Plant roots determine carbon uptake, survivorship, and agricultural yield and represent a large proportion of the world's vegetation carbon pool. Study of belowground competition, unlike aboveground shoot competition, is hampered by our inability to observe roots. We developed a consumer-resource model based in game theory that predicts the root density spatial distribution of individual plants and tested the model predictions in a greenhouse experiment. Plants in the experiment reacted to neighbors as predicted by the model's evolutionary stable equilibrium, by both overinvesting in nearby roots and reducing their root foraging range. We thereby provide a theoretical foundation for belowground allocation of carbon by vegetation that reconciles seemingly contradictory experimental results such as root segregation and the tragedy of the commons in plant roots.