  The understanding of cooperative behavior in social systems has been the
subject of intense research over the past decades. In this regard, the
theoretical models used to explain cooperation in human societies have been
complemented with a growing interest in experimental studies to validate the
proposed mechanisms. In this work, we rely on previous experimental findings to
build a theoretical model based on two cooperation driving mechanisms:
second-order reputation and memory. Specifically, taking the Donation Game as a
starting point, the agents are distributed among three strategies, namely
Unconditional Cooperators, Unconditional Defectors, and Discriminators, where
the latter follow a second-order assessment rule: Shunning, Stern Judging,
Image Scoring, or Simple Standing. A discriminator will cooperate if the
evaluation of the recipient's last actions contained in his memory is above a
threshold of (in)tolerance. In addition to the dynamics inherent to the game,
another imitation dynamics, involving much longer times (generations), is
introduced. The model is approached through a mean-field approximation that
predicts the macroscopic behavior observed in Monte Carlo simulations. We found
that, while in most second-order assessment rules, intolerance hinders
cooperation, it has the opposite (positive) effect under the Simple Standing
rule. Furthermore, we show that, when considering memory, the Stern Judging
rule shows the lowest values of cooperation, while stricter rules show higher
cooperation levels.
