Question

A and B just started selling the next generation of Xbox and Playstation consoles. They both announced that the respective top version (B Playstation 5 & A Xbox Series X) are priced at $ 750 in Australia (ok, $749, but just round it up). There was speculation that they might charge a higher price, for example $900, for these models. And assume that both had to lock in these prices with stores before any of them made a public announcement about the respective price of their console.

Although a substantial number of buyers pick the brand they prefer, there are a few that purchase based on price. If both charge $750, then they split the market and A and B make $50 Million ($50m) profit, if they charge $900, then B cashes in and makes $100m profit, while A gets $65m.

Because some fans are more price sensitive, B reaps $80m when it charges a lower price than A, which makes $25m less than B. If B is more expensive, it loses a lot of customers and earns only $40m, while A is able to increase its own profits by $10m over the outcome where A is more expensive.

1. Draw a complete and fully labelled payoff matrix for this situation.
2. Does A have a dominant strategy? If so what is it, and why is it one? And if not, explain why not.
3. Find the Nash equilibrium and explain why it is the likely outcome for this situation.
4. B does not have a dominant strategy. Is it possible to create a dominant strategy for B when you change one of the firm’s payoff such that the Nash equilibrium from 1c remains a Nash equilibrium? If so, which payoff needs to be changed and by how much? (it’s enough to list one payoff in case they are multiple possibilities). If not, why not?
5. B actually announced its price a few days after A. Explain whether it mattered for B’s choice of a price whether it had to lock in the price before A’s announcement or not, given the payoff matrix above in Q1a.

(and please focus on those two consoles only, for the purpose of this assignment the cheaper ones do not exist and the two firms only had the choice between charging $750 or $900)

Answer 1

This topic comes under game theory. The pay off matrix can be made from the informations given in the question. The pay off matrix can be used to answer further questions.