  We study a system in which N agents have to decide between two strategies
\theta_i (i \in 1... N), for defection or cooperation, when interacting with
other n agents (either spatial neighbors or randomly chosen ones). After each
round, they update their strategy responding nonlinearly to two different
information sources: (i) the payoff a_i(\theta_i, f_i) received from the
strategic interaction with their n counterparts, (ii) the fraction f_i of
cooperators in this interaction. For the latter response, we assume social
herding, i.e. agents adopt their strategy based on the frequencies of the
different strategies in their neighborhood, without taking into account the
consequences of this decision. We note that f_i already determines the payoff,
so there is no additional information assumed. A parameter \zeta defines to
what level agents take the two different information sources into account. For
the strategic interaction, we assume a Prisoner's Dilemma game, i.e. one in
which defection is the evolutionary stable strategy. However, if the additional
dimension of social herding is taken into account, we find instead a stable
outcome where cooperators are the majority. By means of agent-based computer
simulations and analytical investigations, we evaluate the critical conditions
for this transition towards cooperation. We find that, in addition to a high
degree of social herding, there has to be a nonlinear response to the fraction
of cooperators. We argue that the transition to cooperation in our model is
based on less information, i.e. on agents which are not informed about the
payoff matrix, and therefore rely on just observing the strategy of others, to
adopt it. By designing the right mechanisms to respond to this information, the
transition to cooperation can be remarkably enhanced.
