How does resolution of strategy affect network reciprocity in spatial prisoner's dilemma games?

In the canonical framework of evolutionary 22 games, a binary strategy set comprising cooperation (C) and defection (D) has usually been presumed. Inspired by commonly observed real-world facts, we explore what happens if the resolution of strategy increases. As an extreme limit, the infinite resolution case is both a continuous and a mixed strategy defined by a real number in the range of [0,1]. We find that increasing resolution amplifies cooperation in spatial prisoner's dilemma games as compared with the binary strategy definition; however, this enhancement tendency with increasing resolution is not monotonic in the case of a mixed-strategy setting.