The tragedy of the commons has been well known since it was published and has been widely studied not only in human society but also in the biological study. In particular, due to the various characteristics of plants, it has been widely studied in plant research such as underground and aboveground competition respectively. However, in the previous theoretical studies considering the tragedy of the commons game, the amount of root biomass was a strategy and it was fixed which means that did not consider the growth of plant. Our model takes into account the growth of the plant and the resource allocations. This becomes the plant's strategy and the plant's biomass appears as the outcome. We confirmed that our model follows the tragedy of the commons when the fitness of the plant is related to the total biomass or shoot biomass. However, when the fitness of the plant is related to the root biomass, it was observed that the fitness of the plant and the amount of root decreased simultaneously. Our study proposes that when studying competition of plants, it is important to understand the characteristics of plants and measure their fitness could be very appropriate and precisely.