  We study the phase diagram of a minority game where three classes of agents
are present. Two types of agents play a risk-loving game that we model by the
standard Snowdrift Game. The behaviour of the third type of agents is coded by
{\em indifference} w.r.t. the game at all: their dynamics is designed to
account for risk-aversion as an innovative behavioral gambit. From this point
of view, the choice of this solitary strategy is enhanced when innovation
starts, while is depressed when it becomes the majority option. This implies
that the payoff matrix of the game becomes dependent on the global awareness of
the agents measured by the relevance of the population of the indifferent
players. The resulting dynamics is non-trivial with different kinds of phase
transition depending on a few model parameters. The phase diagram is studied on
regular as well as complex networks.
