We study a model of strategic competition among farmers for land use in an agricultural economy. Each agent can take possession of a part of the collective forest land and convert it to farming. Unconverted forest land helps preserving biodiversity, which contributes to reducing the volatility of agricultural production. Agents' utility is given in terms of a Kreps Porteus stochastic dierential utility capable of disentangling risk aversion and aversion to uctuations. We characterize the land used by each farmer and her welfare at the Nash equilibrium, we evaluate the over-exploitation of the land and the agents' welfare loss compared to the socially optimal solution and we study the drivers of the ineciencies of the decentralized equilibrium. After characterizing the value of biodiversity in the model, we use an appropriate decomposition to study the policy implications of the model by identifying in which cases the allocation of property rights is preferable to the introduction of a land conversion tax.