaviour, 1993
Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water... more Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water's edge on a sandy beach. Studies of the responses of birds to disturbances have concentrated on the relationship between group size and the distance from the cause of the disturbance at which members of the group take flight (the flight reaction distance). The study of responses to disturbance is extended to consider the frequencies with which birds took flight; their flight directions (whether towards the approacher and then in behind or ...
Behaviour, 1993
Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water... more Sanderlings Calidris alba were put to flight by walking towards them as they foraged at the water's edge on a sandy beach. Studies of the responses of birds to disturbances have concentrated on the relationship between group size and the distance from the cause of the disturbance at which members of the group take flight (the flight reaction distance). The study of responses to disturbance is extended to consider the frequencies with which birds took flight; their flight directions (whether towards the approacher and then in behind or ...