Ethical theories grounded in utilitarianism suggest that social welfare is improved when agents seek to maximize others' welfare in addition to their own (i.e., are altruistic). However, I use a simple game-theoretic model to demonstrate two shortcomings of this argument. First, altruistic preferences can generate coordination problems where none exist for selfish agents. Second, when agents care somewhat about others' utility but weight their own more highly, total social welfare may be lower than with selfish agents even in the absence of coordination problems.