# payoff

• Feb 22nd 2007, 01:28 AM
jedoob
payoff
Hi,

Can some tell me a step-by-step method to finding the optimal strategies and value of any given payoff matrix.

Thanks.
• Feb 22nd 2007, 08:14 AM
Aryth
Quote:

Originally Posted by jedoob
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.
• Mar 22nd 2007, 10:58 AM
frenzy
Quote:

Originally Posted by jedoob
Hi,

Can some tell me a step-by-step method to finding the optimal strategies and value of any given payoff matrix.

Thanks.

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?