  The perceived risk and reward for a given situation can vary depending on
resource availability, accumulated wealth, and other extrinsic factors such as
individual backgrounds. Based on this general aspect of everyday life, here we
use evolutionary game theory to model a scenario with randomly perturbed
payoffs in a prisoner's dilemma game. The perception diversity is modeled by
adding a zero-average random noise in the payoff entries and a Monte-Carlo
simulation is used to obtain the population dynamics. This payoff heterogeneity
can promote and maintain cooperation in a competitive scenario where only
defectors would survive otherwise. In this work, we give a step further
understanding the role of heterogeneity by investigating the effects of
quenched disorder in the critical properties of random games. We observe that
payoff fluctuations induce a very slow dynamic, making the cooperation decay
behave as power laws with varying exponents, instead of the usual exponential
decay after the critical point, showing the emergence of a Griffiths phase. We
also find a symmetric Griffiths phase near the defector's extinction point when
fluctuations are present, indicating that Griffiths phases may be frequent in
evolutionary game dynamics and play a role in the coexistence of different
strategies.
