game theory is a very easy chapter, and best when solved in reality

1. BY :-

2. History of Game Theory
Game theory was developed
by John Neumann in the 20th
century who is also known as
father of Game Theory.

3. Note on John Neumann
BORN :- Neumann János Lajos December 28, 1903
DIED :- February 8, 1957 (aged 53) Walter Reed General Hospital
Washington, D.C

4. Early life:
He was the eldest of three brothers. His father,
Neumann Miksa was a banker, who held a doctorate in
law. He had moved to Budapest from Pécs at the end of
the 1880s.
Miksa's father (Mihály b. 1839) and grandfather
(Márton) were both born in Ond (now part of the town of
Szerencs), Zemplén county, northern Hungary. John's
mother was Kann Margit (Margaret Kann)

5. He received his Ph.D. in mathematics (with
minors in experimental physics and chemistry) from
Pázmány Péter University in Budapest at the age of
22.
He simultaneously earned a diploma in chemical
engineering from the ETH Zurich in Switzerland at
his father's request, who wanted his son to follow
him into industry.
In 1930, von Neumann was invited to Princeton
University, New Jersey. In 1933, he was offered a
position on the faculty of the Institute for Advanced
Study when the institute's plan to appoint Hermann
Weyl fell through; von Neumann remained a
mathematics professor there until his death. In
1937, von Neumann became a naturalized citizen of
the U.S. In 1938, he was awarded the Bôcher

6. Properties of Game Theory
1. There are finite numbers of
competitors(players).
2. Each player has finite number of course
of action.
3. A Game said to be played when each
player chooses one of his courses of
action.
4. Every combination has an outcome
called payoff, which may be positive,
negative or zero.

7. Methods of solving a Rectangular
Game
 The maximin-minimax principle:
 Step 1: Identify the minimum gain
corresponding to each strategy of A. write the
row minimum on right of each row. Find out
the maximum of these, which is know as
maximin.

8.  Step 2: Identify the maximum loss
corresponding to each strategy of B write the
column maximum at bottom of each column.
Find out the minimum among these, which is
known as minimax.
 If the miximin and minimax are equal, the
Game is said to have a saddle point. Let the
position of saddle point in the pay-off matrix
be(r,s). Then the position is known is : A- A r,
B- B s.

9.  The dominance principle:
 The principle of dominance states that, if
strategy of a player dominates(is superior)
over another strategy then the latter strategy
can be eliminated as the choice of such a
strategy will not benefit the player in anyway (
affect the choice of the solution).
 In such cases of dominance, the size of the
pay- off matrix is reduced by eliminating those
strategies which are dominance by others.

10. General rules for dominance:
1. Lesser row delete.
2. greater column delete.