Question

A monopolist is facing a threat of entry by another firm. First the entrant decides whether or not to enter, and then the incumbent decides whether or not to cut its price (fight) in response. If the entrant decides to stay out, it gets a payoff of 0 and the incumbent gets a payoff of 10 as a monopolist. If the entrant decides to enter the market, two firms’ payoff depends on whether the incumbent fights or not. If the incumbent fights, then both firms end up with a negative payoff -5. If the incumbent decides not to fight, they divide the market profit and both get a payoff of 5. Draw the extensive form of the game and solve the backward induction outcome.

Answer 1

Consider the game here there are two players “Entrant” and “Incumbent”. Now, consider the following extensive form game.

Now, there are two action of “Entrant” now if he chooses “SO” will get “0” as payoff, if he chooses “En”, => “Incumbent” will choose “NF”, since 5 > -5. So, if “Entrant” chooses “En”, => will get payoff “5” > 0. So, the optimum choice of “Entrant” is to choose “En”. So, here the solution of this game is “En, NF” and the corresponding payoff is “5, 5”.