Mayuko Nakamaru

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.

Strict or Graduated Punishment? Effect of Punishment Strictness on the Evolution of Cooperation in Continuous Public Goods Games

Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher’s threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player’s death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results.

Lattice models in ecology and social sciences

Random matching between individuals, or the complete-mixing model, is often assumed in analyzing evolutionary or population dynamics in ecology and game theory or other models in social sciences. Making and analyzing a model is not difficult under this simple assumption. However spatial- or network-structured populations, including the lattice model and the power-law network, are more realistic for many ecological and social phenomena than the complete-mixing model. In this review, I will show first that a lattice model can be useful in investigating the effect of neighborhood interactions on the dynamics, not only of plants and forests, but also of animal and human societies. Second, the lattice model promotes the evolution of spiteful behavior, even though it is well-known that the lattice model promotes the evolution of cooperation. Finally, different social networks result in traits, such as social norms, spreading at different speeds.

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.

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 listeners strategy of incorporating any gossip regardless of speakers usually worked better than an alternative strategy of not believing gossip from untrustworthy players.

Ecological Conditions Favoring Budding in Colonial Organisms under Environmental Disturbance

Dispersal is a topic of great interest in ecology. Many organisms adopt one of two distinct dispersal tactics at reproduction: the production of small offspring that can disperse over long distances (such as seeds and spawned eggs), or budding. The latter is observed in some colonial organisms, such as clonal plants, corals and ants, in which (super)organisms split their body into components of relatively large size that disperse to a short distance. Contrary to the common dispersal viewpoint, short-dispersal colonial organisms often flourish even in environments with frequent disturbances. In this paper, we investigate the conditions that favor budding over long-distance dispersal of small offspring, focusing on the life history of the colony growth and the colony division ratio. These conditions are the relatively high mortality of very small colonies, logistic growth, the ability of dispersers to peacefully seek and settle unoccupied spaces, and small spatial scale of environmental disturbance. If these conditions hold, budding is advantageous even when environmental disturbance is frequent. These results suggest that the demography or life history of the colony underlies the behaviors of the colonial organisms.

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.

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 opponents 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 opponents strength based on the past history of the direct fights, evolves with the large memory capacity, while the TI strategy, which estimates the unknown opponents 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 opponents 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.

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 donors 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.