We study dynamic mean-variance portfolio selection in the presence of transaction costs, aiming to identify time-consistent solutions within a game-theoretic framework. We find that while a mean-variance criterion can yield economically reasonable intrapersonal equilibrium strategies without transaction costs, it may produce economically less plausible strategies when transaction costs are present and the investment horizon is extended.  Our results reveal that applying a game-theoretic framework to long investment horizons presents subtle challenges, and caution is warranted when applying it to long-horizon, time-inconsistent decision problems involving singular control.