This document discusses a game theory example called the "grade game" to illustrate concepts like strategy, payoffs, and optimal choices. It presents a scenario where two students each privately choose to bid either A or B, and their grades depend on whether they match or differ from their paired partner's bid. The payoff matrix is shown, with outcomes like both getting a 7 if they match, or one getting a 10 and the other a 3 if they differ. It asks what students would choose, and discusses thinking about maximizing one's own outcome regardless of the partner, or trying to collude for higher joint grades. Overall it uses this game to introduce game theory ideas.

1. Bijubodheswar
Assistant Professor 1

2. Introduction
We studied models with internal interest
LPP, Transportation, Assignment etc
In practical life, it is required to take decisions
• in a competing situation
• there are two or more opposite parties with
conflicting interest and
• the outcome is controlled by the directions
of all parties concerned
3

3. Let’s play the “grade game”
 If you put A and your pair puts B, then you will get grade 10, and your
pair grade 3;
If both you and your pair put A, then you both will get the grade 7
If you put B and your pair puts A, then you will get the grade 3
and your pair grade 10;
If both you and your pair put B, then you will both get grade 9
4
Write down on a paper either the letter A or the letter B.
Think of this as a "grade bid". I will randomly pair your paper with
one other's paper. Neither you nor your pair will ever know with
whom you were paired. Here is how grades may be assigned for this
class:Rules

4. Outcome matrix
• Just reading the text is hard to absorb, let’s
representing the game:use a concise way
my pair
of
A B
A
me
B
grades 6
7,7 10,3
3,10 9,9

5. The grade game: discussion
What did you choose? Why?
Two possible way of thinking:
– Regardless of my partner choice, there would be better
outcomes for me by choosing A rather than B;
– We could all be collusive and work together, hence by
choosing B we would get higher grades.
•
•
8

7. There may be win win
situations or Win Lose
situations or even Lose
Lose

8. What is a Game....?
1. How many persons are involved...?
2. Is any rule is needed ...?
3. What is the outcome...?

9. What is a Game....?
Game is an activity between two or more
persons according to a set of rules at the
end of which each person receives some
benefits or satisfaction or suffers loss

10. What is a Game theory....?
Is a theory of conflict. It is a mathematical
theory which deals with competitive
situations

11. A Competitive situation is called game
8
•The number of competitors called players
•The players act rationally and intelligently
•Each player has available to him a finite number of choices or
possible course of action called strategies.
•The players select their respective course of action (strategies)
simultaneously
•The players make individual decisions without direct communication
•The payoff is fixed and determined in advance

12. Terms
8
Strategy :- is a course of action taken by one
of the participants in a game
Pay off matrix – is the result or outcome of the
strategy is the pay off
Two person zero sum game: a game of two persons, in
which the gain of one player are the losses of the other
player

13. Decision Making Situations
8
Decision
Making
Under
certainty
Under risk
Under
Uncertainty
Pure
strategy
Mixed
strategy
2x2
(Arithmetical
method)
2xm or nx2
(Graphical
Method)
Mxn (LPP)

14. Pure strategy: is a decision where the
players always choose a particular course
of action
Mixed Strategy : play different strategies
each at a certain time. The player decides
in advance to use all or some of his
available course of action in some fixed
proportion

15. Value of the game: Maximum generated
gain to player. (fair game = value of the game is zero)
1. What is the expectation of a successful
player?
2. What is the expectation of an
unsuccessful player?
Maximin: Maximum of minimum pay off or
outcome
MiniMax: Minimum of the Maximum pay
off

16. Company StrategiesUnionStrategies
I II III IV V
I 2 0 0 50 30
II 40 20 10 20 50
III -40 -30 0 -30 60
IV 50 10 -50 -20 -60
Row
minimu
m
2
10
-40
-60
Column Maximum 50 20 10 50 60
10
10
Saddle Point
Minimum in the row and
maximum in the column
A Company Management and Labour Union are negotiating a new 3 year settlement.
Strategy I. Hard and Aggressive Bargaining II. Reasoning & Logical Approach
III. Legalistic strategy IV. Conciliatory approach

17. Value of Game = 10
Union’s strategy = II – Reasoning and logical approach
Company’s strategy = 3 – Legalistic strategy
Will continue.......