In a competitive market where two companies, A and B, are deciding whether to invest in a new product line, Company A can either invest heavily (high commitment) or cautiously (low commitment). Company B, observing Company A's decision, will choose a strategy based on that. If Company A invests heavily, Company B can either match that investment or opt for a different strategy. How should Company A decide its strategy using backward induction, considering the potential responses from Company B?

To use backward induction, start by thinking about what Company B would do after seeing Company A’s move. If A invests heavily, B will compare the payoff of matching that investment with the payoff of choosing a different strategy; B will pick the one that gives it the higher payoff. Next, consider the case where A invests lightly: B again chooses the best response to a light investment. Knowing B’s two possible responses, Company A looks at the outcomes of each of its own actions and selects the one that gives A the highest payoff when B acts optimally. For example, if matching A’s heavy investment gives B a payoff of 8 and a different strategy gives 5, B will match, so A’s heavy investment yields A a payoff of 7; if a light investment leads B to match with a payoff of 4 for A, then A will choose the heavy investment because 7 > 4.