Two car companies, BDcar and SLcar are competitors. BDcar is deciding whether to enter (Enter) or stay out (Stay Out) of the car market. SLcar can observe BDcars choice and also choose to enter or stay out of the market.

If SLcar chooses to stay out of the market after BDcar enters, BDcar will get a payoff of 100,000 and SLcar will get a payoff of zero.

If SLcar enters the market after BDcar chooses to stay out, SLcar will get a payoff of 100,000 and BDcar will get a payoff of zero. If both firms choose to stay out, they each get a payoff of zero.

If SLcar chooses to enter the market after BDcar chooses to enter, it can decide to compete aggressively (Aggressive) or softly (Soft) with BDcar.

If SLcar competes aggressively both firms get a payoff of 50,000. If SLcar competes softly it gets a payoff of 20,000 while BDcar gets a payoff of 80,000.

a. Depict the game in extensive form.

b. Find a Nash equilibrium of the game using backward induction, explaining the steps.