Question

(2) Assume there are 2 firms a monopolist (incumbent) (Firm A) and an entrant (Firm B). Firm b could enter the market or not and firm A could fight or accommodate. The total Profit in this market is a $100. If firm B enters and A decides to accommodate they will share equally ($50 and $50). Assume that Firm A incurs in a cost (advertising for example) if it decides to fight firm B of $30. Assume that this cost is incurred at the beginning of the game regardless if Firm B enters or not. This game is played only once and both players move at the same time a. Write the game in Normal form b. Obtain the Nash equilibrium. (2) Assume there are 2 firms a monopolist (incumbent) (Firm A) and an entrant (Firm B). Firm b could enter the market or not and firm A could fight or accommodate. The total Profit in this market is a $100. If firm B enters and A decides to accommodate they will share equally ($50 and $50). Assume that Firm A incurs in a cost (advertising for example) if it decides to fight firm B of $30. Assume that this cost is incurred at the beginning of the game regardless if Firm B enters or not. This game is played only once and both players move at the same time a. Write the game in Normal form b. Obtain the Nash equilibrium.

Answer 1

A).

Consider the given problem here there are two firms “firm A” is the “Incumbent” and “firm B” is the “Entrant”. So, here both the firms have two strategies. SO, the normal form game is given below.

So, here if “Incumbent” choose to “Accommodate” then will get “$100” if “Entrant” decide to “not to enter” in the market and will get “$50” if “Entrant” decide to “enter” in the market. Similarly, if “Incumbent” choose to “Fight” then will get “$100-$30=$70” in either case.

B).

Now, if “Entrant” decides to “enter” into the market then the optimum choice for “Incumbent” is to “Fight”, because under “Fight” “incumbent” will get more profit. Similarly, if “Incumbent” decides to “Fight”, => the “Entrant” is indifferent between “E” and “NE”, => here is one “Nash Equilibrium” which is given by “Fight, Enter” with pay off “$70, $0”.

Now, if “Entrant” decides to “not to enter” into the market then the optimum choice for “Incumbent” is to “Accommodate”, because under “Accommodate” “incumbent” will get more profit. Similarly, if “Incumbent” decides to “Accommodate”, => the “Entrant” will decide to “Enter”, => there is no “Nash”

So, here there is only one NE which is “Fight, Enter” with profit “$70, $0”