Game theory in Operation Research ~ Pure Strategy

 

Pure Strategy : Game Theory

The simplest type of game is one where the best strategies for both players are pure strategies. This is the case if and only if, the pay-off matrix contains a saddle point.

Example: Pure Strategy in Game Theory

	Player B
Player A		I	II	III	IV	V
	I	-3	1	1	6	4
	II	5	3	2	4	3
	III	-5	-4	1	-3	7
	IV	6	4	-5	3	-7

What is the optimal plan for both the players?

Solution.

We use the maximin (minimax) principle to analyze the game.

	Player B
Player A		I	II	III	IV	V	Minimum
	I	-3	1	1	6	4	-3
	II	5	3	2	4	3	2
	III	-5	-4	1	-3	7	-5
	IV	6	4	-5	3	-7	-7
Maximum		6	4	2	6	7

Select minimum from the maximum of columns.
Minimax = 2, Player A will choose II strategy, which yields the maximum payoff of 2.

Select maximum from the minimum of rows.
Maximin = 2, similarly, player B will choose III strategy.

Since the value of maximin coincides with the value of the minimax, therefore, saddle point (equilibrium point) = 2.

The optimal strategies for both players are:

Player A must select II strategy and player B must select III strategy.

The value of game is 2, which indicates that player A will gain 2 unit and player B will sacrifice 2 unit.

Example Sum Video --> #Game​ Theory - Part 2 #Purestrategy​ #Mixedstrategy - YouTube