This paper deals with the issue of deforestation, one of the main global environmental problems. We consider two players having different utilities for forest conservation. The first one (call it North) represents a set of countries having as an objective to maximize the size of tropical forest at a certain time horizon. The (South) second player's revenue function involves a trade-off between forest exploitation and agricultural activities. We study two scenarios. In the first one, the assumption is a laisser-faire policy, where the South solves an optimal control problem over a finite horizon. Revenue and optimal forest exploitation obtained represent a benchmark for the second scenario, where the North offers subsidies to the South to reduce the deforestation rate. The two scenarios are analyzed and compared in terms of strategies, outcomes and forest conservation.