Math 326, April 23 - Game Day
We take a brief foray into Game Theory. In a competition, if you know the potential winnings or losses of every possible decision, it can be possible to use math to determine your optimal strategy. Consider the following game. Anna chooses from A, B, C and Bill chooses from I and II. Money is exchanged according to the following table.
Anna
ABC
BillI52-1
II-212

This table lists the amount Anna pays to Bill if they choose the corresponding numbers. If the payout is negative, then Bill pays to Anna.
Suppose the players wish to play to minimize the worst case scenario. If Bill chooses I, the worst that can happen is that he loses $1. If he chooses II, the worst that can happen is he loses $2. So at first glance, he should choose I.
But if Bill always chooses I, Anna will realize this and always choose C, thereby always winning money from Bill. So Bill would benefit from choosing II some of the time, just to keep Anna from always choosing C. The best strategy is a balance, randomly choosing different numbers with a probability selected to optimize the outcome.
Solver Add-in
We will be using the Solver Add-in. Right-click in the dark blue area between the tab names and the Help icon to bring up the Customize Tool Bar window (or click on the Windows icon top-left, choose Excel Options, then click Customize).
In the drop-down menu, choose "All Commands". Scroll down until you see "Add-ins..." and add it to your toolbar. Click Okay.
Click the new Add-ins icon on your toolbar and add the Solver Add-in. A Solver tool now appears under the Data tab.
Additional Questions