Noncooperative resource exploitation by patient players

We consider a discrete-time dynamic game in which a finite number of players extract a non-renewable resource and derive consumption solely from the extracted amount (cake-eating game). Markov perfect Nash equilibria consisting of linear strategies can be constructed in this game not only if the players have time-preference factors that are smaller than 1, but also if these factors are equal to or even larger than 1. We demonstrate this result both for the case of identical players and for the case of heterogeneous players. In addition, we study the influence of the model parameters on the equilibrium.