Paraphrase the following: First, Andre chooses High and Low based on higher pay$-$offs at each step. Basie opts for Bottom in both cases due to superior pay$-$offs.

After Basie's choices, the game tree simplifies, and Andre selects Down for its higher pay$-$off in the final decision.

Through backward induction, the optimal strategies for both players in this sequential game. Andre's strategy is to choose Down, Basie's strategy is to choose Bottom, and Andre's initial move is High. This analysis showcases how game theory aids in unraveling strategic decision$-$making processes and reveals the equilibrium strategy for players in a dynamic environment.