Reference no: EM132414901

Consider a market with two firms (Firm I and Firm E). Each firm must decide whether to set a high price or a low price for its product. The firms decide price simultaneously and their profits depend on both their decisions. If they both price the same, they split the profits equally. If both price high, total profits are 70. If they both price low, total profits are 50. If one firm prices high and the other low, total profits are 60 and the firm that has priced low gets two-thirds of the total profits.

(i) Present the information in table form.

(ii) Identify the nash equilibrium for this game.

(iii) Suppose Firm I chooses its pricing strategy before Firm E, and E knows I's choice before E makes its own pricing decision. How do I use a game tree for this scenario and explain the equilibrium outcome?

Now suppose Firm I is an 'incumbent firm' established in the market and firm E is a potential entrant. If E enters they play the price setting game from part(i). If E does not enter, firm I (which is then a monopolist) gets a payoff of 40 if it chooses to price high and 30 if it chooses to price low. The incumbent firm has to make its price choice before E decides whether or not to enter and if it does enter what price to set (high or low). If E does not enter it saves its entry costs of 26.

(iv) Draw an appropriate decision tree and solve for the optimal strategy of each player, show that the incumbent will choose to price low.

(v) Suppose firm E had an established reputation (from its activities in other markets) of always pricing low. How would this affect the solution in (e)?

(vi) Alternatively, suppose firm E had an established reputation (from its activities in other markets) of always pricing high. How would this affect the solution in (e)?