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Payoff Matrix in Economics: Theory & Examples

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  • 0:01 What Is a Payoff Matrix?
  • 1:28 What a Payoff Matrix…
  • 2:40 Analysis of Outcomes
  • 4:18 Lesson Summary
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Lesson Transcript
Instructor: Adam Gifford

Adam holds an MBA and a MS in Human Resources

In this lesson, you'll define what a payoff matrix is, learn how a payoff matrix is built, and understand how to read each part of the payoff matrix. You'll also determine how to apply your knowledge of the payoff matrix to predict the actions of others.

What is a Payoff Matrix?

One of the most popular games for children (and indecisive adults) is Rock, Paper, Scissors. The rules are simple: count to 3 and show your opponent whether you chose rock, paper, or scissors. Rock is represented by a closed fist; paper is represented by an open hand; and scissors is represented by extending your pointer finger and middle finger. Rock beats scissors; scissors beats paper; and paper beats rock. Rock, Paper, Scissors is one of the most basic games of strategy in existence. It's considered a game of strategy because each player chooses their strategy (rock, paper, or scissors) based on what they think their opponent will choose.

Although the rules for Rock, Paper, Scissors are relatively easy to remember, you can summarize them even better by using a payoff matrix. A payoff matrix_ is defined as a visual representation of all the possible outcomes that can occur when two people or groups have to make a strategic decision. The decision is referred to as a strategic decision because each decision maker has to take into consideration how their choice will affect their opponent's choice and how their opponent's choice will affect their own choice. The payoff matrix illustrates each possible strategy that one side can choose, as well as every combination of outcomes that are possible based on each opponent's choice.

What a Payoff Matrix Looks Like

Now before you run off to play Rock, Paper, Scissors with the closest person that you can find (for educational purposes!), you still need to see what the payoff matrix looks like. Here is an example of the Rock, Paper, Scissors payoff matrix:

Rock, Paper, Scissors

The payoff matrix has three basic parts:

Opponents: In this case, they are Player 1 and Player 2.

Strategies: They are Rock, Paper, and Scissors. The strategies for Player 1 are along the vertical side of the matrix, and the strategies for Player 2 are along the horizontal side of the matrix.

Outcomes: The possible outcomes for this game are: win, lose, tie. A 'win' is represented by a 1, a 'lose' is represented by a -1, and a 'tie' is represented by a 0.

In order to determine the outcome of a game, you will choose the row of the strategy chosen by Player 1 and the column of the strategy chosen by Player 2. The corresponding box has 2 numbers; the first number (in red) is the outcome for Player 1, and the second number (in blue) is the outcome for Player 2. So if Player 1 chooses Rock and Player 2 chooses paper, the outcome will be -1,1 because Player 2 will win.

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