You are considering entering a market serviced by a monopolist. You currently ea

Question

You are considering entering a market serviced by a monopolist. 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.

Explanation / Answer

a) A Nash Equilibrium is a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged.

In the game depicted above the two Nash equilibriums would be (0,5) and (2,2). I f any of the players tries to unilaterally deviate from any of these positions the other would react in a such a way as to render the equilibrium unstable.

c) The sub game perfect equilibrium in the game is (2,2) using the backward induction method. 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 earns a payoff of 2. So he would prefer not engaging in the war. Given this scenario, the entrant(YOU) would earn a payoff of 2 if he enters the market and a payoff of 0 if he doesn’t enter. So he would chose to enter and the monopolist would not wage a price war so the equilibrium would be (2,2).

Ans: Sub perfect game equilibrium: (2,2)

d) Given this scenario I the entrant would choose to enter the market as my payoff here would be 2 against 0 profits when I did not enter the market.

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