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