Part A) Dominant firm 1 and a competitor firm 2 contemplate increasing capacity
ID: 1131050 • Letter: P
Question
Part A) Dominant firm 1 and a competitor firm 2 contemplate increasing capacity aggressively" or "passively". The normal form of the game is represented on the Table below firm 2 gressive 12,5 45 15,0 65 passive 16,5 5,0 firm 1 gressive passiv 18,0 / 6,0 a) Is there any dominant strategy equilibrium of this game? Can an equilibrium be found by the iterated-dominance procedure? Is there a Nash equilibrium? b) What is the equilibrium outcome if firm 1 can move first? Compare the firm's payoffs relative to (a) Comment on your findings c) What is the equilibrium outcome if firm 2 gets the right to move first? Compare the firms' payoffs relative to (a) and (b) Comment on your findings. Part B) Consider a market that will last two years, and assume no discount (the interest rate is zero). There are two players, an incumbent firm A that starts producing and selling product X at the beginning of the first year, and a potential entrant E that contemplates entry at the beginning of the second year. Firm E is producing a good Xe that serves the same needs as X, but is of lower quality. Serving this market requires each firm paying a fixed cost F - 200 in order to install capacity, this cost is paid only once, even if the firm produces in both periods. During the first year the incumbent A pays F and operates alone in the market, choosing a price between the following: P the monopoly price, or Pi, a very low price that threatens (in conjunction with the superiority of X over Xl) to leave any potential entrant with zero sales (stage 1 of the game). If A charges Pm it gets a first-period revenue equal to 2550, whereas the same revenue under P is 1950. At the beginning of the second year, E contemplates entry (stage 2). If E does not enter. the incumbent must charge the same price it did during period one (whether Por P) and make the same revenue. If E enters, the incumbent revises its price having now two choices (stage 3) to either fight the entrant charging Pt, or to accommodate it, charging P The latter is a price between Pa and Pi(P P. P) that allows E to make positive sales and revenue equal to 400 If A accommodates entry, its revenue is equal to 650. If following entry A decides to fight charging the price P. A's revenue is 250 and E's al) Is it possible for the incumbent to deter entry by threatening to charge Pi during the first and the second period? Is charging P during the first period a rational choice for the incumbent? b) Find the equilibrium path (outcome) and t he profits at the SPNEExplanation / Answer
Q1
Yes we have dominant strategy in this game and that is given as below
Firm 1 plays passively and Firm 2 plays aggressive
Yes it can be found using iterated dominant strategy
For Firm 1 aggressive strategy is dominated by passive strategy hence aggressive strategy for Firm 1 can be ignored now left with 2 pairs (Passive,Aggressive);(Passive,Passive)
For which Passive Aggressive pays better payoff to both players.
Hence there exists Nash Equilibrium
Q 2
If firm 1 moves first it would play Passive and hence the equilibrium would remain the same
Hence no first mover advantage in this case
Q 3
If Firm 2 plays first then Firm 2 has highest payoff possible of 18 after playing passive and then Firm 1 has to play Passive in which case Nash Equilibrium will become (Passive,Passive)
That in this case we have first mover advantage and this outcome is pareto superior to original nash equilibrium.