Question

Consider an industry with two firms, 1 and 2, and two technologies, A and B. The profits that

every firm earns from technology = {,} is
= + if firms adopt technology
where denotes the baseline profit that the firm earns from technology , and measures
network effects. When = 0, the number of firms adopting technology does not affect the
profits from adopting it, while when > 0 technology becomes more attractive as more firms
adopt it. Profits are symmetric across firms. We assume that ≡ ― > 0, which indicates
that, in the absence of network effects, technology is regarded as superior by both firms. Every
firm simultaneously and independently chooses between technology and .
a) Represent the game in a normal matrix form.
b) Find the best responses for each firm. You can use words to explain the best responses.
c) Let = = 1, = 2, = 3. Find the pure-strategy Nash Equilibrium of the game.

Answer 1

To represent the game in normal matrix form, create a matrix with technology choices as rows and columns, and fill in the profits for each firm. The best response for each firm is to choose the technology that maximizes their own profits given the other firm's choice.

Step-by-step explanation:

To represent the game in normal matrix form, we consider Firm 1's decision as the rows and Firm 2's decision as the columns. The payoffs in the matrix will be the profits earned by each firm based on their technology choices. Here is the matrix: Technology A Technology B Firm 1 (Technology A) (π1,A, π2,A) (π1,B, π2,B) Firm 1 (Technology B) (π1,B, π2,A) (π1,B, π2,B). The best response for each firm will depend on the profits earned by themselves and their competitor. They will choose the technology that maximizes their own profits given the technology choice of the other firm. The best responses can be determined by comparing the profits in the matrix and selecting the highest value in each row or column.

To find the pure-strategy Nash Equilibrium of the game, we need to find the combination of technology choices (A or B) that result in the highest profits for both firms. This can be done by identifying any intersection point in the matrix where neither firm has an incentive to switch technologies. In other words, both firms are choosing their best responses given the other firm's choice. For the given values of π1,A, π2,A, π1,B, π2,A, π1,B, and π2,B, we need to compare the profits and identify any Nash Equilibrium.