1. ProgressiveEducationSociety’sModernCollegeOf Engineering
DepartmentOfComputerEngineering
By
Soumyashree Bilwar
Department Of Computer
Engineering

2. Overview
 What is Game Theory ( layman’s language)
 Game Theory (Formal Definition)
 Major Assumptions
 Types Of Games
 Representation Of Games
 Nash Equilibrium
 Popular Games
 Prisoner’s Dilemma
 Chicken Game
 General and applied uses
 Conclusion
 References

3. Game Theory?????
Lets us first understand what is a Game??
Game, in the mathematical sense, is defined as
strategic situation in which there are multiple
participants.
Is Sudoku a "game" ?
No.
Is Chess a "game" ?
Yes.

4. What is Game Theory?
(layman’s language)
Game Theory is one way of studying how
an individual or a group makes
a strategic choice.
Practical applications in everyday life:
 Friends choosing where to go for dinner
 Gamblers betting in a card game
 Diplomats negotiating a treaty
 Commuters deciding how to go to work

5. What is Game Theory?
(Formal Definition )
Game Theory is a set of tools and
techniques for decisions under
uncertainty involving two or more
intelligent opponents in which each
opponent aspires to optimize his own
decision at the expense of the other
opponents.

6. Major Assumptions
 Players – the number of participants may be
two or more. A player can be a single
individual or a group with the same objective.
 Timing – the conflicting parties decide
simultaneously.
 Conflicting Goals – each party is interested
in maximizing his or her goal at the expense
of the other.

7. Major Assumptions(cont)
 Repetition – most instances involve
repetitive solution.
 Payoff – the payoffs for each
combination of
decisions are known by all parties.
 Information Availability – all parties are
aware of all pertinent information. Each
player knows all possible courses of action
open to the opponent as well as anticipated
payoffs

8. Types of Games:
Cooperative or non-cooperative
Symmetric and asymmetric
Zero-sum and non-zero-sum
Simultaneous and sequential
Perfect information and imperfect
information
Combinatorial games
Infinitely long games
Discrete and continuous games
Many-player and population games
Metagames

9. Representation of games
Type 1:Extensive form-> Tree
Point of choice for a
player. The player is
specified by a
number listed by
the vertex.
Possible action
for that player.
Payoffs

10. Representation of games
Type 2: Normal form-> Matrix
4,3 -1,-1
0,0 3,4
Player 1
chooses Up
Player 1
chooses Down
Player 2
chooses Left
Player 2
chooses Right
Normal form or payoff matrix of a
2-player, 2-strategy game
Payoffs
Player1 chooses
Rows
Player2 chooses
Columns

11. Nash Equilibrium
John Nash John Nash was a mathematician
and an economist.
 He developed several theories
in economics .
 He was a Princeton and CMU
graduate.
 His most important contribution
was the theory of Nash
equilibrium
 He is the person portrayed in
the movie “A beautiful mind”.

12. What is Nash Equilibrium ?
For any two groups that do not co-operate
there will be a point at which neither
group can benefit from unilateral action ,
and that the groups will hold their
strategies constant at this point.
The Nash equilibrium is not usually the
most effective strategy; it is only the best
one without co-operation.
Through co-operation it is only that both
parties will be able to increase their utility.

13. Some of the popular Games of
Game Theory
Prisoner's dilemma
Battle of the sexes
Deadlock
Rock, Paper, Scissors
Trust game
Cake cutting
Chicken (aka hawk-dove)
Traveller's dilemma

14. Prisoner’s Dilemma
Prisoner B stays silent
Prisoner B confesses
Prisoner A stays silent Each serves 1 month
Prisoner A: 1 year
Prisoner B: goes free
Prisoner A confesses
Prisoner A: goes free
Prisoner B: 1 year
Each serves 3 months
http://pespmc1.vub.ac.be/PRISDIL.html
Cooperation is usually analysed in game theory by
means of a non-zero-sum game called the
"Prisoner's Dilemma“. The prisoner's dilemma is
meant to study short term decision-making .

15. Analysisof Prisoner’sDilemma
Each player gains when both stay silent.
(one month)
 One player stays silent and other confesses then one
who confesses will gain more.
(confess- freed, silent-1 year)
 If both confess , both lose (or gain very little) but not
as much as the "cheated" silent prisoner whose
cooperation is not returned.
(3 months)
Prisoner’s Dilemma has single Nash equilibrium.
Friend or Foe? is a game show that aired from 2002 to
2005 on the Game Show Network in the United States.
It is an example of the prisoner's dilemma game tested
by real people

16. Chicken Game
Driver B
Swerve
Driver B
Straight
Driver A
Swerve
Tie , Tie Lose, Win
Driver A
Straight
Win , Lose Crash
http://pespmc1.vub.ac.be/PRISDIL.html
Chicken is a famous game where two people drive
on a collision course straight towards each other.
Whoever swerves is considered a 'chicken' and
loses, but if nobody swerves, they will both crash.

17. Analysis of Chicken Game
Both lose when both swerve.
 One player wins when one swerves and
other goes straight.
 If both go straight, both lose(lose more
than what they would have lost when
both swerve.
Because if both go straight they CRASH)
 Chicken Game has 2 Nash Equilibrium.

18. General and applied uses
 Economics and business
E.g. modelling competing behaviours of interacting agents ,
auctions, bargaining, social network formation.
 Political Science
E.g. public choice, social choice, players are voters,
politicians , states.
 Biology
E.g. evolution , mobbing, animal communication
 Computer Science and logic
E.g. game semantics, online algorithms , equilibrium in
games and peer to peer systems, time complexity
 Philosophy
E.g. co ordination games , convention , common knowledge

19. Conclusion
Game theory is exciting because although the
principles are simple, the applications are far-
reaching.
Game theory is the study of cooperative and
non cooperative approaches to games and
social situations in which participants must
choose between individual benefits and
collective benefits.
Game theory can be used to design credible
commitments, threats, or promises, or to
assess propositions and statements offered
by others.

20. References
 Research papers and books
 Game Theory at Work by James D. Miller
 Thinking Strategically: Competitive Edge in
Business, Politics and Everyday Life by Avinash Dixit
 Existence of Equilibrium in Discrete Market Games
by Somdeb Lahiri
 URL
 http://en.wikipedia.org/wiki/Game_theory
 http://faculty.lebow.drexel.edu/mccainr/top/eco/gam
e/game-toc.html
 http://www2.owen.vanderbilt.edu/mike.shor/courses
/game-theory/quiz/problems2.html
 http://en.wikipedia.org/wiki/Nash_equilibrium

21. Feedback and Question????