## Math 160: Study Guide - Chapter 8

1. Solve a game. Show all work.
2. Solve a game. Show all work.
3. Solve a game. Show all work.
4. Find the expected value of a game if both player's strategy is random. Find the expected value of the game if one player chooses randomly, but the other player plays their optimal strategy (use the calculator to find the optimal strategy). Show the multiplications that must be performed.
5. Setup and solve a game using the calculator.
6. Solve a game using the calculator. The column player lets the row player know what her strategy will be, find the best a priori strategy for the row player (this is the best strategy for the row player if he knows what the column player will do) and the value of the game under this strategy. Find the value of the game if the row player uses his a priori strategy, but the column player uses her optimal strategy instead of the one she said she was going to use. Find the best a priori strategy for the column player (what should she play if she knows what the row player will do because he thinks he knows what she is going to do).
7. Write the linear programming problems necessary to solve a game. Then, find the solution using the geometric approach to linear programming.
8. Find the solution to a game using the calculator. Find the value if both players play randomly (all choices are not equally likely - you need to have a concept of what a relative frequency is). Find the payoffs for the row player under the expected value criterion, maximax criterion, and maximin criterion.

### Notes

• The solution to a game consists of the optimal row strategy P*, the optimal column strategy Q*, and the value of the game v.
• When solving a game, first check for strictly determined games. Then check for recessive rows or columns.
• Games may be solved with the calculator for problems 4, 5, 6, and 8.
• Work must be shown on problems 1, 2, 3 and 7. You may check your work with the calculator.
• Problems 7 and 8 may be worked in groups of up to three people.
• Move swiftly through the first portion of the test - the group problems will be lengthy.