  Evolution occurs in populations of reproducing individuals. Reproduction
depends on the payoff a strategy receives. The payoff depends on the
environment that may change over time, on intrinsic uncertainties, and on other
sources of randomness. These temporal variations in the payoffs can affect
which traits evolve. Understanding evolutionary game dynamics that are affected
by varying payoffs remains difficult. Here we study the impact of arbitrary
amplitudes and covariances of temporally varying payoffs on the dynamics. The
evolutionary dynamics may be "unfair", meaning that, on average, two coexisting
strategies may persistently receive different payoffs. This mechanism can
induce an anomalous coexistence of cooperators and defectors in the Prisoner's
Dilemma, and an unexpected selection reversal in the Hawk-Dove game.
