I'm reposting this as I did not receive a response.
Posted by Dwane on Wednesday, November 22, 2006 at 1:23pm.
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.
Tough problem. Its been years since I have had to "solve" game-theory problems.
I can tell you where to start. First do some research on game theory, especially on "Nash Equilibrium" and "Prisoner Dilemma". Google is the place to start.
Next, fill in a 2x2 matrix. Lable the rows "Us", lable the columns "Them". Lable row 1 "Stay", and row 2 "down 10%". Lable column 1 "Stay", column 2 "up 10%" -- You get the idea. Then calculate the expected profit under the four scenarios.
Next is the hard part -- calculating the position of the competitors. I suggest you calculate their profits under the 4 scenarios but under two possible states; a) they have the same cost structures, or b) their costs are 10% higher. Then look for the Nash Equilibrium conditions under the two states.
Lotsa luck.
To solve this problem, you need to use bimatrix game theory and analyze the data provided. Here are the steps you can follow to find the answer:
1. Start by doing some research on game theory concepts, such as Nash Equilibrium and Prisoner's Dilemma. You can use search engines like Google to find relevant information and resources.
2. Create a 2x2 matrix to represent the game. Label the rows as "Us" and the columns as "Them." In this case, you can label row 1 as "Stay" and row 2 as "down 10%". Similarly, label column 1 as "Stay" and column 2 as "up 10%".
3. Calculate the expected profits under the four scenarios in the matrix. To do this, you'll need to consider the market share percentages provided in the memo. For example, when both companies charge the same price, the market share is 65%. Use this information to calculate the expected profits for each scenario.
4. Calculate the competitors' profits under the four scenarios based on two possible cost structures: a) the same cost structure as yours, and b) a cost structure 10% higher than yours. This step requires assumptions since you don't have the exact cost structure of the competitor. Make reasonable estimates based on the given information.
5. Look for the Nash Equilibrium conditions under the two possible cost structures for the competitor. Nash Equilibrium is a concept in game theory where no player can improve their outcome by unilaterally changing their strategy. Find the combination of strategies that satisfies this condition for both cost structures.
6. Once you have analyzed the profits, market shares, and Nash Equilibrium conditions, you can make a recommendation regarding whether to maintain the current price or reduce it to $84.95. Consider the programming fees, maintenance, service, and billing costs, as well as the number of households in the relevant area.
Please note that solving game theory problems can be complex and require intricate analysis. It is important to understand the underlying concepts and assumptions, as well as any limitations in the data provided.