I pasted the problem I am to solve below. I missed the first week of class, so the professor told me to do this case as a make-up assignment; however, we are not covering this chapter and I'm confused! My professor did tell me that I need to use the bimatrix game theory and input the data to find the answer. I don't know what in the world to do! See below. Please help!
Memo 7
To: Pricing Manager, District 6SW
From: Vice President, Marketing
Re: Strategic Pricing Decision
Our only competitor in District 6SW currently provides bundled services at $84.95. We are
currently charging a 10% premium over their price, but there are unsubstantiated rumors that
they are contemplating a 10% price increase. We don’t know their cost structure, so we don’t
know whether their potential price increase is driven by cost increases or is merely a strategic
move on their part.
Historically, when we both charge the same price, our market share is about 65%. When we
charge a 10 percent premium over their price, our market share declines to about 60%. It
appears that in those instances where they have charged a 10% premium over our price, our
market share is about 70%.
Please provide a recommendation regarding whether we should maintain our current price or
reduce our price to $84.95. Please factor into your recommendation that we pay
programming fees to providers that amount to $32.50 for each subscriber. In addition,
maintenance, service and billing costs are about $7.60 per subscriber. At present, there are
about 110,000 households in the relevant area.
To solve this problem using bimatrix game theory, we need to first create a payoff matrix with the given information. In a bimatrix game, there are two players, and each player has multiple strategies to choose from. Player 1 in this case is our company, and Player 2 is our competitor.
Let's create a payoff matrix:
```
Competitor increases price by 10% Competitor maintains current price
Our Company Maintain current price Reduce price to $84.95
```
Next, we need to determine the payoffs for each combination of strategies. The payoffs are based on the market shares mentioned in the memo.
From the memo, we know that when both companies charge the same price, our market share is 65%. When we charge a 10% premium over their price, our market share declines to 60%. When they charge a 10% premium over our price, our market share increases to 70%.
Based on the market share information, we can assign payoffs to each combination of strategies. Let's say player 1's payoffs are in terms of market share percentages.
```
Competitor increases price by 10% Competitor maintains current price
Our Company 60% 70%
```
Now, let's calculate the expected payoffs. To calculate the expected payoffs, we multiply each market share percentage by the total revenue for that combination of strategies.
The total revenue for each combination of strategies can be calculated as follows:
1. Maintain current price:
Total revenue = (110,000 households) * ($84.95 - $7.60 - $32.50)
2. Reduce price to $84.95:
Total revenue = (110,000 households) * ($84.95 - $7.60)
Now, multiply the market share percentages by the respective total revenues to calculate the expected payoffs for each combination of strategies.
```
Competitor increases price by 10% Competitor maintains current price
Our Company (0.6 * Total revenue) (0.7 * Total revenue)
```
Compare the expected payoffs for each combination of strategies and determine which one has a higher expected payoff. This will be your recommendation.