Hi,
Can some tell me a step-by-step method to finding the optimal strategies and value of any given payoff matrix.
Thanks.
I do know that the expected value is found by this equation:
e = SPT
Which says that the expected value equals the payoff matrix P times the mixed strategies S and T, where S is a row matrix, representing the row player and T is a column matrix, representing the column player.
The expected value of the game is the average payoff per round if each player uses the associated mixed strategies for a large number of rounds.
Someone else is going to have to help you out with the Optimal Strategies, I do know that a fair game has a value of 0, the rest are unfair or biased.
You can use the Simplex Algorithm (or a few other procedures depending on the game) to find the optimal strategy and the value of the payoff matrix.
Do you have a specific problem in mind?