paraphrase the following: Andre initially chooses High and Low based on the higher pay$-$offs at each step. Basie, on the other hand, chooses 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 are determined. Andre's strategy is to choose Down, Basie's strategy is to choose Bottom, and Andre's initial move is High. This analysis demonstrates how game theory helps unravel strategic decision$-$making processes and reveals the equilibrium strategy for players in a dynamic environment.