Game theory is a branch of applied mathematics that analyzes strategic interactions between rational decision-makers. It was developed by John von Neumann and Oskar Morgenstern in the 1940s. Game theory has applications in economics, military strategy, politics, and other domains involving conflict and cooperation between intelligent decision-makers. The document defines key concepts in game theory like Nash equilibrium, zero-sum games, prisoner's dilemma, and mixed strategies. It also discusses assumptions of game theory and provides examples of classic game theory models.

1. GAME THEORY AND ITS
APPLICATION S
Yen 2

2. CONTENT
hat is game theory
pplications
efinitions
ssumptions
ame theory Models with examples
(Zero sum game, Prisoner’s Dilemma etc…)

3. WHAT IS GAME THEORY
John von Neumann
heory Oskar Morgenstern research of
and is associated with the
in early 1940s
t deals with Bargaining/Decision analysis.
concerned with strategic behavior

4. GAME THEORY APPLICATIONS
n Economics decision making
argaining
ilitary strategies
omputer networking, network security

5. GAME THEORY DEFINITION
Theory of rational behavior for interactive decision problems. In a
game, several agents strive to maximize their (expected) utility index
by choosing particular courses of action, and each agent's final utility
payoffs depend on the profile of courses of action chosen by all
agents. The interactive situation, specified by the set of participants,
the possible courses of action of each agent, and the set of all possible
utility payoffs, is called a game; the agents 'playing' a game are called
the players.

6. DEFINITIONS
Eg : Two companies are the only manufactures of a particular
product, they compete each other for market share

7. DEFINITIONS
Definition: Maximin strategy – If we
determine the least possible payoff for each
strategy, and choose the strategy for which this
minimum payoff is largest, we have the
maximin strategy.

8. FURTHER DEFINITIONS
Definition: Constant-sum and non constant-sum game
– If the payoffs to all players add up to the same
constant, regardless which strategies they choose, then
we have a constant-sum game. The constant may be
zero or any other number, so zero-sum games are a
class of constant-sum games. If the payoff does not add
up to a constant, but varies depending on which
strategies are chosen, then we have a non-constant sum
game

9. GAME THEORY :ASSUMPTIONS
(1) Each decision maker has available to him two or
more well-specified choices or sequences of choices.
(2) Every possible combination of plays available to the
players leads to a well-defined end-state (win, loss, or
draw) that terminates the game.
(3) A specified payoff for each player is associated with
each end-state.

10. GAME THEORY :ASSUMPTIONS
(4) Each decision maker has perfect knowledge of the
game and of his opposition.
(5) All decision makers are rational; that is, each player,
given two alternatives, will select the one that yields him
the greater payoff.

11. GAME THEORY MODELS
Two-person, zero-sum games.
Two-person, constant-sum game.
Two-Person Non constant-Sum Games

12. TWO PERSON ZERO-SUM AND CONSTANT-SUM
GAMES
Two-person zero-sum and constant-sum games are played
according to the following basic assumption:
Each player chooses a strategy that enables him/her to do the best
he/she can, given that his/her opponent knows the strategy he/she is
following.
A two-person zero-sum game has a saddle point if and only if
Max (row minimum) = min (column maximum)
all all
rows columns

13. TWO PERSON ZERO-SUM GAME
Company B
Payoff Matrix
to company A
Maximin strategy
Company A
Strategies
 a1,b1- increase advertising Mini max strategy
 a2,b2-provide discounts
 a3,b3-Extend Warranty
Example from text book

14. ZERO-SUM GAME
• Game theory assumes that the decision maker and the opponent
are rational, and that they subscribe to the maximin criterion as
the decision rule for selecting their strategy
• This is often reasonable if when the other player is an opponent
out to maximize his/her own gains, e.g. competitor for the same
customers.
• Consider:
Player 1 with three strategies S1, S2, and S3 and Player 2 with
four strategies OP1, OP2, OP3, and OP4

15. ZERO-SUM GAME
Player 2
OP1 OP2 OP3 OP4 Row
Minima
S1 12 3 9 8 3
Player 1 S2 5 4 6 5 4 maximin
S3 3 0 6 7 0
Column 12 4 9 8
maxima minimax
• Using the maximin criterion, player 1 records the row minima and
selects the maximum of these (S2)
• Player 1’s gain is player 2’s loss. Player 2 records the column
maxima and select the minimum of these (OP2)
example

16. ZERO-SUM GAME
Player 2
OP1 OP2 OP3 OP4 Row
Minima
S1 12 3 9 8 3
Player 1 S2 5 4 6 5 4 maximin
S3 3 0 6 7 0
Column 12 4 9 8
maxima minimax
• The value 4 achieved by both players is called the value of the game
• The intersection of S2 and OP2 is called a saddle point. A game
with a saddle point is also called a game with an equilibrium
solution.
• At the saddle point, neither player can improve their payoff by
switching strategies
example

17. TWO PERSON NON CONSTANT SUM GAME
• Most game-theoretic models of business situations
are not constant-sum games, because it is unusual for
business competitors to be in total conflict
• As in two-person zero-sum game, a choice of
strategy by each player is an equilibrium point if
neither player can benefit from a unilateral change in
strategy

18. PRISONER’S DILEMMA
wo suspects arrested for a crime
risoners decide whether to confess or not to confess
f both confess, both sentenced to 3 months of jail
f both do not confess, then both will be sentenced to 1 month of jail
f one confesses and the other does not, then the confessor gets freed

19. ormal Form representation – Payoff Matrix
Prisoner 2
Confess Not Confess
Prisoner 1 Confess -3,-3 0,-9
Not Confess -9,0 -1,-1

20. ach player’s predicted strategy is the best response to the
predicted strategies of other players
o incentive to deviate unilaterally Prisoner 2
Confess Not Confess
Prisoner 1 player can benefit from a unilateral change in strategy
either Confess -3,-3 0,-9
Not Confess -9,0 -1,-1
trategically stable or self-enforcing

21. NASH EQUILIBRIUM
Prisoner 2
Confess Not Confess
Prisoner 1 Confess -3,-3 0,-9
Not Confess -9,0 -1,-1

22. MIXED STRATEGIES
probability distribution over the pure strategies of the game
ock-paper-scissors game
– Each player simultaneously forms his or her hand into the shape of either a
rock, a piece of paper, or a pair of scissors
– Rule: rock beats (breaks) scissors, scissors beats (cuts) paper, and paper beats
(covers) rock
o pure strategy Nash equilibrium
ne mixed strategy Nash equilibrium – each player plays rock, paper and

23. FURTHER STUDIES
Will Game Theory give us the optimum or best solution/
decision?
When there is n number of players and n number of
strategies need to go for Leaner programming.

24. Multi agent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
by Yoav Shoham, Kevin Leyton-Brown
Publisher: Cambridge University Press 2008
ISBN/ASIN: 0521899435
ISBN-13: 9780521899437
Number of pages: 532
Description:
Multiagent systems consist of multiple autonomous
entities having different information and/or diverging
interests. This comprehensive introduction to the field
offers a computer science perspective, but also draws
on ideas from game theory, economics, operations
research, logic, philosophy and linguistics. It will serve
as a reference for researchers in each of these fields,
and be used as a text for advanced undergraduate and
graduate courses.

25. Game Theory for Applied Economists
Robert Gibbons
This book introduces one of the most powerful
tools of modern economics to a wide audience:

26. Strategy: An Introduction to Game Theory,
2nd Edition
Joel Watson
Book Description
October 16, 2007 | ISBN-10: 0393929345
Publication Date:
| ISBN-13: 978-0393929348 | Edition: 2
Strategy, Second Edition, is a thorough revision
and update of one of the most successful Game
Theory texts available.
Known for its accurate and simple-yet-thorough
presentation, Joel Watson has refined his text to
make it even more student friendly. Highlights of
the revision include the addition of Guided (or
Solved) Exercises and a significant expansion of
the material for political economists and political
scientists.