An incumbent operating in a market faces a potential entrant. If the entrant does not enter, the incumbent earns a profit of $100. If the entrant enters, both firms earn a profit of $40. The game proceeds as follows. The incumbent first has an opportunity to increase production costs by $50, which reduces profit by $50 for any firm in operation–entrant or incumbent. After the incumbent makes this choice, the entrant decides whether or not to enter.
a. Draw the game tree and find the subgame perfect equilibrium.
b. What action would the incumbent take without any threat of entry?
c. It seems counterintuitive that a firm would deliberately take an action that increases its cost and reduces its profit. How could you explain what is going on to a non-economist?