Question

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 $10 over the situation where it is more expensive.

1. Draw a complete and fully labelled payoff matrix for this situation.
2. Does Microsoft 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. 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?
5. 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)

Answer 1

SOLUTION:

First let's analyze the question one more time clearly,

1. Two companies MICROSOFT - xbox series x AND SONY - playstation 5

2. Both companies have a set price in Australia for $750

3. Assume they may increase the price for $900 in stores, before they announce public.

4. "Few purchase based on price". If both companies sell for $750 they can split and make $50 million profit .

5. If they charge $900, Sony makes $100 milion and Microsoft make $55 million

6. As many buyers are Price Sensitive, Sony and Microsoft may charge a lower price. Sony's profit will be $80 million and Microsoft will make $25 million (less than Sony)

7. If Sony increases its price it may loses customers and earns only $40 million.

8. Using the above step (point 7) has advantage, Microsoft is able to increase its profits by $10 million over the situation where it is more expensive.

These are the steps. Hope you have understood more understandably.

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

Solution and Explanation:

Payoff matrix plays an important role in the firm decison over a product and budget whether to implement this cost or that cost. It is usually called to be a game theory where firms use strategy to be in a first position.

There should be four cells in a matrix. Where I have taken the two firms MICROSOFT and SONY. In each column and row mentioned the profit earned by the revenue in situation where the profit for the firm is $100 million and $55 million when they charge for $900. In case of price sensitive the new profit for the revenue will $80 and $25. In second row and column, considering the profit and the new profit for the firm will be $40 million and $10 million as loss for sony and higher revenue for microsoft.

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

Solution and Explanation:

Yes, microsoft have a dominant strategy that is a strategy that results in the highest payoff to a player regardless of the opponent’s action. An Equilibrium in Dominant Strategies is always a Maximin Equilibrium. As it earns a $10 million by shifting the price low when Sony increases it's price for Playstation 5. A strictly dominant strategy is that strategy that always provides greater utility to a the player, no matter what the other player’s strategy is.

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

Solution and Explanation:

The game between MICROSOFT  and SONY, consider (S&M) both firms can choose strategy S, to receive $100 million, or strategy M, to lose $50 million. Logically, both players choose strategy S and receive a payoff of $100 million. If you revealed S strategy to M and vice versa, you see that no player deviates from the original choice. The outcome strategy of S (Sony) represents a Nash equilibrium.

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?

Solution and Explanation:

Yes, it is possible for SONY to have a dominant strategy by reducing the price of Playstation 5 compared with MICROSOFT. When changing the payoff of Microsoft's equilibrium, where already in the price sensitive sony has the chance of earning more than microsoft. The payoff of $40 million should be changed to more than $80 million because if sony expects more customers when the price of the product falls, it gets more revenue.(In USD million)

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.

Solution and Explanation:

Sony’s choice of a price between $750 to $900 should be locked in the price before Microsoft’s announcement , given the payoff matrix above Sony has to lock $900, Since Sony can make $100 million. Yes it mattered for sony to consider a price of $900 where it should gain the maximum amount of revenue. As long as sony does'nt increases its price above $900 it'll never face a decrease in the revenue of $80 million.