We characterize incentive equilibrium strategies and their credibility conditions for the class of 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 the players' actions. We show that it is possible for two players wanting to optimize their joint payoff over a given planning horizon to achieve this as an incentive equilibrium. This therefore ensures that cooperation will continue from one node to the next. A simple example illustrates these strategies and the credibility conditions. (C) 2016 Elsevier Ltd. All rights reserved.