  Strong reciprocity is a fundamental human characteristic associated with our
extraordinary sociality and cooperation. Laboratory experiments on social
dilemma games and many field studies have quantified well-defined levels of
cooperation and propensity to punish/reward. The level of cooperation is
observed to be strongly dependent on the availability of punishments and/or
rewards. Here, we suggest that the propensity for altruistic punishment and
reward is an emergent property that has co-evolved with cooperation by
providing an efficient feedback mechanism through both biological and cultural
interactions. By favoring high survival probability and large individual gains,
the propensity for altruistic punishment and rewards reconciles self- and group
interests. We show that a simple cost/benefit analysis at the level of a single
agent, who anticipates the action of her fellows, determines an optimal level
of altruistic punishment, which explains quantitatively experimental results on
the third-party punishment game, the ultimatum game and altruistic punishment
games. We also report numerical simulations of an evolutionary agent-based
model of repeated agent interactions with feedback-by-punishments, which
confirms that the propensity to punish is a robust emergent property selected
by the evolutionary rules of the model.
