We study a multi-objective finite-horizon game model of renewable, common resource extraction where the players have two separate objectives (one is economic success; the other describes the players’ environmental concern). We derive the cooperative strategy and the subgame-perfect Pareto equilibrium in linear-state non-stationary feedback strategies by employing the dynamic programming approach. Since the utility is transferable only based on the economic criterion, we need to revise the concept of time consistency and the payoff-distribution procedure to provide a mechanism for sustainable long-term cooperation. All the results are illustrated with a numerical example.