Data set description

The data set used for the co-citation analysis is collected from the bibliometric database ISI Web of Science, which is part of Thomson Reuters’ Web of Knowledge. The majority of the publications available in these databases are natural science and social science journal articles from (according to Thomson Reuters) high-quality journals. The data set is divided in two separate sets. The first set addresses the field of evolutionary game theory. This field is chosen because it can be seen as being strongly related to cooperation. The methodology of evolutionary game theory is often used for approaching the phenomenon of cooperation (e.g., Maynard Smith, Reference Maynard Smith1982, Reference Maynard Smith1991). The second data set addresses the evolution of cooperation. It is expected that the topic of the evolution of cooperation directly addresses mechanisms of cooperation.

For collecting the first data set, the ISI Web of Science has been queried for the keywords ‘evolutionary game theory’. Redundancies were found and erased. The remaining 930 publications are the data set for the bibliometric analysis. In addition, checking for errors inside the data, especially in the reference lists of the publications, is necessary because data from the ISI Web of Science contains errors, such as redundant entries in bibliographies and misspelled author names.

Instead of focusing on the 930 publications from the ISI Web of Science query, the references of these publications are taken into account. This procedure provides a more general data set because publications in the form of books, conference proceedings, and the like are systematically underrepresented in the ISI Web of Science. In the form of citation, however, all kinds of publications are possible. After cleansing, the 930 articles cite in total 38,777 references. Thus, the average article cites 41.7 sources. To conduct the co-citation analysis, the data set must be restricted to focus on the most influential references. Therefore, only entities are selected that are cited at least 10 times. To weight the relations in the co-citation network, the CoCit-value is calculated (Gmür, Reference Gmür2003) and an optimal threshold is determined by maximizing its discriminatory power. Altogether, the resulting network consists of 243 nodes represented by the publications and 559 edges represented by the links that are at least as strong as the threshold of the CoCit-value. The network is subdivided into nine components.

The second data set is collected in the same way as the first one. The ISI Web of Science has been queried, this time for the keywords ‘evolution of cooperation’. The resulting data set consists of 3,314 records after cleansing and these records cite 150,546 references. All entities that are cited at least 15 times are taken into account. Using the optimal CoCit-value threshold, the resulting network consists of 15 components made up of 182 publication nodes connected by 341 links.

Co-citation analysis results

Applying the Newman algorithm for identifying communities inside networks (Clauset et al., Reference Clauset, Newman and Moore2004) to the nine components of the co-citation analysis of evolutionary game theory subdivides the largest component, hereinafter referred to as cluster, into six communities, hereinafter referred to as subcluster. Table 1 lists all clusters’ and subclusters’ labels with its number of nodes, number of links, and its network density. As expected, some of the (sub)clusters of the co-citation network of evolutionary game theory address mechanisms of cooperation. The largest cluster is labeled ‘Spatiality in cooperation’; its content is about the influence of spatial conditions on cooperation. One of its subclusters (Subcluster 1.2) addresses graph selection. Graph selection is a mechanism of cooperation. It addresses the influence of spatiality represented as graphs on cooperation. Another subcluster (Subcluster 1.4) addresses the topic of voluntary or optional participation. Its publication nodes show that the possibility for people to receive a small payoff when not participating in a public good game (i.e., neither contributing nor receiving its benefits) can elicit cooperation. Thus, the subcluster's content represents a mechanism of cooperation. Cluster 3 addresses the mechanism of cooperation called costly signaling or the handicap principle. A handicap is used to demonstrate extraordinary fitness or quality. This induces cooperation with a partner who can interpret the signal. Another mechanism of cooperation is costly punishment (Cluster 6). Spending resources for punishing uncooperative behavior makes cooperation more attractive. Finally, Cluster 9 addresses reciprocal behavior in the context of animals. Making the own behavior conditional to opponent's past behavior can elicit cooperation.

Table 1.

Overview about clusters of evolutionary game theory

The co-citation analysis of the evolution of cooperation results in a network structure consisting of 15 disjoint clusters. The clusters are numbered by roman numbers (I–XV) to avoid confusion with the clusters from the co-citation analysis of evolutionary game theory. The Newman algorithm for identifying communities (Clauset et al., Reference Clauset, Newman and Moore2004) does not lead to a subdivision of the clusters into subcluster. Table 2 provides an overview.

Table 2.

Overview about clusters of evolution of cooperation

The examination of the evolution of cooperation reveals some clusters addressing mechanisms of cooperation. Cluster I in the co-citation network of the evolution of cooperation is very similar to Cluster 1 of the co-citation network of evolutionary game theory. Cooperation in the context of spatiality is the topic here as well. The second largest cluster (Cluster II) of the co-citation network of the evolution of cooperation addresses kin selection or inclusive fitness theory, which is a mechanism of cooperation explaining mutual and unilateral support between relatives. Cluster IV addresses indirect reciprocity, which can explain cooperation in asymmetric and unrepeated interactions. Cluster V focuses on reproductive skew theory; thus, its literature attempts to explain the disparity among group members’ reproduction rates. This content is related to the mechanism of group selection. As in the co-citation analysis of evolutionary game theory, direct reciprocity occupies a cluster in the co-citation analysis of the evolution of cooperation (Cluster VI). Here, reciprocity is also examined based on empirical studies of animals, but it is focused on fish species. Cluster XI addresses costly signaling which is a mechanism of cooperation already identified in the co-citation analysis of evolutionary game theory. Optional participation is represented by Cluster XIV. Some other clusters of the co-citation network of the evolution of cooperation address cooperation (e.g., Clusters VII, X, and XV), but they do not focus on particular mechanisms.

Overall, the co-citation analyses of evolutionary game theory and the evolution of cooperation reveal a considerable number of mechanisms of cooperation. Several mechanisms are addressed in both analyses. The mechanism of optional participation is not addressed in any of the extant review articles and was only identified because of the co-citation analyses. Furthermore, costly signaling has not been addressed by the extant review articles. The bibliometric examination shows in addition that the issue of cooperation in spatial structures is a particularly dynamic and current topic.

Kin selection

One approach for explaining cooperation is to consider the genetic relatedness of the interacting individuals. Individual life can only survive for a limited time and therefore the only way to conserve genes is copying. Relatives, in particular offspring, are containers of the genes. Thus, the genes can survive independently from the carrier. Supporting the offspring increases the genes’ inclusive fitness.

However, kin selection does not lead to stability of a blind support by the replicators to their copies. Through sexual propagation and mutation, the degree of genetic material shared between replicator and copy varies. Consequently, the strength of the relatedness between the supporting and the supported individual in a relationship of kin selection must be taken into account. Furthermore, the cost for the supporter, in addition to the benefit for the supported, is crucial. The relation between these parameters has been discussed early. John B. S. Haldane is regarded as the first who discovered the theory about inclusive fitness or kin selection. The formalized theory of kinship is the legacy of William D. Hamilton, who developed the rule for the stability of inclusive fitness. The genetic relatedness (r) of the players must exceed the ratio of the costs (c) for the supporter and the benefit for the supported (b) to lead to cooperation (Hamilton, Reference Hamilton1964a, Reference Hamilton1964b): c/b < r.

Possibilities to observe kin selection in nature are numerous. For instance, the eusocial behavior of the naked mole-rat is characterized by the support of the queen's offspring by her sisters instead of breeding themselves (Jarvis, Reference Jarvis1981). This can be explained by their strong genetic relatedness, which is in an average colony higher than 80% (Reeve et al., Reference Reeve, Westneat, Noon, Sherman and Aquadro1990). The most apparent example for kin selection is the colony life of social insects,Footnote ¹ which can be found in ants, wasps, and honeybees.Footnote ²

Empirical evidence for kin selection in humans can be taken from the area of evolutionary psychology. For example does care giving by grandmothers of their grandchildren depend on the fact whether she is the grandchildren's mother's mother or its father's mother. The maternal grandmother provides significantly more intense support to her grandchildren than the paternal grandmother does (Euler and Weitzel, Reference Euler and Weitzel1996). This is because through females the parenthood is confident but through males it is not. Therefore, costly care taking is directed to the one with the higher probability of genetic relatedness. Examples for kin selection in economics can be found in all cases of nepotism (e.g., Laker and Williams, Reference Laker and Williams2003). Moreover, the strength of family businesses relies on cooperation caused by kin selection.

Kin selection is represented in the co-citation analysis of the evolution of cooperation (Cluster II) and in all review articles. The co-citation analysis reveals that kin selection plays a considerable role in the literature because it is the second-largest cluster in the analysis of the evolution of cooperation. The main publication outlet is the Journal of Theoretical Biology, which contains more than 21% of the publications in the cluster. The average article is published between 2000 and 2001. This indicates some activities in the topic despite kin selection theory's age.

Green beard selection

The reasoning about the mechanism with the peculiar name green beard selection is straightforwardly derived from kin selection. Whereas in kin selection relatives are supported because they have partly the same genes, the same happens in green beard selection but without the necessity of kinship. When genes in different organisms are identical, support can be evolutionary stable. However, there is the need for a trait that can be recognized by potential supporters for the purpose of identifying carriers of the particular gene. Therefore, this trait must be a characteristic of the phenotype. This trait can be anything conspicuous, thus also a green beard.Footnote ³

The term ‘green beard’ coins Dawkins (Reference Dawkins2006 [1976]). He derives green beard selection theoretically but argues that the likelihood of green beard selection occurring is low. One reason for that is the low probability for two green beards meeting each other. In kin selection, this is no problem because here the proximity is given naturally. For green beard selection, however, this must be alleviated by a high degree of mobility. An additional problem is that the same gene that is responsible for the green beard must also determine the degree of support for the other green beards, because otherwise opportunity is given for free-riders by adapting the mimicry of the identifying trait but not the tendency for cooperation. These free-riders can therefore benefit from the cooperation by the true green beards, but save the costs for supporting others. According to this, the strategy of free-riding will invade and displace the true green beards.

By assuming that cheating is not possible, Hamilton's rule applies as much for green beard selection as for kin selection. By weakening this assumption, the possibility of cheating induces that the relatedness (r) must be increased by the inverse of the probability (p) of meeting a cheater: c/b < r · (1 − p)⁻¹.

In spite of green beards’ low likelihood for occurring, empirical research seems to show that it can evolve in animals (e.g., Keller and Ross, Reference Keller and Ross1998). Much more information based on scientific literature in context of green beard selection is provided for humans. Genetic similarity theory (Rushton et al., Reference Rushton, Russell and Wells1984) avers that genetically similar individuals are able to detect each other. Ethnic nepotism is just one salient example. In this context, it should be mentioned that green beard selection has the potential for contributing to social identity theory (Tajfel and Turner, Reference Tajfel, Turner, Worchel and Austin1986) from an evolutionary viewpoint.

Direct reciprocity

Direct reciprocity enables cooperation even between unrelated individuals. Individuals that for any reason trust in each other's reciprocation of an action that is costly for the actor but advantageous for the opponent can end up in mutual beneficial cooperation. Direct reciprocity depends on repeated interactions. Under this condition, and when the players react sensitively to each other's actions, the folk theorem becomes relevant (see, e.g., Aumann, Reference Aumann and Feiwel1985; Rubinstein, Reference Rubinstein1979) and makes cooperation a solution in Nash equilibrium. Indeed, under these conditions, cooperators perform better than defectors.

The well-known computer tournaments by Axelrod and Hamilton (Reference Axelrod and Hamilton1981) and Axelrod (Reference Axelrod1984) show that in the prisoner's dilemma, the ‘shadow of the future’ is the crucial element for the evolution of cooperation in direct reciprocity. It points out that future interactions influence current decisions. Formally, it is the probability that the game is repeated in the next iteration. It works as a discount rate of future payoffs. A general rule for the cooperation under direct reciprocity is based on the shadow of the future (ω): c/b < ω (Nowak, Reference Nowak2006).

To profit from repeated interactions, players need a memory at least capable of storing the result from the last interaction. Another requirement of direct reciprocity is that noise, in the meaning of misunderstandings of the opponents’ actions, must not be too strong (e.g., Molander, Reference Molander1985; Nowak and Sigmund, Reference Nowak and Sigmund1993).

In humans, direct reciprocity seems to be strongly related to emotions. Most importantly, the emotion of gratitude plays a central role for reciprocity. From an evolutionary viewpoint, one could even argue that gratitude and also revenge are results of adaptation processes to enable direct reciprocity.

From an analytical perspective, direct reciprocity has been examined first by Trivers (Reference Trivers1971). He analyzed reciprocal behavior based on cleaning fishes and cleaning shrimps together with their symbiotic partners, the predator fishes. After a cleaner had served by removing parasites and leftovers from the mouth of a predator fish, the latter could take the opportunity and eat the cleaner. This, however, does not happen normally. About 10 years later, the previously mentioned works (e.g., Axelrod, Reference Axelrod1984; Axelrod and Hamilton, Reference Axelrod and Hamilton1981) focus on the strategies of participants in repeated games. Therefore, computer-based simulations have been combined with genetic algorithms, and earlier, computer tournaments have been conducted. The result of identifying tit-for-tat as the best-performing strategy is well known. Later in the history of research about direct reciprocity, the assumption of absence of noise has been weakened (e.g., Nowak and Sigmund, Reference Nowak and Sigmund1993). In consequence, other strategies could demonstrate their advantages (e.g., win-stay-lose-shift).

Direct reciprocity is represented in both co-citation analyses (Cluster 9 and Cluster VI) and in all of the review articles. This reflects not only its importance for cooperation, but also its role in the scientific development of cooperation theory. However, the clusters in the co-citation analyses are not very prominent. Their focus is shaped by the discipline of biology. The main publication outlets are Behavioral Ecology and Sociobiology (Cluster VI) and Nature (Cluster 9); and the average publication is from 1989, 1990 respectively.

Overall, direct reciprocity provides an excellent explanation for the evolution of cooperation, particularly in humans. The ability to memorize is well developed in humans and seems to be a vital element in combination with reciprocity for the origin of societies. The mechanism's potential for cooperation between unrelated individuals makes reciprocity to be one of the most important aspects for human interactions in general.

Indirect reciprocity

Indirect reciprocity, in stark contrast to direct reciprocity, is not based on repeated interactions between the same individuals (e.g., Boyd and Richerson, Reference Boyd and Richerson1989; Nowak and Sigmund, Reference Nowak and Sigmund1998a, Reference Nowak and Sigmund1998b; Sigmund, Reference Sigmund2012). Thus, it provides a possible explanation for cooperation between individuals that have never met before and the likelihood of meeting again is negligible. Whereas direct reciprocity can be simplified to ‘I help you and you help me’, the case of indirect reciprocity works by ‘I help you and somebody else helps me’ (Nowak and Sigmund, Reference Nowak and Sigmund2005: 1,291; Taylor and Nowak, Reference Taylor, Nowak and Levin2009: 44, 45). This opens a potential that is much larger for welfare increase than the potential of direct reciprocity. The reason is that indirect reciprocity is not limited to the same pair of individuals. Instead, other links with larger benefit-to-cost ratios can be utilized. Therefore, indirect reciprocity can be seen as a generalization of reciprocity and it allows the exchange of resources between individuals that cannot pay their opponent directly.

Existing models and research activities regarding indirect reciprocity are methodologically based on mathematics (e.g., Nowak and Sigmund, Reference Nowak and Sigmund1998a, Reference Nowak and Sigmund1998b; Ohtsuki and Iwasa, Reference Ohtsuki and Iwasa2004; Sigmund, Reference Sigmund2010), on computer-based simulation (e.g., Brandt and Sigmund, Reference Brandt and Sigmund2004; Leimar and Hammerstein, Reference Leimar and Hammerstein2001; Nowak and Sigmund, Reference Nowak and Sigmund2005; Ohtsuki et al., Reference Ohtsuki, Iwasa and Nowak2009), and, recently, on human subject experiments (e.g., Engelmann and Fischbacher, Reference Engelmann and Fischbacher2009; Milinski et al., Reference Milinski, Semmann, Bakker and Krambeck2001, Reference Milinski, Semmann and Krambeck2002).

In general, indirect reciprocity seems to become more relevant because of an increase in specialization. The more specialization, the more diversified are the consumption possibilities, and the less frequent are the repeated interactions between the same individuals in relation to the total number of interactions. For instance, an individual who needs dental treatment and a new garden gate sees for both issues the blacksmith when she or he is part of a rather low-specialized society. Under high specialization, however, she or he has to interact with two completely different suppliers, but each time only once. In this environment, a kind of mechanism is appropriate that is not dependent on repeated interactions between the same individuals. Accordingly, the relevance of indirect reciprocity is elevated by an increase of specialization, in particular, relative to direct reciprocity. Furthermore, the relevance of indirect reciprocity increases with the rise of work in projects, as well as new opportunities in e-commerce, such as online trade. Similar to the reasoning about the increase of specialization, the decrease of repeated interactions is the point here. In projects, employees work together only for the duration of the particular project and in online trading (e.g., eBay.com and amazon.com), repeated interactions are even rarer than in project work. Accordingly, the shadow of the future is small, and hence direct reciprocity is limited. Indirect reciprocity, however, can lead to cooperation in this kind of situations.

Reputation or social status of an individual determined by its behavior reduces the problem of free-riding in indirect reciprocity. If, for example, individuals only cooperate with those of a reputation signaling that they have cooperated before, free-riding is inhibited. Thus, reputation is a key element in indirect reciprocity. The need for reputation in indirect reciprocity opens two issues. First, it demands high cognitive abilities. Second, different possibilities for determining the reputation come into play.

The high demand for cognitive abilities can be explained by examining the environmental conditions of indirect reciprocity. An audience, which is interested in the activities of others and which can understand them, is necessary for indirect reciprocity (Alexander, Reference Alexander1987). To this audience, or to parts of it, the source for reciprocation of the cooperative act is related. Moreover, communicating of the observed can extend indirect reciprocity's efficacy, but demands sophisticated communication abilities.

Furthermore, communication in general does not always deliver correct information, but noise is inevitable. Moreover, noise raises a possibility for opportunism. The deliberate manipulation of the reputation of others during the communication process could improve the communicator's situation. Such opportunism by influencing information of reputation has not yet been examined, although it represents a serious vulnerability for indirect reciprocity.

Overall, the issue of the cognitive abilities in the context of indirect reciprocity seems to be fulfilled by humans. Individuals can process the information observed by them or received from others. The usage of language to communicate the activities of others makes this possible. It increases the sphere of indirect reciprocity. Nowak and Sigmund (Reference Nowak, Sigmund, May and McLean2007: 13) even say that ‘[i]t is likely that indirect reciprocity has provided a very selective scenario that led to cerebral expansion in human evolution’ (for similar statements, see Fehr and Fischbacher, Reference Fehr and Fischbacher2004: 189; Nowak and Sigmund, Reference Nowak and Sigmund2005: 1,293).

Reputation determination is the second issue of reputation under indirect reciprocity, besides the high cognitive abilities of the participants. Here, a large set of possibilities must be considered. Even by reducing reputation to a binary value, such as good and bad, multiple ways are possible to determine it. For example, the question rises whether and how the reputation of a recipient should be considered by evaluating an individual that is asked to support (i.e., to cooperate with) that recipient. Furthermore, the reputation of the donor also can influence the evaluation. To solve that problem, a specific mechanism of reputation determination, usually called assessment rule, is necessary.

Assessment rules can be divided into first-, second-, and third-order rules (Uchida and Sigmund, Reference Uchida and Sigmund2010). A first-order rule takes only the action of the individual into account that is asked for support. If that individual (the donor) is asked to support a recipient, the donor either supports or not. The only useful first-order assessment rule is to assign a good reputation if and only if the donor helps. This assessment rule is called image scoring. Nowak and Sigmund (Reference Nowak and Sigmund1998a, Reference Nowak and Sigmund1998b) show that for the case of image scoring as definition for reputation determination, the condition c/b < q is the prerequisite for evolutionary stability of cooperation under indirect reciprocity; where q is the probability of knowing someone's reputation. In second-order assessment, there are 16 possibilities. Here, the reputation of the recipient is considered in addition to the donor's decision. This also is either good or bad. A third-order assessment rule extends the set of second-order rules by considering the reputation of the donor. Thus, 256 possibilities exist.

Particularly in business interactions, examples for indirect reciprocity can be identified. For instance, the existence of reputation scores of the traders in online auctions, such as eBay.com, shows that indirect reciprocity takes place here. With the reputation scores, the business partners can evaluate each other and the result is a reputation as percentage value. Thus, users that have never interacted before can engage in a trade relation.

Moreover, the phenomenon of knowledge transfer should receive a special attention in the context of indirect reciprocity (Zaggl and Troitzsch, Reference Zaggl, Troitzsch and Koch2012). The exchange of knowledge between users in internet fora provides an example. Here, questions and answers to different topics are exchanged. A person does not get help by the same participants she or he helped before, but others in the forum help her or him. In many of these fora it is counted how many answers each user gives. Evaluation of the answers’ quality is also common. Indirect reciprocity in the context of knowledge exchange is in particular important because it is almost impossible to measure the value of knowledge or information. According to the Arrow information paradox, the value of information cannot be estimated for a potential purchaser without knowing the information, but when the potential purchaser knows the information, there is no reason anymore to pay for it or give a truthful evaluation of the willingness to pay (see Arrow, Reference Arrow1962: 615, Reference Arrow1971: 152). Therefore, market mechanisms are not suitable for exchanging information and knowledge. Indirect reciprocity, however, allows exchanging information and knowledge without the need of the evaluation of its value. The low costs of sharing knowledge combined with the high benefit for the supported drives the potential of indirect reciprocity particularly for the exchange of knowledge.

Indirect reciprocity is represented in the co-citation analysis of the evolution of cooperation (Cluster IV). Furthermore, some of the reviews deal with it (Bergmüller et al., Reference Bergmüller, Johnstone, Russell and Bshary2007; Nowak, Reference Nowak2006; Taylor and Nowak, Reference Taylor, Nowak and Levin2009; West et al., Reference West, Griffin and Gardner2006). In Cluster IV, the main publication is the Journal of Theoretical Biology with more than 53% of all publications. Average publication year is 2002/2003. Thus, research of indirect reciprocity can be seen as driven from the discipline of biology and to be quite young.

Strong reciprocity

Strong reciprocity is often denoted as altruistic punishment (e.g., Boyd et al., Reference Boyd, Gintis, Bowles and Richerson2003; Fehr and Gächter, Reference Fehr and Gächter2002; Gintis et al., Reference Gintis, Henrich, Bowles, Boyd and Fehr2008; Rockenbach and Milinski, Reference Rockenbach and Milinski2006). This term is appropriate in the negative form of strong reciprocity. An individual is a strong reciprocator if it spends own resources to punish others who show adverse behavior (e.g., Fehr et al., Reference Fehr, Fischbacher and Gächter2002). However, also individuals spending own resources to reward others who show the desired behavior are strong reciprocators.

From a game theoretic perspective, strong reciprocity works by changing the players’ payoffs. If disliked behavior is punished, then the temptation for this behavior is reduced because disutility through punishment must be considered in addition to the actual payoff. The same applies reversely for strong positive reciprocity.

One argument for the importance of strong reciprocity derives from the weakness of (in)direct reciprocity; that is the dependence on future interactions. In situations, in which individuals are faced with serious problems in form of crises like famines, natural catastrophes, or wars – just when cooperation is needed the most – direct reciprocity fails because the probability of future interactions with the same individuals decreases tremendously (see also Gintis, Reference Gintis2000). Indirect reciprocity also depends on future interactions, not with the same individual, but with individuals from the same society. However, the continuity of that society in a crisis is questionable. Hence, indirect reciprocity neither is qualified to sustain cooperation in crises. Furthermore, it can be assumed that the costs for cooperation in such situations increase. Consequently, the general rules for the conditions of direct and indirect reciprocity predict a vanishing of cooperation in tough situations. Strong reciprocity, in contrast to (in)direct reciprocity, has the potential of sustaining cooperation even in crises.

The general problem of strong reciprocity, however, is the costs for the strong reciprocator. Although it is better for a group, and even for its individual members, when individuals who punish on own costs are present, nobody wants to pay the costs for punishing. Dreber et al. (Reference Dreber, Rand, Fudenberg and Nowak2008) support this with a human subject experiment: People who tend to punish on own costs are worse off than people who forgo costly punishment. Nonetheless, strong reciprocity can be observed empirically in many different situations.

In situations, in which the costs for the strong reciprocators are low, strong reciprocity becomes more likely to be a possible outcome of evolution. This is the case in the context of hierarchies (see also Hooper et al., Reference Hooper, Kaplan and Boone2010; Seymour et al., Reference Seymour, Singer and Dolan2007). When a highly ranked individual punishes lower ranked individuals, it can be assumed that the costs for the punisher are low and the impact of punishment is high. It can be speculated that costly punishment has developed under such conditions. Another possibility in addition to hierarchies to explain strong reciprocity as an evolutionary outcome is relating strong reciprocity to unpredictability. This holds in particular for the negative form (i.e., costly punishment). This is reasoned as follows. Perfectly predictable punishment is easy to outwit. One who knows how to provoke his opponent's punishment activity does consequently also know how to avoid provocation. Accordingly, she or he can maximize her or his opportunism under consideration of the punishment triggers. This makes the punishment activities inefficient. If, however, the punishing activities are hard to predict,Footnote ⁴ the opponent of a strong reciprocator cannot maximize his or her payoff by opportunism.

An example for strong reciprocity in the business context provides any case of a boycott by customers. Often customers avoid consuming products from companies that disappointed them in the past. If such a costumer cannot satisfy her or his demand with a substitute, her or his payoff is negatively affected.

Strong reciprocity is represented in the co-citation analysis of evolutionary game theory (Cluster 6). Furthermore, it is a topic in two of the review articles (Stevens et al., Reference Stevens, Cushman and Hauser2005; West et al., Reference West, Griffin and Gardner2006). In Cluster 6, Nature is the main publication outlet. Most of the authors of the cluster's publications are economists (e.g., Samuel Bowles, Ernst Fehr, and Herbert Gintis). This makes sense against the background of the fact that strong reciprocity is a mechanism strongly tied to humans.

Overall, the implementation of strong reciprocity to foster cooperation seems to be simple. Thus, it is one of the most important cooperation mechanisms for institutional design. The effects of hierarchy and unpredictability shall be considered. Both are crucial for reducing the costs of the strong reciprocators.

Group selection

The theory of group selection, trait-group selection, or between-group selection is about how the formations of groups, such as herds, nations, or entire species, influence selection (Bergstrom, Reference Bergstrom2002; Choi and Bowles, Reference Choi and Bowles2007).Footnote ⁵ Individuals contributing to the benefit of the group are disadvantaged relative to their non-contributing peers. However, groups with a large number of contributing members are favored over groups mainly consisting of free-riders. This trade-off has received awareness early on (Darwin, Reference Darwin1871: 163, 166) and has been solved sometimes extremely by assigning groups an equal role as individuals in evolutionary processes (Wynne-Edwards, Reference Wynne-Edwards1962). The formalization of group selection has driven deep insights and it has been shown that it induces cooperation under evolutionary conditions (Maynard Smith, Reference Maynard Smith1964; Wade, Reference Wade1978; Wilson, Reference Wilson1975). Traulsen and Nowak (Reference Traulsen and Nowak2006) show analytically the conditions for the evolution of cooperation based on group selection working under compliance of individual selection. For that purpose, they modeled a population subdivided into groups. Only the unconditional strategies cooperation and defection characterize the individuals. Cooperators support the group members while defectors do not pay the costs for cooperation, but receive the benefits provided by the cooperators in the same way as the cooperators do. The individuals reproduce proportional to their payoff and the offspring is added to their parents’ group. If a group has reached a certain size, it either splits up into two groups or one member is removed. When the group splits up, another group of the population is removed. Generally, cooperation evolves if the ratio of the benefit (b) generated by cooperation and its costs (c) is larger than the maximum group size (n) divided by the number of groups (m) plus one: b/c > 1 + n/m. An earlier model supporting group selection is provided by Wilson (Reference Wilson1975). Furthermore, each haystack model supports group selection.

Zoology provides some empirical insights about group selection. Predator inspection in fish species helps the group to survive to the disadvantage of the inspecting individuals. It is interpreted by Dugatkin and Mesterton-Gibbons (Reference Dugatkin and Mesterton-Gibbons1996) as group selection. A single fish or a small subgroup departs the fish school to approach a potential predator. The advantage for the whole group is to find out whether the predator is a threat. The disadvantages, such as reduced foraging and, even more important, the risk of death by predation, are born only by the inspecting fish. Further examples can be found by looking at warning calls in birds (e.g., Taylor et al., Reference Taylor, Balph and Balph1990) and even in microbiology (e.g., Johnson, Reference Johnson1986). In humans in general, solidarity in groups, for example nations, can be considered an instance of group selection. In wars, characteristics of group selection become salient; also, conflicts between different religions can be seen as examples for group selection in humans (Choi and Bowles, Reference Choi and Bowles2007; van den Bergh and Gowdy, Reference van den Bergh and Gowdy2009). It is intuitively correct to say that whenever the threats from outside a group are rising, then the group cohesion increases. This may be the reason why groups often stress the potential of threats from outside.

The greatest potential of the mechanism of group selection is not necessarily its capability to induce cooperation directly (as it has been shown by the models of, e.g., Choi and Bowles, Reference Choi and Bowles2007; Maynard Smith, Reference Maynard Smith1964; Traulsen and Nowak, Reference Traulsen and Nowak2006). Instead one can focus on the fertile ground groups provide for other mechanisms, such as strong and indirect reciprocity. For instance, the problem of higher order free-riding in costly punishment can vanish in the group context. Participants able to choose between groups, in which free-riders are either punished or not, prefer the punishing environment (Gürerk et al., Reference Gürerk, Irlenbusch and Rockenbach2006). In the presence of groups with low performance, punishers are likely to be better off than the majority. For indirect reciprocity, groups provide a useful environment that ensures the conformity of assessment rules. Even more fundamentally, groups have the potential for making sure that reputation is accepted as a kind of currency for exchange. Strong and indirect reciprocity do not only profit from group selection. Reversely, the mechanisms of reciprocity push the effect of group selection by strengthening the members of the groups employing them. Also the mechanism of optional participation seems to have a strong relation with group selection. It may play a central role for the initial formation of groups. The interactions of other mechanisms with group selection make it hard to isolate it in empirical observations. However, one can speculate that the interactions shift the potential for cooperation significantly.

Costly signaling

Costly signaling is rooted in evolutionary biology as well as in economics. The development of the theory is triggered by the observation that in some animal species, especially birds, the males impose a burden on themselves by showing a salient appearance (e.g., the pheasant and the peacock). This appearance is accompanied by disadvantages, e.g., the predation risk increases because of lower escaping chances.

Zahavi (Reference Zahavi1975) first approached the question of how these animals developed their handicaps under the conditions of natural selection. Surely, sexual selection by females is an explanation, but this fact alone is not sufficient. Since sexual selection itself is subject of natural selection, an additional element is needed that explains stability. The answer is that the males of the mentioned bird species are able to demonstrate an extraordinary fitness through the handicap. Because the females cannot verify their fitness directly, the males take the burden of a handicap. The fitter males’ costs for affording the handicap are relatively lower than the costs for less fit males. Consequently, the females’ quality of information for evaluating potential mates is improved. Important is that the signal can only be credible if it is costly (Maynard Smith, Reference Maynard Smith1991). Thus, the costs must directly be connected to the signal (Grafen, Reference Grafen1990).

Costly signaling plays an important role in humans as well. Besides costly signals in sexual selection, for instance luxury cars or other status symbols, examples in economics are apparent. Thus, it is possible that costly signaling has the potential to explain the Veblen (Reference Veblen1899) effect. In business interactions as in the case of mating, information asymmetries are prevailing. Therefore, investing in a signal often makes sense for the party with hidden qualities.Footnote ⁶

Spence (Reference Spence1973), even earlier than Zahavi (Reference Zahavi1975), used costly signaling theory in economics, more precisely in the context of job markets. The reasoning is the same. A signal must affect productivity negatively to distinguish different job applicants; in other words, it must be costly. Thus, education is an example for a signal in this context. The better-qualified applicant shows that she or he has to pay lower costs for the education. Other examples in economics are all kinds of warranties voluntarily provided by suppliers. These are costly signals send to the consumer. The supplier has more information about the product and attempts to convince the customer of the hidden quality of the product. The supplier with the better product has lower costs for offering the warranties in contrast to her or his competitors.

Costly signaling is represented in the co-citation analysis of evolutionary game theory (Cluster 3). Furthermore, it is represented in combination with religions in the co-citation analysis of the evolution of cooperation (Cluster XI). According to Cluster 3, costly signaling is closely associated with the discipline of biology. Journal of Theoretical Biology and Animal Behavior together have a share of 75% of the publications. The economics literature mentioned is not part of the cluster.

Overall, costly signaling is highly relevant whenever unequally informed parties interact. The problem of hidden characteristics and hidden information can be overcome, at least partly, with costly signaling.

Graph selection

The idea of graph selection theory is to consider spatial structures between individuals or players. This is implicitly done in all models dealing with cooperation, but in most cases either pairwise interaction or playing the field (i.e., random pairing or global interaction with all others at the same time) is assumed. Graph selection, however, approaches to explain cooperation explicitly dependent on the spatial structure (Durrett and Levin, Reference Durrett and Levin1994; Ebel and Bornholdt, Reference Ebel and Bornholdt2002).

In general, the modeling of spatial structures can be represented by grids (e.g., cellular automata; Hassell et al., Reference Hassell, Comins and May1994; Hauert and Doebeli, Reference Hauert and Doebeli2004; Nakamaru et al., Reference Nakamaru, Matsuda and Iwasa1997, Reference Nakamaru, Nogami and Iwasa1998) or networks (Lieberman et al., Reference Lieberman, Hauert and Nowak2005; Santos and Pacheco, Reference Santos and Pacheco2005; Santos et al., Reference Santos, Pacheco and Lenaerts2006a, Reference Santos, Rodrigues and Pacheco2006b; Skyrms and Pemantle, Reference Skyrms and Pemantle2000). The spatial structure is crucial for the origin of cooperation (Nowak and May, Reference Nowak and May1992, Reference Nowak and May1993; Nowak et al., Reference Nowak, Bonhoeffer and May1994). For example, Abramson and Kuperman (Reference Abramson and Kuperman2001) show that even with players that are only able to play two pure unconditional strategies (cooperation and defection) and imitate the most successful neighbor's strategy, a cooperating community can emerge. Thus, cooperation can derive merely from the spatial structure. A general approximation for a rule for the stability of cooperation on regular graphs can be derived analytically (Ohtsuki and Nowak, Reference Ohtsuki and Nowak2006; Ohtsuki et al., Reference Ohtsuki, Hauert, Lieberman and Nowak2006): b/c > k. The number of neighbors (k) must be smaller than the benefit–cost ratio.

An early approach for spatial modeling of cooperation games comes from Axelrod (Reference Axelrod1984: 158–168). Straightforward from the exploration of optimal strategies in the prisoner's dilemma, he applied a two-dimensional structure to model territoriality. Overall, the theory of graph selection is very young and seems to develop further. Providing examples for graph selection lacks of empirical studies that are specifically designed for this. In the era of Web 2.0 and especially in online games, powerful possibilities have arisen for gathering data containing information about spatial influences on cooperation.

Graph selection is represented in both co-citation analyses (Subcluster 1.2 and Cluster I). Furthermore, only two review articles address it (Nowak, Reference Nowak2006; Taylor and Nowak, Reference Taylor, Nowak and Levin2009). The mechanism plays the most prominent role in both co-citation analyses. Cluster 1.2 reveals that the discipline of physics has a crucial impact on graph selection theory's development. More than 48% of the publications are published in Physical Review E or in Physical Review Letters. In Cluster I, Physical Review E accounts for more than 36%. Moreover, the publications are very young. The average publication year in both clusters is between 2005 and 2006.

Set selection

Set selection, or evolutionary set theory, is closely tied to graph selection.Footnote ⁷ Both share the characteristic of spatiality in cooperation. The underlying representations differ, however. In set selection, the probability of interaction between two players is not homogeneously deviated over the population as it is in well-mixed models. Instead, players interact depending on their memberships in sets. Basically, a member of a set interacts with all other members of the same set. Sets can overlap, and thus, players can interact multiple times.

Evolutionary set theory is the youngest of the mechanisms explaining cooperation. Tarnita et al. (Reference Tarnita, Antal, Ohtsuki and Nowak2009) originally introduce it with a model that includes evolutionary updating of the player's strategies and a static environment of sets. As long as the number of memberships in sets for all players is equal, an analytical approach is possible. Weakening this assumption requires simulations.

In contrast to most of the graph models, fixed spatial structures are not assumed in set selection. Instead, the set membership of the players can change. Thus, set selection models represent systems with a large degree of dynamics. This trait makes set selection a promising candidate for modeling issues of cultural evolution.

Optional participation

Optional (or voluntarily) participation is an interesting mechanism for the evolution of cooperation. Making participation voluntary can drive cooperation in dilemma games. Thereby non-participation provides a small payoff. Consequently, three basic strategies are possible: participating and contributing (cooperation); participating and not contributing (defection) i.e., free-riding; and not participating (loner). Hauert et al. (Reference Hauert, Monte, Hofbauer and Sigmund2002b) and Semmann et al. (Reference Semmann, Krambeck and Milinski2003) show analytically and experimentally that optional participation leads to a cyclic change of the three strategies. In consequence, the degree of cooperation is considerably higher than without the option of not participating.

The cyclic change of the strategies is a sequence of loner; followed by cooperation in the public good game, because the group can generate higher payoffs; followed by defection in the public good game, because free-riding dominates cooperation; followed again by loner, because self-supply generates higher payoffs. The relative dominance of the three strategies is opposed by this sequence of the three states. Figure 1 shows the cyclic sequence and the relation between the strategies. This sequence is sufficient to prevent a permanent invasion by free-riders.

Figure 1.

Sequence dynamics and strategy dominance of optional participation.

Looking at optional participation from an abstract view reveals a fundamental logic. Therefore, it is useful to start with a normal public good game. Defection represents the only equilibrium when considering both basic pure strategies (i.e., unconditional cooperation and unconditional defection). The solution to the dilemma is introducing a third strategy with the characteristic that it dominates defection but itself is dominated by cooperation. This strategy is self-supply (i.e., the loner strategy). Overall, a transitive system is altered to an antitransitive system.

In such dynamics, which can also be found in the rock–paper–scissors game, a clear and unilateral relation of dominance between two strategies results when the third strategy dies out. This leads to a direct implication: It is not useful to over-dominate competitors, because they are the only element that protects oneself of being dominated. Furthermore, the dynamics reveal a fundamental limitation: The mechanism of cooperation can never lead to a first-best solution. The phases of not contributing to the public good game and the loner phases are essential parts of the cyclic dynamics. Here, the potential of increasing welfare by cooperation remains unexploited.

Besides its importance for cooperation, optional participation seems to be a crucial ingredient for the development of social systems including norms. This puts optional participation, in addition to its function as a mechanism of cooperation on its own, into the role of a supporter for the development of other mechanisms, such as group selection or strong reciprocity. In particular, strong reciprocity cannot evolve in populations dominated by defectors because it includes higher-order public good problems: Single or a small group of strong reciprocators are not able to establish without further explanation. However, optional instead of obligatory participation – as shown analytically and with computer-based simulations by Hauert et al. (Reference Hauert, Traulsen, Nowak and Sigmund2007) – makes it much more likely that societies evolve using punishment for sustaining cooperation.

Optional participation is represented in both co-citation analyses (Subcluster 1.4 and Cluster XIV). No review article addresses it. The clusters indicate that the theory of optional participation is quite young. The average publication is from 2002 to 2003. Furthermore, the clusters are very small suggesting only a few activities in the literature.

By-product mutualism

By-product mutualism is a simple but restricted mechanism for the evolution of cooperation (see, e.g., Clutton-Brock, Reference Clutton-Brock2009; Dugatkin, Reference Dugatkin1997a). By-product mutualism leads to cooperation because the optimal decision, even for purely self-regarding players and without further conditions, results in the optimal outcome for the opponent(s) as well. Thus, ‘[a]ny individual that defects (i.e., does not cooperate) in mutualistic situations will, by definition, do worse than a cooperator [. .]’ (Stevens et al., Reference Stevens, Cushman and Hauser2005: 500). Single individuals that benefit from aggregating their power, for instance fish or bird swarms, are cases of by-product mutualism.Footnote ⁸

In consequence, it is important that situations allowing for by-product mutualism are not characterized by rivalry between cooperators. From an economic perspective, by-product mutualism is nothing else than a positive externality of an individual's action. In the examples of swarms, the benefit of the externality comes only into being when enough individuals participate. However, in dyadic relations, by-product mutualism is also possible. In situations characterized by strong rivalry, in contrast, by-product mutualism is not possible. The mechanism is restricted to games characterized by the following payoff matrix: $\begin{array}{cc} \scriptsize{\begin{array}{l} cooperate \\ defect \end{array}} & \scriptsize{{\big( {\begin{array}{*{20}c} R & S \\ T & P \end{array}} \big)}}\end{array}$, with R > T and S > P. A general rule for by-product mutualism is defined by c < 0; thus, the cost for the player must be negative to induce cooperation. Thus, in a strict sense, interactions based on by-product mutualism do not fulfill the definition of cooperation.

Examples from animals in the literature are numerous, particularly in fish species (Dugatkin, Reference Dugatkin1997a; Dugatkin and Mesterton-Gibbons, Reference Dugatkin and Mesterton-Gibbons1996). Utility from products with network externalities can be seen as examples for by-product mutualism in economics. The classical example for network externalities is the telephone. Each individual that acquires a telephone increases the utility of all other telephone users.

By-product mutualism has an enormous potential from the perspective of mechanism design. The behavior of players can be influenced by subsidizing particular outcomes. Accordingly, the player's payoff for the decision that leads to the result preferred by the designer is increased. From the player's perspective each action conform to such an incentive produces a positive by-product for the benefit of the designer. The costs for the subvention of the payoffs must not be too high to assure an efficient use. Examples for artificially created by-product mutualism are all kinds of compensation contracts to generate incentives.

Overall, by-product mutualism leads directly to a set of interesting questions in the social sciences with relevance for economics. For instance, repeated interactions between players are more realistically modeled when the payoffs vary over time. Not all interactions have the same costs and benefits. Thus, human interactions characterized by positive externalities are mixed with interactions characterized by dilemma structures. It could have a crucial effect on reciprocal behavior if the players are able to distinguish between cases of cooperation that are either costly (as in a prisoner's dilemma) or not costly for the opponent (as in the payoff matrix of the harmony game above, where R > T and S > P). Interesting issues in this context are communication and signaling. A player, who cooperates based on by-product mutualism, could try to exaggerate his cooperativeness to convince his opponent to cooperate in the next dilemma situation. Overall, by-product mutualism plays therefore an important role, in particular, in the context of other mechanisms.