Figure 1.
Imitative trust and indirect reciprocity.
Panel A and B show, respectively, the average payoff per actor and the average strategies (solid red line) and
(dashed blue line) observed in the population across different levels of imitation
(x-axis). Bars correspond to 2 standard deviations. Values are calculated over 1000 simulations considering the generation when the population has reached a fixated common strategy
,
.
Figure 2.
Alternative cooperative mechanisms to imitation.
The figure compares the average payoff per actor (see Fig. 1A) generated by imitative trust (black line) against the average payoff obtained by replacing imitative trust with random-trusting (green dashed line) and share-alike (red dashed line) mechanisms. Values are calculated over 1000 simulations considering the generation when the population has reached a fixated common strategy ,
.
Figure 3.
Vulnerability of cooperative strategies.
We analyze the vulnerability of imitation and indirect reciprocity strategies on distributing similar resources when actors are subject to implementation errors. We introduce a probability that donors mistakenly act in the opposite way as it was expected from their strategy. Note that without errors we would expect all actors with the same amount of resources. Panels A–D show the correlation between Gini coefficients (shades) and the frequency of fixated strategies (circles) for
,
,
and
respectively. Gini coefficients and frequencies are reported as the average over
simulations considering the generation when the population has reached a fixated common strategy
,
. The frequency of occurrence for each strategy is proportional to the area of the circles.
Figure 4.
To investigate the emergence of cooperation and the co-existence of imitation and indirect reciprocity, we consider that new actors will adopt a randomly chosen strategy with probability (see text). Additionally, to differentiate between actors using only indirect reciprocity, imitation or a mix of the two, we introduce a third dimension
that takes values of
(blue line),
(red line), or
(green line) respectively. We initialize the population with
and
, i.e. unconditional defectors. Panel A shows the average payoff per actors per generation for a single simulation. Note that the population continuously fluctuate between maximum cooperation and defection. Panel B shows that the strategies
also fluctuate across generations. This reveals that although there is no stable strategy, actors can adopt cooperative imitative and indirect reciprocity strategies.