  Cooperation and defection are social traits whose evolutionary origin is
still unresolved. Recent behavioral experiments with humans suggested that
strategy changes are driven mainly by the individuals' expectations and not by
imitation. This work theoretically analyzes and numerically explores an
aspiration-driven strategy updating in a well-mixed population playing games.
The payoffs of the game matrix and the aspiration are condensed into just two
parameters that allow a comprehensive description of the dynamics. We find
continuous and abrupt transitions in the cooperation density with excellent
agreement between theory and the Gillespie simulations. Under strong selection,
the system can display several levels of steady cooperation or get trapped into
absorbing states. These states are still relevant for experiments even when
irrational choices are made due to their prolonged relaxation times. Finally,
we show that for the particular case of the Prisoner Dilemma, where defection
is the dominant strategy under imitation mechanisms, the self-evaluation update
instead favors cooperation nonlinearly with the level of aspiration. Thus, our
work provides insights into the distinct role between imitation and
self-evaluation with no learning dynamics.
