Question

Imagine that, by chance, the scientists at Bayer and Pfizer -two of the largest pharmaceutical companies in the world- discover independently a new use for an already existing vaccine. This new use would allow them to enter a new market niche. 

However, the entrance in this new market niche is not for free but it requires the creation of new plants, the investments in new machineries and the hiring of new workers. An independent market research has estimated that 

• if either Bayer or Pfizer decides to enter the niche, it will make $30 million profits; 

• if both Bayer and Pfizer decide to enter the niche, they will make losses by $10 million. 

To this extent: 

(a) Write the game in normal form. 

(b) Are there dominated strategies? Motivate your answer. 

(c) Identify the best responses in pure strategies. 

(d) How many Nash Equilibrium are there? Motivate your answer. 

(e) Now, let’s assume Bayer does not know whether Pfizer will decide or not to enter the niche, but it has some beliefs regarding this strategy. In particular, the management of Bayer believes that the probability that Pfizer will enter the market equals to 45%: 

1- write Bayer’s expected payoffs; 

2- identify the best pure strategy response in this situation. 

(f) How things would change if Bayer’s belief would equal 85%? 

(g) By labeling p the probability that Pfizer decides to enter the niche and q the probability that Bayer decides to enter the niche 

1- compute the mixed-strategy Nash Equilibrium; 

2- interpret this result.

(h) Now assume that Bayer is less efficient than Pfizer when becomes a monopolist and is able to make $10 million of profits instead of $30 million: 

1- compute the pure strategy Nash equilibrium of this game; 

2- compute the mixed-strategy Nash equilibrium of this game; 

3- compare these equilibria with the previous ones and comment