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Game Theory 2

Computer solutions

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QM for WindowsTo do the first example from the other set of notes, open the program -> go to Module on menu and scroll to game theory -> go to file new -> say there are 2 row strategies and 2 column strategies and hit ok -> you will see the input screen is much like an Excel spreadsheet and you can resize things or type over the generic labels they have -> input the data ->hit the solve button toward the upper right.

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When you hit the solve button you are taken to the output sections. We want the “Game Theory Results” section. I have this section reproduced on the next screen. You may want to print that slide as a slide in PowerPoint to see it better.

In the output you can see the input data is reproduced with additions. An additional column is really telling you about the row player. Since you and I already know the row player had a pure strategy, the 1 in the last column , first row means the row player should play that strategy – The 1 literally means play that strategy 100% of the time.

An additional row is really telling you about the column player. Since you and I already know the column player had a pure strategy, the 1 in the last row, first column means the column player should play that strategy.

The value of the game = 1 means the row player gains 1 and the column player loses 1. When both players have a dominant strategy the value of the game will be the cell value of those strategies.

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These 1’s mean each player has a dominant strategy

Since both have a dominant strategy this cell value of 1 is the value of the game.

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Note on QM for Windows

If you go to tools on the main menu in QM for Windows and scroll down to “ANNOTATE” you will see a text window opens on the bottom of the screen.

You can use this screen to type in your interpretation of the output. In other words, you explain how you understand a solution to a situation or problem.

We will use the computer to solve problems for us, but you must indicate where answers are on the output and what they mean.

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On the next screen you see the output for the second problem in the notes done in QM for windows.

You may want to print this slide in slide mode in Powerpoint.

Notice the computer tells you what % of time each player will play each option and what the value of the game turns out to be.

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=10/12

2/12

8/12

4/12

The value of the game for the row player is 3.33 and minus 3.33 for the column player.