This dissertation is an attempt at establishing a bridge between biology and physics leading naturally from the field of phase transitions in physics to the cooperative nature of living systems. We show that this aim can be realized by supplementing the current field of evolutionary game theory with a new form of self-organized temporal criticality. In the case of ordinary criticality, the units of a system choosing either cooperation or defection under the influence of the choices done by their nearest neighbors, undergo a significant change of behavior when the intensity of social influence has a critical value. At criticality, the behavior of the individual units is correlated with that of all other units, in addition to the behavior of the nearest neighbors. The spontaneous transition to criticality of this work is realized as follows: the units change their behavior (defection or cooperation) under the social influence of their nearest neighbors and update the intensity of their social influence spontaneously by the feedback they get from the payoffs of the game (environment). If units, which are selfish, get higher benefit with respect to their previous play, they increase their interest to interact with other units and vice versa. Doing this, the behavior of single units and the whole system spontaneously evolve towards criticality, thereby realizing a global behavior favoring cooperation. In the case when the interacting units are oscillators with their own periodicity, homeodynamics concerns, the individual payoff is the synchronization with the nearest neighbors (i.e., lowering the energy of the system), the spontaneous transition to criticality generates fluctuations characterized by the joint action of periodicity and crucial events of the same kind as those revealed by the current analysis of the dynamics of the brain. This result is expected to explain the efficiency of enzyme catalyzers, on the basis of a new non-equilibrium statistical physics. We argue that the results obtained apply to sociological and psychological systems as well as to elementary biological systems.