When there is neither saddle point nor dominance in a problem of game theory and the payoff matrix is of order 3x3 or higher, the probability and graphical methods cannot be employed. In such a case, linear programming approach may be followed to solve the game.
Linear programming technique
A general approach to solve a game by linear
programming technique is presented below. Consider the following game:
We can
use simplex method to solve the above problem. For this purpose, we have to introduce non-negative slack variables s_{1} , s_{2} ,..., s_{m} to each of the inequalities. So the problem can be restated as follows:
Restatement of the problem:
In a similar manner we can
determine the optimal strategy for player A. Application We illustrate the method for a
2X2 zero sum game.
Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
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