  Evolutionary game theory, encompassing discrete, continuous, and mixed
strategies, is pivotal for understanding cooperation dynamics. Discrete
strategies involve deterministic actions with a fixed probability of one,
whereas continuous strategies employ intermediate probabilities to convey the
extent of cooperation and emphasize expected payoffs. Mixed strategies, though
akin to continuous ones, calculate immediate payoffs based on the action chosen
at a given moment within intermediate probabilities. Although previous research
has highlighted the distinct impacts of these strategic approaches on fostering
cooperation, the reasons behind the differing levels of cooperation among these
approaches have remained somewhat unclear. This study explores how these
strategic approaches influence cooperation in the context of the prisoner's
dilemma game, particularly in networked populations with varying clustering
coefficients. Our research goes beyond existing studies by revealing that the
differences in cooperation levels between these strategic approaches are not
confined to finite populations; they also depend on the clustering coefficients
of these populations. In populations with nonzero clustering coefficients, we
observed varying degrees of stable cooperation for each strategic approach
across multiple simulations, with mixed strategies showing the most
variability, followed by continuous and discrete strategies. However, this
variability in cooperation evolution decreased in populations with a clustering
coefficient of zero, narrowing the differences in cooperation levels among the
strategies. These findings suggest that in more realistic settings, the
robustness of cooperation systems may be compromised, as the evolution of
cooperation through mixed and continuous strategies introduces a degree of
unpredictability.
