ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games

Open-loop Stackelberg equilibria in linear-state games are subgame perfect. This result holds under the hypothesis of unconstrained final state; whereas we need to take into account suitable final-state conditions in order to correctly formalize certain economic problems. A striking contribution of this paper is that it tackles the consistency problem for an open-loop Stackelberg equilibrium in linear-state games with a final-state constraint in the leader’s problem. In this paper, after proving that such a type of equilibrium is not subgame perfect, we introduce a weaker definition of subgame perfectness, which we call ε-subgame perfectness. This new definition can be applied to the open-loop Stackelberg equilibrium of a constrained linear-state game. Finally, we present some explanatory examples to show how the definition of ε-subgame perfectness can be meaningful.