  The emergence and maintenance of cooperation has attracted intensive
scholarly interest and has been analysed within the framework of evolutionary
game theory. The role of innovation, which introduces novel strategies into the
population, is a relatively understudied aspect of evolutionary game theory.
Here, we investigate the effects of two sources of innovation---mutation and
heterogeneous updating rules. These mechanisms allow agents to adopt strategies
that do not rely on the imitation of other individuals. The model
introduces---in addition to canonical imitation-based strategy
updating---aspiration-based updating, whereby agents switch their strategy by
referring solely to the performance of their own strategy; mutation also
introduces novel strategies into the population. Our simulation results show
that the introduction of aspiration-based rules into a population of imitators
leads to the deterioration of cooperation. In addition, mutation, in
combination with heterogeneous updating rules, also diminishes cooperators.
This phenomenon is prominent when a large proportion of the population consists
of imitators rather than adopters of aspiration-based updating. Nevertheless, a
high mutation rate, in combination with a low aspiration level, has positive
nonlinear effects, and a heterogeneous population achieves a higher level of
cooperation than the weighted average of homogeneous populations. Our results
demonstrate the profound role of innovation in the evolution of cooperation.
