Formulate the following situation as an extensive-form game (game tree) and then solve it using backward induction:
Bingo Corporation and Canal Corporation are the only competitors in a particular electronics market. Bingo is considering and R&D investment to improve its product. Bingo can choose from three levels of investment - high, medium, or low. Following Bingo's investment, canal will have to choose between continuing to compete with its current product or investing in some R&D of its own. Canal, however, only has one investment choice , so its options are to invest or not invest.
The net payoffs to Bingo if it invests high, medium, or low given that Canal chooses to invest would be $50, $40, and $30 respectively, and corresponding payoffs to Canal would be $5, $10 and $15.
On the other hand, the net payoffs to Bingo if it invests high, medium, or low given that Canal chooses not to invest high, medium, low given that Canal chooses not to invest would be $100, $80, and $60 respectively, and the corresponding payoffs to Canal would be $0, $15, and $20.
What will Bingo choose to do? What wll Canal do in response? Is there any "threat" that canal could make that might change the outcome of the game? Explain all your answers.