In plants, investment in height improves access to light, but incurs costs in construction and maintenance of the stem. Because the benefits of plant height depend on which other height strategies are present, competition for light can usefully be framed as a game-theoretic problem. The vertical structure of the world's vegetation, which is inefficient for plant growth, can then be understood as the outcome of evolutionary and ecological arms races. In addition, game-theoretic models predict taller vegetation on sites of higher leaf area index, and allocation to reproduction only after an initial period of height growth. However, of 14 game-theoretic models for height reviewed here, only one predicts coexistence of a mix of height strategies, a conspicuous feature of most vegetation. We suggest that game-theoretic models could help account for observed mixtures of height strategies if they incorporated processes for coexistence along spectra of light income and time since disturbance.