Stability of cooperation under image scoring in group interactions

Image scoring sustains cooperation in the repeated two-player prisoner's dilemma through indirect reciprocity, even though defection is the uniquely dominant selfish behaviour in the one-shot game. Many real-world dilemma situations, however, firstly, take place in groups and, secondly, lack the necessary transparency to inform subjects reliably of others' individual past actions. Instead, there is revelation of information regarding groups, which allows for `group scoring' but not for image scoring. Here, we study how sensitive the positive results related to image scoring are to information based on group scoring. We combine analytic results and computer simulations to specify the conditions for the emergence of cooperation. We show that under pure group scoring, that is, under the complete absence of image-scoring information, cooperation is unsustainable. Away from this extreme case, however, the necessary degree of image scoring relative to group scoring depends on the population size and is generally very small. We thus conclude that the positive results based on image scoring apply to a much broader range of informational settings that are relevant in the real world than previously assumed.Comment: 6 two-column pages, 4 figures; accepted for publication in Scientific Report

Groupwise information sharing promotes ingroup favoritism in indirect reciprocity

Indirect reciprocity is a mechanism for cooperation in social dilemma situations, in which an individual is motivated to help another to acquire a good reputation and receive help from others afterwards. Ingroup favoritism is another aspect of human cooperation, whereby individuals help members in their own group more often than those in other groups. Ingroup favoritism is a puzzle for the theory of cooperation because it is not easily evolutionarily stable. In the context of indirect reciprocity, ingroup favoritism has been shown to be a consequence of employing a double standard when assigning reputations to ingroup and outgroup members; e.g., helping an ingroup member is regarded as good, whereas the same action toward an outgroup member is regarded as bad. We analyze a model of indirect reciprocity in which information sharing is conducted groupwise. In our model, individuals play social dilemma games within and across groups, and the information about their reputations is shared within each group. We show that evolutionarily stable ingroup favoritism emerges even if all the players use the same reputation assignment rule regardless of group (i.e., a single standard). Two reputation assignment rules called simple standing and stern judging yield ingroup favoritism. Stern judging induces much stronger ingroup favoritism than does simple standing. Simple standing and stern judging are evolutionarily stable against each other when groups employing different assignment rules compete and the number of groups is sufficiently large. In addition, we analytically show as a limiting case that homogeneous populations of reciprocators that use reputations are unstable when individuals independently infer reputations of individuals, which is consistent with previously reported numerical results.Comment: 25 pages, 7 figures. The Abstract is shortened to fill in arXiv's abstract for

Emergence of social networks via direct and indirect reciprocity

Many models of social network formation implicitly assume that network properties are static in steady-state. In contrast, actual social networks are highly dynamic: allegiances and collaborations expire and may or may not be renewed at a later date. Moreover, empirical studies show that human social networks are dynamic at the individual level but static at the global level: individuals' degree rankings change considerably over time, whereas network-level metrics such as network diameter and clustering coefficient are relatively stable. There have been some attempts to explain these properties of empirical social networks using agent-based models in which agents play social dilemma games with their immediate neighbours, but can also manipulate their network connections to strategic advantage. However, such models cannot straightforwardly account for reciprocal behaviour based on reputation scores ("indirect reciprocity"), which is known to play an important role in many economic interactions. In order to account for indirect reciprocity, we model the network in a bottom-up fashion: the network emerges from the low-level interactions between agents. By so doing we are able to simultaneously account for the effect of both direct reciprocity (e.g. "tit-for-tat") as well as indirect reciprocity (helping strangers in order to increase one's reputation). This leads to a strategic equilibrium in the frequencies with which strategies are adopted in the population as a whole, but intermittent cycling over different strategies at the level of individual agents, which in turn gives rise to social networks which are dynamic at the individual level but stable at the network level

On the stability of cooperation under indirect reciprocity with first-order information

Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in large groups where partners meet only once. The first model for which this has been demonstrated was the image scoring mechanism. But analytical work on the simplest possible case, the binary scoring model, has shown that even small errors in implementation destabilize any cooperative regime. It has thus been claimed that for indirect reciprocity to stabilize cooperation, assessments of reputation must be based on higher-order information. Is indirect reciprocity relying on frst-order information doomed to fail? We use a simple analytical model of image scoring to show that this need not be the case. Indeed, in the general image scoring model the introduction of implementation errors has just the opposite effect as in the binary scoring model: it may stabilize instead of destabilize cooperation

Local reputation, local selection, and the leading eight norms

Humans are capable of solving cooperation problems following social norms. Social norms dictate appropriate behaviour and judgement on others in response to their previous actions and reputation. Recently, the so-called leading eight norms have been identified from many potential social norms that can sustain cooperation through a reputation-based indirect reciprocity mechanism. Despite indirect reciprocity being claimed to extend direct reciprocity in larger populations where direct experiences cannot be accumulated, the success of social norms have been analysed in models with global information and evolution. This study is the first to analyse the leading eight norms with local information and evolution. We find that the leading eight are robust against selfish players within most scenarios and can maintain a high level of cooperation also with local information and evolution. In fact, local evolution sustains cooperation under a wider set of conditions than global evolution, while local reputation does not hinder cooperation compared to global reputation. Four of the leading eight norms that do not reward justified defection offer better chances for cooperation with quick evolution, reputation with noise, larger networks, and when unconditional defectors enter the population

Understanding reciprocity

This paper surveys the evolutionary game theoretic literature on reciprocity in human interactions, dealing both with long-term relationships and with sporadic interactions. Four basic themes, repetition, commitment, assortation, and parochialism, appear repeatedly throughout the literature. Repetition can give rise to the evolution of behavior that exhibits reciprocity-like features but a vast array of other behaviors are also stable. In sporadic interactions, reciprocity can be stable if the propensity to punish selfish actions can induce opportunists to cooperate, if reciprocators themselves behave opportunistically when they expect others to do so, or if matching is sufficiently assortative.Reciprocity, Evolution, Assortation, Commitment, Parochialism