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Most of the straight-forward learning approaches in cooperative robotics imply for each learning robot a state space growth exponential in the number of team members. To remedy the exponentially large state space, we propose to investigate a less demanding cooperation mechanism—i.e., various levels of awareness—instead of communication. We define awareness as the perception of other robots locations and actions. We recognize four different levels (or degrees) of awareness which imply different amounts of additional information and therefore have different impacts on the search space size (Θ(0), Θ(1), Θ(N), o(N),1 where N is the number of robots in the team). There are trivial arguments in favor of avoiding binding the increase of the search space size to the number of team members. We advocate that, by studying the maximum number of neighbor robots in the application context, it is possible to tune the parameters associated with a Θ(1) increase of the search space size and allow good learning performance. We use the cooperative multi-robot observation of multiple moving targets (CMOMMT) application to illustrate our method. We verify that awareness allows cooperation, that cooperation shows better performance than a purely collective behavior and that learned cooperation shows better results than learned collective behavior.