Microsoft and Sony just started selling the next generation of Xbox and Playstation consoles. They both announced that the respective top version (Sony Playstation 5 & Microsoft 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 make $50 Million ($50m) profit, if they charge $900, then Sony cashes in and makes $100m profit, while Microsoft gets $55m.

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

a)Draw a complete and fully labelled payoff matrix for this situation.

b)Does Microsoft have a dominant strategy? If so what is it, and why is it one? And if not, explain why not.

c)Find the Nash equilibrium and explain why it is the likely outcome for this situation.

d)Sony does not have a dominant strategy. Is it possible to create a dominant strategy for Sony when you change one of the firm's payoff (without changing the 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?

e)Sony actually announced its price a few days after Microsoft. Explain whether it mattered for Sony's choice of a price whether it had to lock in the price before Microsoft's announcement or not, given the payoff matrix above.

(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)