1. Solutions Sample Games 1
Find the saddle point for the game having the following payoff table.
Use the minimax criteria to find the best strategy for each player. Does this game have a saddle point? Is it a stable game?
Soln: Shown below.
The maximum of the minimums is strategy 3 for player 1 and the maximum of the minimums is strategy 2 for player 2. Payoff for the game is -1 which is the same element for each player. This is the saddle point for the game. Game is stable.
If we were to do an LP formulation for this game x*=(0,0,1) and y*=(0,1,0,0).

2. Solutions Sample Games 2
Consider the game having the following payoff table.
We note the minimum of the maximums and the maximum of the minimums do not translate to the same elements; game is not stable. Consequently, we must formulate and solve through some other means.
For Player 1, For Player 2

3. Solutions Sample Games 3
Consider the game having the following payoff table.
For Player 1,

4. Solutions Sample Games 4
Consider the game having the following payoff table.
For Player 2

5. Solutions Sample Games 5
Consider the game having the following payoff table:
Use the graphical procedure to determine the value of the game and the optimal mixed strategy for each player.

6. Solutions Sample Games 6
At minimax point then,

7. Solutions Sample Games 7
At minimax point then,
Solving for y*, at x1=0,