Question

You are considering entering a market serviced by a monopolist in Malaysian telecommunication industry. You currently earn $0 economic profits, while the monopolist earns $5. If you enter the market and the monopolist engages in a price war, you will lose $5 and the monopolist will earn $1. If the monopolist doesn't engage in a price war, you will each earn profits of $2.

a. Write out the extensive form of the above game.

b. There are two Nash equilibria for the game. What are they?

c. Is there a subgame perfect equilibrium? Explain.

d. If you were the potential entrant, would you enter? Explain why or why not.

Answer 1

a) Generally a nash equilibrium is a stable state of a system involving the interaction of the different participants, in which no other participant can gain by a unilateral change of the strategy if the strategies of the others remains un-altered.

b) In the game depicted above there are two Nash equilibriums would be (0.5) and (2.2) as if any of the players tries to unilaterally gets deviate from any of these positions the other would react in such a way to render the equilibrium unstable.

c) The sub game perfect equilibrium in this game is (2,2) by using the backward induction method. As if the entrant enters the market the monopolist has two choices; either to initiate or price war or doesn't engage in a price war. If he does he gets a payoff of 1. If he doesn't engage in a price war he will earn a payoff of 2. Hence he would prefer not engaging in the war. As per the scenario the entrant would earn a payoff of 2. Hence he must choose to enter and monopolist would not wage a price war so the equlibrium would be (2,2).

d) According to the given scenario, I none other than the entrant would choose to enter the market as my payoff would be 2 against o profits when i did not enter into the market.