Question

Describe the advantage in using a payoff matrix to analyse decisions. Explain the steps required in developing such a matrix.

Answer 1

Dear Student,

Pay off matrice is important tool in risk analysis

and decision making that are used to identify risk in both everyday and multibillion-dollar business decisions. The payoff matrix method breaks the decision process down into decision alternatives and states of nature.

Advantage -

Advantages of Keeping Thought

Belief

How does holding your thought or belief
make your life seem more manageable, safer,
or easier to handle? Does the thought or
belief provide you with a sense of control,
security, or predictability of the future.

Advantages of Changing Thought or Belief
How could changing your thought or belief
improve your life? Consider whether
changing your thought or belief would
reduce distressing feelings and free you of
concerns about past events

Steps
Step 1: Define the Players

In every game / multi-person interaction, you will have multiple players.
The first step to constructing game theory analysis is to write down the names of the players involved. For simplicity, it’s best to keep the number of players down to two. Adding more players than two becomes extremely complicated so if your game has more than two players, try to group the players into two broad groups with similar goals.

In continuing the example above, all we have is Motorola and for the sake of argument let’s call the competitor Samsung.

Here’s our list of players:

Motorola
Samsung

Step 2: List the Most Relevant Choices Available to Each Player

This part is pretty simple as well. All we do is take each player and list the choices available to each player. To do this I’ll simply copy the choices mentioned earlier.

Motorola
Prioritize User Needs First
Prioritize Carrier Needs first
Samsung
Prioritize User Needs First
Prioritize Carrier Needs First
Note that I created the choices to be symmetrical meaning that the same choices are available for each player. This doesn’t always need to be the case *and in many cases won’t be* but for this simple example keeping the choices the same between the two players works out quite well.

tep 3: Create The Scenarios Matrix

Most people explain game theory - college professors, etc.
skip this step and jump straight to figuring out the payoff matrix. I’ve found that to be a mistake because often the most challenging part of game theory is simply creating an accurate payoff matrix. By creating a scenarios matrix first, we make it easy to create a payoff matrix.

So what is a scenarios matrix?

A scenarios matrix shows the players and list of choices available to the players in a table or matrix format. The cells inside the matrix represent the specific scenarios that can play out.

tep 4: List How Much Each Player Values Each Choice

This is the step that is usually the most challenging to figure out with a reasonable level of accuracy. But there are a few ways to do it that are relatively easy and straightforward. In our example, since we are playing the part of Motorola we should be able to do market research and make reasonable relative estimates of the payoffs we might enjoy under each scenario.

In this case, lets imagine there are 10 consumers who are looking for a smartphone and we decide to survey them to determine their likelihood of buying a Motorola phone under each scenario. To do this, all we need to do is create questions that relate to each scenario. For example the survey could say:

Question 1: What are your preferences regarding Verizon specific applications? (this question is not a specific scenario but is used to validate/invalidate the basic premise of the analysis, that users think carrier-specific apps are useless and annoying)
I like them – 0
I don’t like them – 8
I am indifferent to them – 2
Question 2: Suppose you were to were to walk into a Verizon store and see two essentially identical phones, Phone M and Phone S, from different manufacturers that both meet your needs and neither phone has Verizon specific applications included, which phone would you choose? (in practice this question is unnecessary because we know it should follow a random distribution and split 50/50 but I include it here for sake of being comprehensive with this example)
Phone M – 5
Phone S – 5
Question 3: Suppose Phone M and Phone S are still essentially identical except for one difference, one phone includes Verizon-specific applications while the other does not, which phone would you buy?
The one without Verizon apps – 8
The one with Verizon apps – 2 (note: I recognize that these two could go either way but let’s put them with Phone S and assume that the Verizon salesman swayed them)
Question 4: Suppose Phone M and Phone S were essentially identical and both included Verizon-specific applications, which phone would you buy?
Phone M – 3
Phone S – 3
I would not buy either – 4
Now all we need to do is list these values in a payoff matrix such as the one below. To make it easy to keep track of the payoffs for each I’ve color coded the payoff values to correspond with either Motorola or Samsung.

tep 5: Look For Dominant Strategies
Nash Equilibrium

This is game theory gets really interesting. The first step in this analysis is to determine if any of the choices / strategies for either player are dominant over the other choices.

Hope this will help you.

Thanks