  Innovation and evolution are two processes of paramount relevance for social
and biological systems. In general, the former allows to introduce elements of
novelty, while the latter is responsible for the motion of a system in its
phase space. Often, these processes are strongly related, since an innovation
can trigger the evolution, and the latter can provide the optimal conditions
for the emergence of innovations. Both processes can be studied by using the
framework of Evolutionary Game Theory, where evolution constitutes an intrinsic
mechanism, while innovation requires an opportune representation. Notably,
innovation can be modeled as a strategy, or can constitute the underlying
mechanism which allows agents to change strategy. Here, we analyze the second
case, investigating the behavior of a heterogeneous population, composed of
imitative and innovative agents. Imitative agents change strategy only by
imitating that of their neighbors, whereas innovative ones change strategy
without the need of a copying source. The proposed model is analyzed by means
of analytical calculations and numerical simulations in a square lattice.
Remarkably, results indicate that the mixing of mechanisms can lead to
different behaviors, being sometimes beneficial and others detrimental to
cooperation. Our investigation sheds some light on the complex dynamics
emerging from the heterogeneity of strategy revision methods, highlighting the
role of innovation in evolutionary games.
