We study evolutionary games in which the rest points of the evolutionary dynamic cluster in connected components, focusing on what we call the Resource Game as a canonical example. The long-term outcome in such games can depend critically on second-order forces that were excluded from the evolutionary dynamics because they are typically insignificant compared with selection pressures. We show that the influence of second-order forces on long-term outcomes can depend on whether the reproduction underlying the evolutionary dynamics is sexual or asexual. An implication is that care is needed in adopting the convenience of an asexual model when examining the behavior of a sexual population in games with nontrivial components of rest points.