Game theoretical models predict that plant competition for light leads to reduced productivity of vegetation stands through selection for traits that maximize carbon gains of individuals. Using empirical results from a 5-year competition experiment with 10 genotypes of the clonal plant Potentilla reptans, we tested this prediction by analyzing the effects of the existing leaf area values on the carbon gain of the different genotypes and the consequent whole canopy carbon gain. We focused on specific leaf area (SLA) due to its role in the trade-off between light capture area and photosynthetic capacity per unit area. By combining a canopy model based on measured leaf area and light profiles with a game theoretical approach, we analyzed how changes in the SLA affected genotypic and whole-stand carbon gain. This showed that all genotypes contributed to reduced stand productivity. The dominant genotype maximized its share of total carbon gain, resulting in lower than maximal absolute gain. Other genotypes did not maximize their share. Hypothetical mutants of the dominant genotype were not able to achieve a higher carbon gain. Conversely, in other genotypes, some mutations did result in increased carbon gain. Hence, genotypic differences in the ability to maximize performance may determine genotype frequency. It shows how genotypic selection may result in lower carbon gains of the whole vegetation, and of the individual genotypes it consists of, through similar mechanisms as those that lead to the tragedy of the commons.