We consider a linear-state dynamic game played over an event tree and determine analytically the price of anarchy (PoA), which is given by the ratio of player's outcome in the cooperative game to her outcome in the noncooperative game. Next, we illustrate our findings in the context of a pollution control problem. We conduct a sensitivity analysis to assess the impact on PoA, and its lower and upper bounds, of varying the different parameter values. (C) 2016 Elsevier B.V. All rights reserved.