In this article, we characterize incentive equilibrium strategies and their credibility conditions for the classes of linear-state and linear-quadratic dynamic games played over event trees. In such games, the transition from one node to another is nature's decision and cannot be influenced by players' actions. Assuming that two players wish to optimize their joint payoff over a given planning horizon, we show that this outcome can be achieved as an incentive equilibrium, and hence ensures that cooperation will continue from one node onward. Two simple examples illustrate these strategies and the credibility conditions.