Human-induced rapid environmental change (HIREC) has recently led to alterations in the fitness and behavior of many organisms. Game theory is an important tool of behavioral ecology for analyzing evolutionary situations involving multiple individuals. However, game theory bypasses the details by which behavioral phenotypes are determined, taking the functional perspective straight from expected payoffs to predicted frequencies of behaviors. In contrast with optimization approaches, we identify that to use existing game theoretic models to predict HIREC effects, additional mechanistic details (or assumptions) will often be required. We illustrate this in relation to the hawk-dove game by showing that three different mechanisms, each of which support the same ESS prior to HIREC (fixed polymorphism, probabilistic choice, or cue dependency), can have a substantial effect on behavior (and success) following HIREC. Surprisingly, an increase in the value of resources can lead to a reduction in payoffs (and vice versa), both in the immediate- and long-term following HIREC. An increase in expected costs also increases expected payoffs. Along with these counter-intuitive findings, this work shows that simply understanding the behavioral payoffs of existing games is insufficient to make predictions about the effects of HIREC.