A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the Prisoner's Dilemma game

Evolution of spite versus evolution of altruism through a disbandment mechanism

Altruism and spite are costly to the actor, making their evolution unlikely without specific mechanisms. Nonetheless, both altruistic and spiteful behaviors are present in individuals, which suggests the existence of an underlying mechanism that drives their evolution. If altruistic individuals are more likely to be recipients of altruism than non-altruistic individuals, then altruism can be favored by natural selection. Similarly, if spiteful individuals are less likely to be recipients of spite than non-spiteful individuals, then spite can be favored by natural selection. Spite is altruism's evil twin, ugly sister of altruism, or a shady relative of altruism. In some mechanisms, such as repeated interactions, if altruism is favored by natural selection, then spite is also favored by natural selection. However, there has been limited investigation into whether both behaviors evolve to the same extent. In this study, we focus on the mechanism by which individuals choose to keep or stop the interaction according to the opponent's behavior. Using the evolutionary game theory, we investigate the evolution of altruism and spite under this mechanism. Our model revealed that the evolution of spite is less likely than the evolution of altruism.

Disbandment rules that most facilitate the evolution of cooperation

Cooperation is considered a mysterious phenomenon from the perspective of adaptive evolution. However, if an individual can separate from an unsatisfactory group and join another, then this can facilitate positive assortment between cooperative types and promote the evolution of cooperation. What kind of disbandment rule most facilitates the evolution of cooperation? A previous study investigated exogenous disbandment rules and showed that, when games are played between two players, a rule where heterogeneous groups disband facilitates the evolution of cooperation. However, in groups of more than two individuals, a rule strictly requiring homogeneity applied if and only if the expected number of rounds played in a group was greater than some critical value. How large is the critical value? In this study, we make a mathematical analysis using evolutionary game theory. Our results show that the critical number of rounds increases greatly as the group size increases. Consequently, for species with large group sizes, e.g., Homo sapiens, under plausible parameter values, the strict homogeneity rule is unlikely to facilitate the evolution of cooperation. We find instead that a disbandment rule that requires a threshold level of homogeneity outperformed the strict homogeneity rule. Furthermore, we calculate the position of internal equilibria at which cooperators and defectors coexist and show that the initial evolution of cooperation is most encouraged when cooperators are tolerant (intolerant) of defectors if the benefit-to-cost ratio is large (small).

Evolution of spite in an n-player game with an opting-out option

The evolution of altruism and spite is facilitated by positive and negative assortments, respectively. Animals repeatedly meet the same opponents and can choose to keep or terminate the interaction. Previous studies have showed that if the probability that the interaction stops depends on how the pairs are, then a positive assortment can emerge, encouraging the evolution of altruism in dyadic interactions and in interactions involving more than two individuals. In contrast, according to another previous study if the probability that the interaction stops depends on how the pairs are, then a negative assortment can emerge, encouraging the evolution of spite in dyadic interactions. Is the evolution of spite facilitated by interactions involving more than two individuals, in addition to dyadic interactions? The present study shows that the evolution of spite in interactions involving many individuals is possible by studying the repeated n-player game played using spiteful and nonspiteful strategies with opting-out options. These results suggest that spite in large groups may evolve through an opt-out mechanism. It also promotes the investigation about whether there are any examples of spiteful behavior in large groups that have evolved through negative assortment in opt-out options in nature.

The Dark Side of Mentalizing: Learning Signals in the Default Network During Social Exchanges Support Cooperation and Exploitation

The evolution of human social cognitive capacities such as mentalizing was associated with the expansion of frontoparietal cortical networks, particularly the default network. Mentalizing supports prosocial behaviors, but recent evidence indicates it may also serve a darker side of human social behavior. Using a computational reinforcement learning model of decision-making on a social exchange task, we examined how individuals optimized their approach to social interactions based on a counterpart's behavior and prior reputation. We found that learning signals encoded in the default network scaled with reciprocal cooperation and were stronger in individuals who were more exploitative and manipulative, but weaker in those who were more callous and less empathic. These learning signals, which help to update predictions about others' behavior, accounted for associations between exploitativeness, callousness, and social reciprocity. Separately, we found that callousness, but not exploitativeness, was associated with a behavioral insensitivity to prior reputation effects. While the entire default network was involved in reciprocal cooperation, sensitivity to reputation was selectively related to the activity of the medial temporal subsystem. Overall, our findings suggest that the emergence of social cognitive capacities associated with the expansion of the default network likely enabled humans to not only cooperate effectively with others, but to exploit and manipulate others as well.

Evolution of trustfulness in the case where resources for cooperation are sometimes absent

It is worth investigating the existence of cooperation, which is costly for the actor but beneficial to the recipient (precisely because it is costly for the former). If players, when they approach defectors, stop their relationship with them, cooperation can pay off and favorably emerge in the course of evolutionary dynamics. The present study examines the situation in which animals, even when they want to cooperate, sometimes lack the necessary resources, and are thereby prevented from cooperating with others. In addition, it is also considered that the underlying information about the presence or absence of these resources can be conveyed to the opponent player. Here, the opponent who defects-has no resources for cooperation-may be a cooperator or a defector. Therefore, it is not clear which behavior is more likely to evolve, if it is keeping the interaction with such an opponent (i.e., being trustful) or stopping the interaction with such an opponent (i.e., being not trustful). By using evolutionary game theory, it is revealed that those who want to keep the interaction with those without the resources to cooperate are favored by natural selection. This study sheds new light on the role of keeping and stopping interaction in the evolution of cooperation under variable availability of resources.

Effect of the group size on the evolution of cooperation when an exit option is present

The evolution of cooperation has been one of the main topics in evolutionary biology. If cooperators maintain interaction with cooperators and halt interaction with defectors, then cooperation can pay and can be favored by natural selection. This is called an exit option. Here, not only cooperation in dyadic interactions but also cooperation in sizable groups can be observed. Rivalry is about whether usage of the benefit by one individual reduces its availability to others or not. A common good is a rivalrous good, whereas a public good is a non-rivalrous good. In this paper, by analyzing n-player prisoner's dilemma games, we examine whether the effect of the group size on cooperation is positive or negative in the context of exit option. When goods are common goods, defectors always dominate cooperators when the group size is infinitely large. Thus, the group size has only negative effects on the evolution of cooperation when goods are common goods. In contrast, when goods are public goods, an increase in group size has positive effects as well as negative effects on the evolution of cooperation. In addition, we reveal that it has both positive and negative effects on the evolution of cooperation for cooperators to tolerate some defection and hope to keep the interaction.

The consequences of switching strategies in a two-player iterated survival game

We consider two-player iterated survival games in which players are able to switch from a more cooperative behavior to a less cooperative one at some step of an n-step game. Payoffs are survival probabilities and lone individuals have to finish the game on their own. We explore the potential of these games to support cooperation, focusing on the case in which each single step is a Prisoner’s Dilemma. We find that incentives for or against cooperation depend on the number of defections at the end of the game, as opposed to the number of steps in the game. Broadly, cooperation is supported when the survival prospects of lone individuals are relatively bleak. Specifically, we find three critical values or cutoffs for the loner survival probability which, in concert with other survival parameters, determine the incentives for or against cooperation. One cutoff determines the existence of an optimal number of defections against a fully cooperative partner, one determines whether additional defections eventually become disfavored as the number of defections by the partner increases, and one determines whether additional cooperations eventually become favored as the number of defections by the partner increases. We obtain expressions for these switch-points and for optimal numbers of defections against partners with various strategies. These typically involve small numbers of defections even in very long games. We show that potentially long stretches of equilibria may exist, in which there is no incentive to defect more or cooperate more. We describe how individuals find equilibria in best-response walks among n-step strategies.

The effect of the opting-out strategy on conditions for selection to favor the evolution of cooperation in a finite population

We consider a Prisoner's Dilemma (PD) that is repeated with some probability 1-ρ only between cooperators as a result of an opting-out strategy adopted by all individuals. The population is made of N pairs of individuals and is updated at every time step by a birth-death event according to a Moran model. Assuming an intensity of selection of order 1/N and taking 2N² birth-death events as unit of time, a diffusion approximation exhibiting two time scales, a fast one for pair frequencies and a slow one for cooperation (C) and defection (D) frequencies, is ascertained in the limit of a large population size. This diffusion approximation is applied to an additive PD game, cooperation by an individual incurring a cost c to the individual but providing a benefit b to the opponent. This is used to obtain the probability of ultimate fixation of C introduced as a single mutant in an all D population under selection, which can be compared to the probability under neutrality, 1/(2N), as well as the corresponding probability for a single D introduced in an all C population under selection. This gives conditions for cooperation to be favored by selection. We show that these conditions are satisfied when the benefit-to-cost ratio, b/c, exceeds some increasing function of ρ that is approximately given by (1+ρ)/(1-ρ). This condition is more stringent, however, than the condition for tit-for-tat (TFT) to be favored against always-defect (AllD) in the absence of opting-out.

Trinidadian guppies use a social heuristic that can support cooperation among non-kin

Cooperation among non-kin is well documented in humans and widespread in non-human animals, but explaining the occurrence of cooperation in the absence of inclusive fitness benefits has proven a significant challenge. Current theoretical explanations converge on a single point: cooperators can prevail when they cluster in social space. However, we know very little about the real-world mechanisms that drive such clustering, particularly in systems where cognitive limitations make it unlikely that mechanisms such as score keeping and reputation are at play. Here, we show that Trinidadian guppies (Poecilia reticulata) use a 'walk away' strategy, a simple social heuristic by which assortment by cooperativeness can come about among mobile agents. Guppies cooperate during predator inspection and we found that when experiencing defection in this context, individuals prefer to move to a new social environment, despite having no prior information about this new social group. Our results provide evidence in non-human animals that individuals use a simple social partner updating strategy in response to defection, supporting theoretical work applying heuristics to understanding the proximate mechanisms underpinning the evolution of cooperation among non-kin.

The opportunity cost of walking away in the spatial iterated prisoner's dilemma

Previous work with the spatial iterated prisoner's dilemma has shown that the ability to respond to a partner's defection by simply "walking away" allows so-called walk away cooperators to outcompete defectors as well as cooperators that do not respond to defection. These findings are important because they suggest a relatively simple route by which cooperation can evolve. But it remains to be seen just how robust the walk away strategy is to ecologically important variables such as population density, strategic error, and offspring dispersal. The results of our simulation experiments show that the evolutionary success of walk away cooperators decreases with decreasing population density and/or with increasing error. This relationship is best explained by the ways in which population density and error jointly affect the opportunity cost of walking away. This opportunity cost also explains why naive cooperators regularly outcompete walk away cooperators in pair-wise competition, something not observed in previous studies. Our results further show that local offspring dispersal can inhibit the evolution of cooperation by negating the protection low population density affords the most vulnerable cooperators. Our research identifies socio-ecological conditions in which forgiveness trumps flight in the spatial iterated prisoner's dilemma.

Asymmetric evolutionary game dynamics based on individuals' own volition

For the pairwise interactions, the evolution of individual behavior should involve two major factors: one is what you will do in an interaction with a given opponent, and another is what type of opponents you prefer to interact with. In this study, we developed a two-phenotype iterated bimatrix replicator dynamics model based on individuals' own volition, where, different from the classic iterated game model, we assume that (i) for all interaction pairs, the maximum expected interaction time is same and it is limited even if two individuals in an interaction pair would like to keep their interaction; and (ii) all individuals are able to unilaterally break off the interactions with their opponents according to their own volition. Therefore, we define that, at any time t, an interaction pair will be disbanded with a given probability and the new interaction pairs will be randomly formed. The main results show that: (i) the existence of locally asymmetrically stable interior equilibrium is possible; and (ii) the evolutionary stability of the system is similar to the classic asymmetric evolutionary game. These results may provide a new insight for revealing the evolutionary significance of asymmetric game dynamics.

Optional interactions and suspicious behaviour facilitates trustful cooperation in prisoners dilemma

In evolutionary game theory interactions between individuals are often assumed obligatory. However, in many real-life situations, individuals can decide to opt out of an interaction depending on the information they have about the opponent. We consider a simple evolutionary game theoretic model to study such a scenario, where at each encounter between two individuals the type of the opponent (cooperator/defector) is known with some probability, and where each individual either accepts or opts out of the interaction. If the type of the opponent is unknown, a trustful individual accepts the interaction, whereas a suspicious individual opts out of the interaction. If either of the two individuals opt out both individuals remain without an interaction. We show that in the prisoners dilemma optional interactions along with suspicious behaviour facilitates the emergence of trustful cooperation.