Heuristics Facilitates the Evolution of Transitive Inference and Social Hierarchy in a Large Group.

Transitive inference (TI) refers to social cognition that facilitates the discernment of unknown relationships between individuals using known relationships. It is extensively reported that TI evolves in animals living in a large group because TI could assess relative rank without deducing all dyadic relationships, which averts costly fights. The relationships in a large group become so complex that social cognition may not be developed adequately to handle such complexity. If members apply TI to all possible members in the group, TI requires extremely highly developed cognitive abilities especially in a large group. Instead of developing cognitive abilities significantly, animals may apply simplified TI we call reference TI in this study as heuristic approaches. The reference TI allows members to recognize and remember social interactions only among a set of reference members rather than all potential members. Our study assumes that information processes in the reference TI comprises (1) the number of reference members based on which individuals infer transitively, (2) the number of reference members shared by the same strategists, and (3) memory capacity. We examined how information processes evolve in a large group using evolutionary simulations in the hawk-dove game. Information processes with almost any numbers of reference members could evolve in a large group as long as the numbers of shared reference member are high because information from the others' experiences is shared. TI dominates immediate inference, which assesses relative rank on direct interactions, because TI could establish social hierarchy more rapidly applying information from others' experiences.

Ecological features benefiting sustainable harvesters in socio-ecological systems: a case study of Swiftlets in Malaysia.

A major challenge in biodiversity management is overharvesting by unsustainable harvesters. If a scenario could be created where sustainable harvesters benefit more than the unsustainable ones, even in the short term, the issue of overharvesting would be solved. Everyone would then follow the lead of sustainable harvesters. However, creating such a scenario is not an easy task; the difficulty is intensified if the habitat is open access and there is no property rights system. Swiftlets in Sarawak, Malaysia, present a special case where sustainable harvesters are believed to be more beneficial than unsustainable harvesters. Edible nests built by adult Swiftlets are used as ingredients for a traditional luxurious soup in Chinese cuisine. A rise in nest prices has increased the instances of unsustainable harvesters wrongfully collecting nests along with the eggs and fledglings, which are then abandoned. Swiftlets live in caves and build nests on cave ceilings. It is known that Swiftlets escape from cave ceilings when these harvesters take the nests, never to return to the same place. This ecological feature appears to work as the Swiftlet's indirect punishment against unsustainable harvesters. This study constructs a stage-structured population model and examines the effect of property rights and the indirect punishment by Swiftlets on the population dynamics of the bird, and on the economic return of both sustainable and unsustainable harvesters. Our findings are as follows: the indirect punishment by Swiftlets provides sustainable harvesters a higher short-term return than unsustainable harvesters under the property rights system, as long as Swiftlets return to their original cave after escaping from the unsustainable harvesters. While previous studies regarding the management of the commons have stressed the importance of rules and regulations for sustainable harvesting without considering the ecological uniqueness of each species, this study suggests that ecological exploration and the discovery of ecological features are also essential for designing a sustainable framework.

Preservation of the value of rice paddy fields: Investigating how to prevent farmers from abandoning the fields by means of evolutionary game theory.

The evolution of group cooperation is still an evolutionary puzzle and has been studied from the perspective of not only evolutionary ecology but also social sciences. Some socio-ecological problems are caused by collapse of group cooperation. By applying theoretical studies about the evolution of cooperation, we can elucidate what causes the problems and find solutions. One of the appropriate examples is maintaining rice paddy field landscapes, which are a grand spectacle in Asia, and some are UNESCO world heritage sites. These magnificent landscapes and the associated biodiversity are at risk of abandonment for social and financial reasons. Rice paddy fields can be preserved not only by regular cultivation, which requires farmers to invest effort in cultivation, but also by the maintenance of common facilities such as irrigation canals. To investigate how this landscape might be preserved, we developed an agent-based model in which each farmer makes two types of efforts: an effort for land cultivation and an effort for collective action such as common facility maintenance. Additionally, we consider the side effects of rice production such as field deterioration from abandonment and water use competition. These factors determine the utility of each player who imitates the level of efforts necessary to invest in land cultivation and common facility maintenance of one with higher utility. This decision-making of each player can be described by the evolutionary game theory. We find that maintenance effort promotes cultivation effort, but not vice versa, even though we usually consider that each farmer's cultivation effort makes rice field landscape sustainable. We also find that if players and their near neighbors are responsible for maintaining their common facilities together, they continue to maintain them and cultivate, but if all players are responsible for maintaining all facilities in the whole farmland, players are likely to quit facility maintenance and stop cultivation. Competition for water use among all players, however, promotes cultivation more than competition among neighbors only. Therefore, rice paddy field landscapes can be sustainable if neighbors, but not the whole players, are responsible for maintaining their common facilities and cooperate together, and if the water usage of all players, but not neighbors, influences the productivity of each rice field.

Large group size promotes the evolution of cooperation in the mutual-aid game.

Our society is based on group cooperation, but this remains an unsolved problem from the viewpoint of evolutionary biology and the social sciences. Group cooperation is often studied through the public goods game, and it has been shown that large group size never promotes the evolution of cooperation. We consider the mutual-aid game, in which one member of the group is chosen randomly as the aid recipient, and other members decide whether to help the recipient. This game can describe the early stage of insurance provision in England, for example. With reference to existing indirect reciprocity studies, we investigate what promotes the evolution of cooperation in the mutual-aid game by means of replicator equations and agent-based simulations. Our key findings are as follows. In a multilateral relationship in which members play the mutual-aid game in a group whose size is greater than two, once two or more defectors are in bad standing, they remain bad under the rule that a donor's bad reputation remains bad, whether or not the donor helps a recipient with a bad reputation. Then, cooperators never help them, and mutation helps the invasion of rare cooperators more when the group size is larger in the finite population, even when implementation and perception errors occur. Meanwhile, this rule never helps the invasion in the bilateral relationship in which the group size is two. Our results suggest that large group cooperation can be sustainable if social institutions are equipped with systems such as those in the mutual-aid game.

The coevolution of transitive inference and memory capacity in the hawk-dove game.

Transitive inference (TI) that uses known relationships to deduce unknown ones (using A > B and B > C to infer A > C given no direct interactions between A and C) to assess the opponent's strength, or resource-holding potential (RHP), is widely reported in animals living in a group. This sounds counter-intuitive because TI seems to require social cognition and larger memory capacity than other inference that does not require social cognition as much as TI; individuals need abilities to identify others, observe contests among others and keep the results in memory. We examine the coevolution of memory and transitive inference by the evolutionary simulations, using the asymmetric hawk-dove game. When a cost for losers is higher than a reward for winners, we found that the immediate inference strategy (II), which estimates the opponent's strength based on the past history of the direct fights, evolves with the large memory capacity, while the TI strategy, which estimates the unknown opponent's strength by transitive inference, evolves with the limited memory capacity. When a cost for losers is slightly higher than a reward for winners, the II strategy with the large memory capacity has an evolutionary advantage over the TI strategy with the limited memory capacity. It is because the direct fights are not so costly that more information about the fights leads to more accurate estimation of the opponent's strength and results in the accurate rank of the RHPs. When a cost for losers is much higher than a reward for winners, the TI strategy with the limited memory capacity has an evolutionary advantage. It is because a good way to avoid the costly fights is the prompt formation of the dominance hierarchy which does not necessarily reflect the actual rank of the RHPs; the TI strategy builds the dominance hierarchy much faster than the II strategy regardless of memory capacity, and the large amounts of information are not required for the TI strategy to form the dominance hierarchy promptly. Our study suggests that even smaller memory capacity is evolutionarily favored in TI. The TI strategy tends to reinforce the hierarchy once it is built, regardless of whether it is consistent with RHP or not, because results of direct fights are always counted. Smaller memory capacity allows players to adjust the hierarchy well if it does not represent RHP. These results prove that TI can evolve without a requirement for large memory.

The effect of sanctions on the evolution of cooperation in linear division of labor.

The evolution of cooperation is an unsolved research topic and has been investigated from the viewpoint of not only biology and other natural sciences but also social sciences. Much extant research has focused on the evolution of cooperation among peers. While, different players belonging to different organizations play different social roles, and players playing different social roles cooperate together to achieve their goals. We focus on the evolution of cooperation in linear division of labor that is defined as follows: a player in the i-th role interacts with a player in the i + 1-th role, and a player in the n-th role achieves their goal (1 ≤ i < n) if there are n roles in the division of labor. We take the industrial waste treatment process as an example for illustration. We consider three organizational roles and Bi is the i-th role. The player of Bi can choose two strategies: legal treatment or illegal dumping, which can be interpreted as cooperation or defection (i = 1-3). With legally required treatment, the player of Bj pays a cost to ask the player of Bj+1 to treat the waste (j = 1, 2). Then, the cooperator of Bj+1 pays a cost to treat the waste properly. With illegal dumping, the player of Bi dumps the waste and does not pay any cost (i = 1-3). However, the waste dumped by the defector has negative environmental consequences, which all players in all roles suffer from. This situation is equivalent to a social dilemma encountered in common-pool resource management contexts. The administrative organ in Japan introduces two sanction systems to address the illegal dumping problem: the actor responsibility system and the producer responsibility system. In the actor responsibility system, if players in any role who choose defection are monitored and discovered, they are penalized via a fine. However, it is difficult to monitor and detect the violators, and this system does not work well. While, in the producer responsibility system, the player in B1 is fined if the player cannot hand the manifest to the local administrative organ because the players of Bi (i = 1-3) who choose defection do not hand the manifest to the player of B1. We analyze this situation using the replicator equation. We reveal that (1) the three-role model has more empirical credibility than the two-role model including B1 and B3, and (2) the producer responsibility system promotes the evolution of cooperation more than the system without sanctioning. (3) the actor responsibility system does not promote the evolution of cooperation if monitoring and detecting defectors is unsuccessful.

Evolution of costly explicit memory and cumulative culture.

Humans can acquire new information and modify it (cumulative culture) based on their learning and memory abilities, especially explicit memory, through the processes of encoding, consolidation, storage, and retrieval. Explicit memory is categorized into semantic and episodic memories. Animals have semantic memory, while episodic memory is unique to humans and essential for innovation and the evolution of culture. As both episodic and semantic memory are needed for innovation, the evolution of explicit memory influences the evolution of culture. However, previous theoretical studies have shown that environmental fluctuations influence the evolution of imitation (social learning) and innovation (individual learning) and assume that memory is not an evolutionary trait. If individuals can store and retrieve acquired information properly, they can modify it and innovate new information. Therefore, being able to store and retrieve information is essential from the perspective of cultural evolution. However, if both storage and retrieval were too costly, forgetting and relearning would have an advantage over storing and retrieving acquired information. In this study, using mathematical analysis and individual-based simulations, we investigate whether cumulative culture can promote the coevolution of costly memory and social and individual learning, assuming that cumulative culture improves the fitness of each individual. The conclusions are: (1) without cumulative culture, a social learning cost is essential for the evolution of storage-retrieval. Costly storage-retrieval can evolve with individual learning but costly social learning does not evolve. When low-cost social learning evolves, the repetition of forgetting and learning is favored more than the evolution of costly storage-retrieval, even though a cultural trait improves the fitness. (2) When cumulative culture exists and improves fitness, storage-retrieval can evolve with social and/or individual learning, which is not influenced by the degree of the social learning cost. Whether individuals socially learn a low level of culture from observing a high or the low level of culture influences the evolution of memory and learning, especially individual learning.

A model for gossip-mediated evolution of altruism with various types of false information by speakers and assessment by listeners.

Indirect reciprocity is considered to be important for explaining altruism among humans. The evolution of altruism has been modeled using several types of reputational scores, most of which were assumed to be updated immediately after each game session. In this study, we introduce gossip sessions held between game sessions to capture the spread of reputation and examine the effects of false information intentionally introduced by some players. Analytical and individual-based simulation results indicated that the frequent exchange of gossip favored the evolution of altruism when no players started false information. In contrast, intermediate repetitions of gossip sessions were favored when the population included liars or biased gossipers. In addition, we found that a gossip listener's strategy of incorporating any gossip regardless of speakers usually worked better than an alternative strategy of not believing gossip from untrustworthy players.

How intergenerational interaction affects attitude-behavior inconsistency.

Social norms play an important role in maintaining social order, but at the same time, they can act as a constraint that compels people to take specific actions which run contrary to their attitudes. This paper treats the latter case: we investigate conditions in which attitude-behavior inconsistency persists, constructing mathematical models combining evolutionary games and cultural transmissions. In particular, we focus on the effect of intergenerational interactions. Our models show that both information about others' attitude (e.g., through social surveys) and the combination of intra- and inter-generational interactions are key factors to generate the situation where all people adopt the same behavior but different people have different attitudes.

The evolution of cooperation in the unidirectional division of labour on a tree network.

Division of labour on complex networks is rarely investigated using evolutionary game theory. We investigate a division of labour where divided roles are assigned to groups on the nodes of a general unidirectional finite tree graph network. From the network's original node, a task flows and is divided along the branches. A player is randomly selected in each group of cooperators and defectors, who receives a benefit from a cooperator in the upstream group and a part of the task. A cooperator completes their part by paying a cost and then passing it downstream until the entire task is completed. Defectors do not do anything and the division of labour stops, causing all groups to suffer losses due to the incomplete task. We develop a novel method to analyse the local stability in this general tree. We discover that not the benefits but the costs of the cooperation influence the evolution of cooperation, and defections in groups that are directly related to that group's task cause damage to players in that group. We introduce two sanction systems, one of which induces the evolution of cooperation more than the system without sanctions, and promote the coexistence of cooperator and defector groups.

The evolution of cooperation in the unidirectional linear division of labour of finite roles.

Evolution of cooperation is a puzzle in evolutionary biology and social sciences. Previous studies assumed that players are equal and have symmetric relationships. In our society, players are in different roles, have an asymmetric relationship and cooperate together. We focused on the linear division of labour in a unidirectional chain that has finite roles, each of which is assigned to one group with cooperators and defectors. A cooperator in an upstream group produces and modifies a product, paying a cost of cooperation, and hands it to a player in a downstream group who obtains the benefit from the product. If players in all roles cooperate, a final product can be completed. However, if a player in a group chooses defection, the division of labour stops, the final product cannot be completed and all players in all roles suffer damage. By using the replicator equations of the asymmetric game, we investigate which sanction system promotes the evolution of cooperation in the division of labour. We find that not the benefit of the product but the cost of cooperation matters to the evolutionary dynamics and that the probability of finding a defector determines which sanction system promotes the evolution of cooperation.

How inconsistency between attitude and behavior persists through cultural transmission.

Individuals tend to conform their behavior to that of the majority. Consequently, an individual's behavior is not always consistent with his or her attitude, and such inconsistency sometimes causes mental distress. Understanding the mechanism of sustaining inconsistency between attitude and behavior is a challenging problem from the viewpoint of evolutionary theory. We constructed an evolutionary game theory model in which each player has an attitude and behavior toward a single social norm, and the players' attitudes and behaviors are affected by three types of cultural transmission: vertical, oblique, and horizontal. We assumed that strategy is a combination of attitude and behavior and that the process of learning or transmitting the social norm depends on the life stage of each player. Adults play a coordination game in which players whose behaviors match those of the majority obtain a high payoff, which is diminished by any inconsistency between attitude and behavior. The adults' strategies are passed to newborns via vertical transmission, and the frequency of a newborn's replication of strategy is proportional to the corresponding adult's payoff. Newborns imitate behaviors of unrelated adults via oblique transmission. Juveniles change their attitudes or behaviors by observing other juveniles' behaviors or inferring other juveniles' attitudes (horizontal transmission). We conclude that the key factor for sustaining inconsistency between attitude and behavior is the ability of players to infer and imitate others' attitudes, and that oblique transmission promotes inconsistency.

Evolution of cooperation in rotating indivisible goods game.

Collective behavior is theoretically and experimentally studied through a public goods game in which players contribute resources or efforts to produce goods (or pool), which are then divided equally among all players regardless of the amount of their contribution. However, if goods are indivisible, only one player can receive the goods. In this case, the problem is how to distribute indivisible goods, and here therefore we propose a new game, namely the "rotating indivisible goods game." In this game, the goods are not divided but distributed by regular rotation. An example is rotating savings and credit associations (ROSCAs), which exist all over the world and serve as efficient and informal institutions for collecting savings for small investments. In a ROSCA, members regularly contribute money to produce goods and to distribute them to each member on a regular rotation. It has been pointed out that ROSCA members are selected based on their reliability or reputation, and that defectors who stop contributing are excluded. We elucidate mechanisms that sustain cooperation in rotating indivisible goods games by means of evolutionary simulations. First, we investigate the effect of the peer selection rule by which the group chooses members based on the players reputation, also by which players choose groups based on their reputation. Regardless of the peer selection rule, cooperation is not sustainable in a rotating indivisible goods game. Second, we introduce the forfeiture rule that forbids a member who has not contributed earlier from receiving goods. These analyses show that employing these two rules can sustain cooperation in the rotating indivisible goods game, although employing either of the two cannot. Finally, we prove that evolutionary simulation can be a tool for investigating institutional designs that promote cooperation.

Anti-social punishment can prevent the co-evolution of punishment and cooperation.

The evolution of cooperation is one of the great puzzles in evolutionary biology. Punishment has been suggested as one solution to this problem. Here punishment is generally defined as incurring a cost to inflict harm on a wrong-doer. In the presence of punishers, cooperators can gain higher payoffs than non-cooperators. Therefore cooperation may evolve as long as punishment is prevalent in the population. Theoretical models have revealed that spatial structure can favor the co-evolution of punishment and cooperation, by allowing individuals to only play and compete with those in their immediate neighborhood. However, those models have usually assumed that punishment is always targeted at non-cooperators. In light of recent empirical evidence of punishment targeted at cooperators, we relax this assumption and study the effect of so-called 'anti-social punishment'. We find that evolution can favor anti-social punishment, and that when anti-social punishment is possible costly punishment no longer promotes cooperation. As there is no reason to assume that cooperators cannot be the target of punishment during evolution, our results demonstrate serious restrictions on the ability of costly punishment to allow the evolution of cooperation in spatially structured populations. Our results also help to make sense of the empirical observation that defectors will sometimes pay to punish cooperators.

Runaway selection for cooperation and strict-and-severe punishment.

Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.

Effect of the presence of empty sites on the evolution of cooperation by costly punishment in spatial games.

Cooperation and spiteful behavior are still evolutionary puzzles. Costly punishment, for which the game payoff is the same as that of spiteful behavior, is one mechanism for promoting the evolution of cooperation. A spatially structured population facilitates the evolution of either cooperation or spite/punishment if cooperation is linked explicitly or implicitly with spite/punishment; a cooperator cooperates with another cooperator and punishes/spites the other type of player. Different updating rules in the evolutionary game produce different evolutionary outcomes: with one updating rule-the score-dependent viability model, in which a player dies with a probability inversely proportional to the game score and the resulting unoccupied site is colonized by one player chosen randomly-the evolution of spite/punishment is promoted more than with the other updating rule-the score-dependent fertility model, in which, after a player dies randomly, the site is colonized by a player with a higher game score. If the population has empty sites, spiteful players or punishers should have less chance to interact with others and then spite/punish others. Thus the presence of empty sites would affect the evolutionary dynamics of spite/punishment. Here, we investigated whether the presence of empty sites discourages the evolution of spite/punishment in both a lattice-structured population and a completely mixing population where players interact with others randomly, especially when the score-dependent viability model is adopted. In the lattice-structured population adopting this viability model, the presence of empty sites promoted the evolution of cooperation and did not reduce the effect of spite/punishment. In the completely mixing population, the presence of empty sites did not promote evolution of cooperation by punishment. The evolutionary dynamics of the score-dependent viability model with empty sites were close to those of the score-dependent fertility model.

Reciprocity and exclusion in informal financial institutions: An experimental study of rotating savings and credit associations.

Group cooperation is fundamental to human society. The public goods game is often used to describe the difficulty of group cooperation. However, there are other structures of institutions to maintain group cooperation such as Rotating savings and credit associations (ROSCAs). ROSCAs are informal financial institutions that exist worldwide, in which all participants contribute to a common fund and take turns to receive a return. ROSCAs are common in developing countries and among migrant groups in developed countries. There are various types of ROSCAs, and they share a crucial problem in that participants whose turn to receive a return has passed have an incentive to default on their contributions. We conducted a laboratory experiment to investigate the mechanisms that can prevent default in a fixed ROSCA, in which the order of receipt of returns is determined before starting and is also known to members. The findings are as follows. (i) Excluding low contributors from ROSCA groups by voting increased contribution rates both before and after the receipt of returns. (ii) ROSCA members exhibited reciprocity and a sense of revenge: that is, members contributed to the returns payments of other members who had contributed to them, and did not contribute to the returns payments of non-contributors. Voluntary behaviors thus sustained ROSCAs. Meanwhile, an exogenous punishment whereby subjects were prevented from receiving returns payments unless they had themselves contributed previously did not increase contribution rates.

Extinction risk to bird populations caused by DDT exposure.

The impact of toxic chemicals on wild animals and plants can be quantified in terms of the enhanced risk of population extinction. To illustrate a method for doing this, we estimated such impact for two bird species: herring gull (Larus argentatus) in Long Island, NY, and sparrowhawk (Accipiter nisus) in eastern England, when they were exposed to DDT (p,p(')-dichlorodiphenyltrichloroethane) and its metabolites (called DDTs). The method we used is based on a formula of the mean time to population extinction derived for a stochastic differential equation (the canonical model). The intrinsic rate of natural population growth was estimated from an exponentially growing population, and the intensity of the environmental fluctuation was estimated from the magnitude of population size fluctuation. The effect of exposure to DDTs in reducing the population growth rate was evaluated based on an age-structured population model, by assuming that age-specific fertility is density-dependent and sensitive to DDTs exposure, but age-specific survivorship is not. The results are expressed in terms of the risk equivalent--the decrease in carrying capacity K that causes the same enhancement of extinction risk as chemical exposure at a given level. The risk equivalent can be used in mitigation banking.

Extinction risk to herring gull populations from DDT exposure.

The impact of toxic chemicals on wild animals and plants can be quantified in terms of the enhanced risk of population extinction. To illustrate the method, we estimated it for herring gull (Larus argentatus) populations in Long Island (NY, USA) exposed to DDT (p,p'-dichlorodiphenyltrichloroethane) and its metabolites (abbreviated as DDTs) with a strong biomagnification effect. The method is based on a formula of the mean time to population extinction derived for a stochastic differential equation (the canonical model). The intrinsic rate of natural population growth was estimated from the doubling time of an exponentially growing population and the intensity of the environmental fluctuation from the magnitude of population size fluctuation. The effect of exposure to DDTs in reducing the population growth rate was evaluated based on an age-structured population model by assuming that age-specific fertilities (including chick survivorship) are density dependent and sensitive to DDTs exposure but age-specific survivorships are not. The results are expressed in terms of the risk equivalent-the decrease in the carrying capacity K that causes the same enhancement of extinction risk as chemical exposure at a given level. The high concentration reported in Long Island in the 1960s corresponds to the equivalent loss of carrying capacity by 42.5% when K is 100 (the number of breeding females), and coefficient of variation (CV) = 0.2 (sigma2 = 0.0298) [corrected]. Risk equivalent allows us to compare different risk factors and is useful in mitigation banking.

The effect of ostracism and optional participation on the evolution of cooperation in the voluntary public goods game.

Not only animals, plants and microbes but also humans cooperate in groups. The evolution of cooperation in a group is an evolutionary puzzle, because defectors always obtain a higher benefit than cooperators. When people participate in a group, they evaluate group member's reputations and then decide whether to participate in it. In some groups, membership is open to all who are willing to participate in the group. In other groups, a candidate is excluded from membership if group members regard the candidate's reputation as bad. We developed an evolutionary game model and investigated how participation in groups and ostracism influence the evolution of cooperation in groups when group members play the voluntary public goods game, by means of computer simulation. When group membership is open to all candidates and those candidates can decide whether to participate in a group, cooperation cannot be sustainable. However, cooperation is sustainable when a candidate cannot be a member unless all group members admit them to membership. Therefore, it is not participation in a group but rather ostracism, which functions as costless punishment on defectors, that is essential to sustain cooperation in the voluntary public goods game.