Social norms in indirect reciprocity with ternary reputations

Indirect reciprocity is a key mechanism that promotes cooperation in social dilemmas by means of reputation. Although it has been a common practice to represent reputations by binary values, either ‘good’ or ‘bad’, such a dichotomy is a crude approximation considering the complexity of reality. In this work, we studied norms with three different reputations, i.e., ‘good’, ‘neutral’, and ‘bad’. Through massive supercomputing for handling more than thirty billion possibilities, we fully identified which norms achieve cooperation and possess evolutionary stability against behavioural mutants. By systematically categorizing all these norms according to their behaviours, we found similarities and dissimilarities to their binary-reputation counterpart, the leading eight. We obtained four rules that should be satisfied by the successful norms, and the behaviour of the leading eight can be understood as a special case of these rules. A couple of norms that show counter-intuitive behaviours are also presented. We believe the findings are also useful for designing successful norms with more general reputation systems.

Religiosity and Cooperation: The COVID-19 Pandemic in Slovenia

We researched the COVID-19 pandemic as a give-some social dilemma. The success of solving the dilemma depends on an adequate proportion of cooperative actors. We were interested in the difference between how religious and non-religious Slovenian citizens reported their level of cooperation with government measures aimed at limiting the spread of the virus during the pandemic. Our research shows that during the first wave of the epidemic in Slovenia, religious citizens were slightly more cooperative than non-religious citizens. However, this statistically significant difference was not the consequence of religiosity per se. Regression analysis suggests that the observable difference was due to factors such as age, gender, concern about health, and trust in the ruling government. We explain the effect of these factors in light of the existing corpus of knowledge about social dilemmas.

Spatial social dilemmas promote diversity

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.