We consider a dynamic model of non-renewable resource extraction under the assumption that players do not know their opponents' utility functions. Agents form conjectures on the behavior of others. Two forms of beliefs are introduced, namely, beliefs based on the state of the resource, and beliefs based on the state of the resource and on the strategy of other agents (their consumption). We focus on consistent equilibria, where states corresponding to the players' beliefs must be consistent with observed past plays. Closed form expressions of the optimal consumption plans and of the state dynamics are derived. Comparisons are made with the full information benchmark case. It is proved that, depending on the initial consumption levels, the present process might lead to different patterns of management of the resource in the long run. With strategy and state based beliefs, the agents behave more (respectively, less) agressively than in the non-cooperative benchmark when initial consumption is high (respectively, intermediate). When initial consumption is low, the optimal consumption path lies below that of the cooperative benchmark.