This paper investigates equilibrium and stability analysis in a two-agent non-cooperative dynamic game. Almost all existing papers handling finite-horizon dynamic games assume the common prediction horizon length, whereas this paper considers an asymmetric length case due to differences in personal values. We thus propose two possible control strategies without the knowledge of the other agent's horizon information through a linear-quadratic game. One of the proposed control strategies is the receding horizon control based on an open-loop Nash equilibrium with the common horizon case. The other is an iterative optimization-based control with each agent estimating the other's feedback gain from the state information. We also discuss the effectiveness of the proposed strategies and the stability condition of the corresponding closed-loop systems through numerical examples.