Consider the following model of price competition. Two firms set prices in a market whose demand curve is given by equation: Q=6-2
Where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced outfit. For example, if firm 1 and 2 post prices equal to 2 and 4 dollars respectively, then firm 1- as the lower priced firm - meets all of the market demand and, hence, sells 4 units. If the two firms post the same prices p, then they each get half the market, that is they each get 6-p/2. Suppose that prices can only be quoted in dollars units, such as 0,1,2 3, 4,5 and 6 dollars. Suppose, furthermore, that cost of production are zero for both firm.
(a) Write down the strategy form of this game assuming that each firm cares only about its own profits?
Specifically, if the auctioneer finds both bidders are in the auction at a bid of $3,000 but neither bid at $4000 then she awards the Renoir to bidder 1 at a price of $3000.
(b) Show that the strategy of posting a price of $5 (weakly) dominates the strategy of posting a price of $6. Does it strongly dominate as well?
(c) Are there other (weakly) dominated strategies for firm 1? Explain.
(d) Is there a strategy for firm 1? Explain.