Heterogeneity stabilizes reciprocal altruism interactions

In considering the phenomena of reciprocal altruism few would dispute that there are differences in individual quality-in particular, that for some individuals, at least on occasion, the cost of doing favors will exceed the potential of future benefits. That is, at any given time, a typical population is heterogeneous with respect to the affordability of reciprocal altruism. However, methodological limitations of the traditional analytical framework-Single Type (symmetric) Evolutionary Game Theory-have restricted previous analytical efforts to addressing populations idealized in terms of their averages. Here we use the methods of Multitype Evolutionary Game Theory to analyse the role of individual differences in direct reciprocity interactions. Multitype analysis shows that non-idealized populations possess an ESS profile wherein individuals who cannot afford reciprocity (low-quality) defect, while individuals who derive net benefits from reciprocity (high-quality) cooperate. Furthermore, this cooperation is implemented via unmodified tit-for-tat (TfT) strategy. Hence, our results may help resolve a long-standing problem concerning the evolutionary stability of TfT in direct reciprocal altruism. Finally, this difference between idealized and real populations is not restricted to direct reciprocal cooperation. Previously (Lotem et al., 1999) we have demonstrated evolutionarily stable indirect reciprocal cooperation among high-quality individuals in heterogeneous populations.     

Cooperators benefit through reputation-based partner choice in economic games

Explaining unconditional cooperation, such as donations to charities or contributions to public goods, continues to present a problem. One possibility is that cooperation can pay through developing a reputation that makes one more likely to be chosen for a profitable cooperative partnership, a process termed competitive altruism (CA) or reputation-based partner choice. Here, we show, to our knowledge, for the first time, that investing in a cooperative reputation can bring net benefits through access to more cooperative partners. Participants played a public goods game (PGG) followed by an opportunity to select a partner for a second cooperative game. We found that those who gave more in the PGG were more often selected as desired partners and received more in the paired cooperative game. Reputational competition was even stronger when it was possible for participants to receive a higher payoff from partner choice. The benefits of being selected by a more cooperative partner outweighed the costs of cooperation in the reputation building phase. CA therefore provides an alternative to indirect reciprocity as an explanation for reputation-building behaviour. Furthermore, while indirect reciprocity depends upon individuals giving preference to those of good standing, CA can explain unconditional cooperation.     

Competitive altruism: from reciprocity to the handicap principle

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 altruistic partners and non-altruists may become ostracized. I refer to this phenomenon as competitive altruism and propose that it can represent a move away from the dynamic responsiveness of reciprocity. Altruism may be rewarded in kind, but rewards may be indirectly accrued or may not involve the return of altruism at all, for example if altruists tend to be chosen as mates. This variety makes the idea of competitive altruism relevant to behaviours which cannot be explained by reciprocity. I consider whether altruism might act as a signal of quality, as proposed by the handicap principle. I suggest that altruistic acts could make particularly effective signals because of the inherent benefits to receivers. I consider how reciprocity and competitive altruism are related and how they may be distinguished.     

Indirect reciprocity among imperfect individuals

Reciprocal cooperation occurs when the overall benefits of receiving help exceed the costs of donating help (Q. Rev. Biol. 46 (197) 35). That is, individuals in good condition--for whom the pertinent costs are relatively small; donate help in order to secure reciprocity in their hour of need--when the benefits of receiving a donation are large. Consequently, reciprocity occurs among individuals who occasionally need help. In particular, such individuals will be unable to help others, no matter how deserving, when in need of help themselves--involuntary defection. This paper deals with the effects of involuntary defection in the context of a specific model of indirect reciprocity (i.e. reciprocal altruism that is directed toward all the cooperative members of the community) due to Nowak and Sigmund (J. Theor. Biol.194 (1998b) 561: Sections 2-4). In that model, the authors formulate the decision rules for conditional cooperation in the context of indirect reciprocity, and demonstrate that these decision rules can account for a long-term persistence of cooperation. Here we show that addition of involuntary defection to the decision rules formulated by Nowak and Sigmund results in indirect reciprocity that is evolutionary stable under appropriate conditions. Moreover, for a wide range of parameter values, evolutionary stability of cooperation requires a mixture of conditional- and unconditional-altruist behaviors. To recollect, unconditional altruist strategy can be viewed as conditional altruist strategy sans the ability to decide when the help-soliciting individual should be refused help. That is, given involuntary defection, stability of cooperation requires an occasional forgiveness, if only by default, of a failure to donate help. Thus, we see that evolutionary stable indirect reciprocity does not require perfection in either the ability to assess the merits of the help-soliciting individuals, or the ability to donate help when it is merited. On the contrary, we are forced to conclude that reciprocity, at least in the current case, is stable only among imperfect individuals.     

Error-proneness as a handicap signal

This paper describes two discrete signalling models in which the error-proneness of signals can serve as a handicap signal. In the first model, the direct handicap of sending a high-quality signal is not large enough to assure that a low-quality signaller will not send it. However, if the receiver sometimes mistakes a high-quality signal for a low-quality one, then there is an indirect handicap to sending a high-quality signal. The total handicap of sending such a signal may then still be such that a low-quality signaller would not want to send it. In the second model, there is no direct handicap of sending signals, so that nothing would seem to stop a signaller from always sending a high-quality signal. However, the receiver sometimes fails to detect signals, and this causes an indirect handicap of sending a high-quality signal that still stops the low-quality signaller of sending such a signal. The conditions for honesty are that the probability of an error of detection is higher for a high-quality than for a low-quality signal, and that the signaller who does not detect a signal adopts a response that is bad to the signaller. In both our models, we thus obtain the result that signal accuracy should not lie above a certain level in order for honest signalling to be possible. Moreover, we show that the maximal accuracy that can be achieved is higher the lower the degree of conflict between signaller and receiver. As well, we show that it is the conditions for honest signalling that may be constraining signal accuracy, rather than the signaller trying to make honest signals as effective as possible given receiver psychology, or the signaller adapting the accuracy of honest signals depending on his interests.     

Signalling among relatives. I. Is costly signalling too costly?

Zahavi''s handicap principle,originally proposed as an explanation for sexual selection ofelaborate male traits, suggests that a sufficient cost to dishonest signals can outweigh the rewards of deception and allow individuals to communicate honestly. Maynard Smith (1991) and Johnstone and Grafen (1992) introduce the Sir Philip Sidney game in order to extend the handicap principle to interactions among related individuals, and to demonstrate that stable costly signalling systems can exist among relatives.In this paper we demonstrate that despite the benefits associated with honest information transfer, the costs incurred in a stable costly signalling system may leave all participants worse off than they would be in a system with no signalling at all. In both the discrete and continuous forms of the Sir Philip Sidney game, there exist conditions under which costly signalling among relatives, while stable, is so costly that it is disadvantageous compared with no signalling at all. We determine the factors which dictate signal cost and signal benefit in a generalized version of this game, and explain how signal cost can exceed signal value. Such results raise concerns about theevolutionary pathways which could have led to the existence of signalling equilibria in nature. The paper stresses the importance of comparing signalling equilibria with other possible strategies, beforedrawing conclusions regarding the optimality of signalling.     

Altruism may arise from individual selection

The fact that humans cooperate with non-kin in large groups, or with people they will never meet again, is a long-standing evolutionary puzzle. Altruism, the capacity to perform costly acts that confer benefits on others, is at the core of cooperative behavior. Behavioral experiments show that humans have a predisposition to cooperate with others and to punish non-cooperators at personal cost (so-called strong reciprocity) which, according to standard evolutionary game theory arguments, cannot arise from selection acting on individuals. This has led to the suggestion of group and cultural selection as the only mechanisms that can explain the evolutionary origin of human altruism. We introduce an agent-based model inspired on the Ultimatum Game, that allows us to go beyond the limitations of standard evolutionary game theory and show that individual selection can indeed give rise to strong reciprocity. Our results are consistent with the existence of neural correlates of fairness and in good agreement with observations on humans and monkeys.     

Three-person game facilitates indirect reciprocity under image scoring

Reputation building plays an important role in the evolution of reciprocal altruism when the same individuals do not interact repeatedly because, by referring to reputation, a reciprocator can know which partners are cooperative and can reciprocate with a cooperator. This reciprocity based on reputation is called indirect reciprocity. Previous studies of indirect reciprocity have focused only on two-person games in which only two individuals participate in a single interaction, and have claimed that indirectly reciprocal cooperation cannot be established under image scoring reputation criterion where the reputation of an individual who has cooperated (defected) becomes good (bad). In this study, we specifically examine three-person games, and reveal that indirectly reciprocal cooperation can be formed and maintained stably, even under image scoring, by a nucleus shield mechanism. In the nucleus shield, reciprocators are a shield that keeps out unconditional defectors, whereas unconditional cooperators are the backbone of cooperation that retains a good reputation among the population.     

Reputation-based partner choice is an effective alternative to indirect reciprocity in solving social dilemmas

When group interests clash with individual ones, maintaining cooperation poses a problem. However, cooperation can be facilitated by introducing reputational incentives. Through indirect reciprocity, people who cooperate in a social dilemma are more likely to receive cooperative acts from others. Another mechanism that enhances group cooperation is reputation-based partner choice, or competitive altruism. According to this framework, cooperators benefit via increased access to cooperative partners. Our study compared the effectiveness of indirect reciprocity and competitive altruism in re-establishing cooperation after the typical decline found during repeated public goods games. Twenty groups of four participants first played a series of public goods games, which confirmed the expected decline. Subsequently, public goods games were alternated with either indirect reciprocity games (in which participants had an opportunity to give to another individual from whom they would never receive a direct return) or competitive altruism games (in which they could choose partners for directly reciprocal interactions). We found that public goods game contributions increased when interspersed with competitive altruism games; they were also higher than in public goods games interspersed with indirect reciprocity games. Investing in reputation by increasing contributions to public goods was a profitable strategy in that it increased returns in subsequent competitive altruism and indirect reciprocity games. There was also some evidence that these returns were greater under competitive altruism than indirect reciprocity. Our findings indicate that strategic reputation building through competitive altruism provides an effective alternative to indirect reciprocity as a means for restoring cooperation in social dilemmas.     

Can low-quality parents exploit their high-quality partners to gain higher fitness?

An individual's optimal investment in parental care potentially depends on many variables, including its future fitness prospects, the expected costs of providing care and its partner's expected or observed parental behaviour. Previous models suggested that low-quality parents could evolve to exploit their high-quality partners by reducing care, leading to the paradoxical prediction that low-quality parents could have higher fitness than their high-quality partners. However, these studies lacked a complete and consistent life-history model. Here, we challenge this result, developing a consistent analytical model of parental care strategies given individual variation in quality, and checking our results using agent-based simulations. In contrast to previous models, we predict that high-quality individuals always outcompete low-quality individuals in fitness terms. However, care effort may differ between high- and low-quality parents in either direction: low-quality individuals care more than high-quality individuals if their baseline mortality is higher, but less if their mortality increases more steeply with increasing care. We also highlight the ambiguity of the term ‘quality’ and stress the need for ‘genealogical consistency’ in evolutionary models.     

The long-term benefits of human generosity in indirect reciprocity

Among the theories that have been proposed to explain the evolution of altruism are direct reciprocity and indirect reciprocity. The idea of the latter is that helping someone or refusing to do so has an impact on one's reputation within a group. This reputation is constantly assessed and reassessed by others and is taken into account by them in future social interactions. Generosity in indirect reciprocity can evolve if and only if it eventually leads to a net benefit in the long term. Here, we show that this key assumption is met. We let 114 students play for money in an indirect and a subsequent direct reciprocity game. We found that although being generous, i.e., giving something of value to others, had the obvious short-term costs, it paid in the long run because it builds up a reputation that is rewarded by third parties (who thereby themselves increase their reputation). A reputation of being generous also provided an advantage in the subsequent direct reciprocity game, probably because it builds up trust that can lead to more stable cooperation.     

The truthful signalling hypothesis: an explicit general equilibrium model

In mating competition, the truthful signalling hypothesis (TSH), sometimes known as the handicap principle, asserts that higher-quality males signal while lower-quality males do not (or else emit smaller signals). Also, the signals are "believed", that is, females mate preferentially with higher-signalling males. Our analysis employs specific functional forms to generate analytic solutions and numerical simulations that illuminate the conditions needed to validate the TSH. Analytic innovations include: (1) A Mating Success Function indicates how female mating choices respond to higher and lower signalling levels. (2) A congestion function rules out corner solutions in which females would mate exclusively with higher-quality males. (3) A Malthusian condition determines equilibrium population size as related to per-capita resource availability. Equilibria validating the TSH are achieved over a wide range of parameters, though not universally. For TSH equilibria it is not strictly necessary that the high-quality males have an advantage in terms of lower per-unit signalling costs, but a cost difference in favor of the low-quality males cannot be too great if a TSH equilibrium is to persist. And although the literature has paid less attention to these points, TSH equilibria may also fail if: the quality disparity among males is too great, or the proportion of high-quality males in the population is too large, or if the congestion effect is too weak. Signalling being unprofitable in aggregate, it can take off from a no-signalling equilibrium only if the trait used for signalling is not initially a handicap, but instead is functionally useful at low levels. Selection for this trait sets in motion a bandwagon, whereby the initially useful indicator is pushed by male-male competition into the domain where it does indeed become a handicap.     

Indirect selection and individual selection in sociobiology: my personal views on theories of social behaviour

This is the story of my involvement in sociobiological studies. I first discuss group selection models, which were common in the 1950s. I then move on to kin selection and reciprocity models, which were developed to replace group selection models and are still being used by many sociobiologists, even though I argue that they contain the same weaknesses that led group selection to be rejected. As an alternative, I present the handicap principle, an essential component in all signalling. The handicap principle is useful in understanding many components of social systems, not the least of which is why individuals invest in the benefit of other members of a social system (altruism). Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.     

Tag-based indirect reciprocity by incomplete social information

Evolution of altruistic behaviour in interacting individuals is accounted for by, for example, kin selection, direct reciprocity, spatially limited interaction and indirect reciprocity. Real social agents, particularly humans, often take actions based on similarity between themselves and others. Although tag-based indirect reciprocity in which altruism occurs exclusively among similar flocks is a natural expectation, its mechanism has not really been established. We propose a model of tag-based indirect reciprocity by assuming that each player may note strategies of others. We show that tag-based altruism can evolve to eradicate other strategies, including unconditional defectors for various initial strategy configurations and parameter sets. A prerequisite for altruism is that the strategy is sometimes, but not always, visible to others. Without visibility of strategies, policing does not take place and defection is optimal. With perfect visibility, what a player does is always witnessed by others and cooperation is optimal. In the intermediate regime, discriminators based on tag proximity, rather than mixture of generous players and defectors, are most likely to evolve. In this situation, altruism is realized based on homophily in which players are exclusively good to similar others.     

Evolution of indirect reciprocity by social information: the role of trust and reputation in evolution of altruism

The complexity of human's cooperative behavior cannot be fully explained by theories of kin selection and group selection. If reciprocal altruism is to provide an explanation for altruistic behavior, it would have to depart from direct reciprocity, which requires dyads of individuals to interact repeatedly. For indirect reciprocity to rationalize cooperation among genetically unrelated or even culturally dissimilar individuals, information about the reputation of individuals must be assessed and propagated in a population. Here, we propose a new framework for the evolution of indirect reciprocity by social information: information selectively retrieved from and propagated through dynamically evolving networks of friends and acquaintances. We show that for indirect reciprocity to be evolutionarily stable, the differential probability of trusting and helping a reputable individual over a disreputable individual, at a point in time, must exceed the cost-to-benefit ratio of the altruistic act. In other words, the benefit received by the trustworthy must out-weigh the cost of helping the untrustworthy.     

Evolution of indirect reciprocity in groups of various sizes and comparison with direct reciprocity

Recently many studies have investigated the evolution of indirect reciprocity through which cooperative action is returned by a third individual, e.g. individual A helped B and then receives help from C. Most studies on indirect reciprocity have presumed that only two individuals take part in a single interaction (group), e.g. A helps B and C helps A. In this paper, we investigate the evolution of indirect reciprocity when more than two individuals take part in a single group, and compare the result with direct reciprocity through which cooperative action is directly returned by the recipient. Our analyses show the following. In the population with discriminating cooperators and unconditional defectors, whether implementation error is included or not, (i) both strategies are evolutionarily stable and the evolution of indirect reciprocity becomes more difficult as group size increases, and (ii) the condition for the evolution of indirect reciprocity under standing reputation criterion where the third individuals distinguish between justified and unjustified defections is more relaxed than that under image scoring reputation criterion in which the third individuals do not distinguish with. Furthermore, in the population that also includes unconditional cooperators, (iii) in the presence of errors in implementation, the discriminating strategy is evolutionarily stable not only under standing but also under image scoring if group size is larger than two. Finally, (iv) in the absence of errors in implementation, the condition for the evolution of direct reciprocity is equivalent to that for the evolution of indirect reciprocity under standing, and, in the presence of errors, the condition for the evolution of direct reciprocity is very close to that for the evolution of indirect reciprocity under image scoring.     

Distinctions among reciprocal altruism,kin selection,and cooperation and a model for the initial evolution of beneficent behavior

Reciprocal altruism is usually regarded as distinct from kin selection. However, because reciprocators are likely to establish long-term relations and to deliver most of their aid to other individuals genetically predisposed to reciprocation, most acts of reciprocal altruism should involve indirect increments to inclusive fitness, at least as regards alleles for reciprocation. Thus, as usually defined, reciprocal altruism is not clearly distinct from kin selection because both involve indirect increments to inclusive fitness. We propose a new definition for reciprocal altruism that makes the phenomenon distinct from kin selection and allows for reciprocation between nonrelatives in which current costs exceed future benefits returned to the reciprocal altruist. Cooperation and reciprocal altruism are often considered synonymous or different only in the timing of donating and receiving aid. We show, however, that there are other critical differences between reciprocal altruism and other forms of cooperation, most importantly, the latter often involve no clearly identifiable aid. We propose a four-category system to encompass the range of cooperative and beneficent behaviors that occur in nature (reciprocal altruism, pseudoreciprocity, simultaneous cooperation and by-product beneficence). Reciprocal altruism must involve aid that is returned to an original donor as a result of behavior that has a net cost to an original recipient. Our simplest category of cooperative/beneficent behavior, “by-product beneficence,” occurs when a selfish act also benefits another individual and requires no prior or subsequent interactions between the individuals involved. By-product beneficence may be the primitive state from which more complicated types of cooperative/beneficent behavior evolved. We show via simple models that by-product beneficence can allow for the initial increase of helping behavior in a completely unstructured population although the individuals showing such behavior pay all the costs while sharing the benefits with other individuals. Previous models that attempted to explain the initial increase of cooperative/beneficent behavior were much more complex and were based on the prisoner's dilemma, which does not accurately reflect most forms of cooperation and beneficence that occur in nature.     

How should we define goodness?--reputation dynamics in indirect reciprocity

Theory of indirect reciprocity is important in explaining cooperation between humans. Since a partner of a social interaction often changes, an individual should assess his partner by using social information such as reputation and make decisions whether to help him or not. To those who have 'good' social reputation does a player give aid as reciprocation, whereas he has to refuse to help those who have 'bad' reputation. Otherwise benefits of altruism is easily exploited by them. Little has been known, however, about the definition of 'goodness' in reputation. What kind of actions are and should be regarded as good and what kind of actions bad? And what sort of goodness enables sustaining exchange of altruism? We herein challenge this question with an evolutionary perspective. We generalize social reputation as 'Honor-score' (H-score) and examine the conditions under which individuals in a group stably maintain cooperative relationships based on indirect reciprocity. We examine the condition for evolutionarily stable strategies (ESSs) over 4096 possible cases exhaustively. Mathematical analysis reveals that only eight cases called 'leading eight' are crucial to the evolution of indirect reciprocity. Each in the leading eight shares two common characteristics: (i) cooperation with good persons is regarded as good while defection against them is regarded as bad, and (ii) defection against bad persons should be regarded as a good behavior because it works as sanction. Our results give one solution to the definition of goodness from an evolutionary viewpoint. In addition, we believe that the formalism of reputation dynamics gives general insights into the way social information is generated, handled, and transmitted in animal societies.     

Mistakes allow evolutionary stability in the repeated prisoner's dilemma game

The repeated prisoner's dilemma game has been widely used in analyses of the evolution of reciprocal altruism. Recently it was shown that no pure strategy could be evolutionarily stable in the repeated prisoner's dilemma. Here I show that if there is always some probability that individuals will make a mistake, then a pure strategy can be evolutionarily stable provided that it is "strong perfect equilibria" against itself. To be a strong perfect equilibrium against itself, a strategy must be the best response to itself after every possible sequence of behavior. I show that both unconditional defection and a modified version of tit-for-tat have this property.     

The cost of dishonesty

The handicap principle states that stable biological signals must be honest and costly to produce. The cost of the signal should reflect the true quality of the signaller. Here, it is argued that honest signalling may be maintained although the used signals are not handicaps. A game theoretic model in the form of a game of signalling is presented: all the existing evolutionarily stable strategies (ESSs) are found. Honest and cheap signalling of male quality is shown to be evolutionarily stable if females divorce the mate if it turns out that he has cheated about his quality. However, for this ESS to apply, the cost of lost time must not be too great. The stability of the honest signalling is based on deceivers being prevented from spreading in the population because they suffer from a cost of divorce. Under some fairly strict conditions, a mixed polymorphism of dishonesty and honesty represents another possible ESS.