Question

Homework 2. Show that in a payoff matrix, if exists, saddle point is unique

İt is a Game theory question two person zero sum game

Answer 1

Defination of two person zero sum game- Only two persons are involved in the game and the gain made by one player is equal to the loss of the other.

A game with unique saddle point.

players A	players B	Row
	B1 B2 B3 B4	minimum
A1	-5 2 1 10	-5
A2	6 5 4 7	4
A3	4 -2 0 -5	-5
Column maximum	6 5 4 10	4

here value of this game is 4 because the minimum and maximum value is same.

if the maximin value and minimax value are the same at the same location than that point as kmown  as a saddle point.since the maximin value is 4 and minimax value is 4 and in the payoff matrix the 4 is situated at only one place, this is called the game with unique saddle point.

So in this matrix the saddle point is 4.