When a resource shifts from one player to another, e.g. due to climate change, the conservation incentive of the player losing the resource decreases while the conservation incentive increases for the player at the receiving end. We set up an analytical model to study how the structure of the game changes when the shift occurs either fast or slow, or gradual or abrupt. We also investigate whether there is a self-enforcing agreement that aligns incentives. We find that the longer the expected duration of the shift, the less intensive the exploitation of the resource and the larger the scope for cooperation. In some cases there is no stable agreement, even when there are only two players.