Tropical deforestation is the second largest source of anthropogenic GHG emissions and the major driver of the ongoing wave of mass species extinction. Yet, despite strong international pressure and diverse initiatives by tropical countries, the conversion rate has remained unabated for more than 25 years. Here we introduce a dynamic marginal approach that analyses the distribution of conservation benefits and costs across geopolitical scales and their behavior as deforestation advances. The case study focused on the Brazilian Amazon projects that under the current regime of incentives the conversion will continue until 70% of the original forest is gone. Despite a few quantitative uncertainties, this approach provides insights for future research and points to a systematic international cooperation as the key to halt tropical deforestation.