In a competitive market, two companies, A and B, are deciding whether to launch a new product. Company A moves first and chooses between a high investment or a low investment. Company B observes A's choice and then decides on its own investment level. If A chooses high investment, B can either choose high or low investment. If A chooses low investment, B similarly has the option to choose high or low. How should Company A decide on its investment using backward induction to maximize its payoff?

In backward induction you start with the last mover, B, and find its best response to each of A’s possible moves. If A invests high, B will choose the investment that gives B the larger payoff; if A invests low, B will again choose the higher payoff option. For example, if A’s high investment gives B a payoff of 5 when B also invests high and 3 when B invests low, B will invest high. If A’s low investment gives B a payoff of 4 when B invests high and 2 when B invests low, B will again invest high. Knowing B will always invest high, A compares the payoffs from its own high versus low investment and picks the one that yields the larger payoff, thus maximizing A’s payoff.