Game theory is the analysis of strategic decision making between intelligent rational players. It uses models and solution concepts to analyze interactions in fields like economics, politics, and biology. Important concepts in game theory include Nash equilibrium, where each player's strategy is optimal given the other players' strategies, and mixed strategies, which involve randomizing between pure strategies. Game theory has applications in many domains and seeks to predict outcomes of interactions between decision makers.

1. GAME THEORY

2. Outline
 What is game theory?
 History of game theory.
 Application of game theory.
 Key elements of game theory.
 Types of game.
 Nash Equilibrium(NB)
 Pure strategies and mixed strategies.
 2 players Zero- sum game.

3. Game theory
Game theoryi s the analysis of conflict and cooperation
among intelligent rational decision makers.
A decision maker is said to be rational if he makes
decisions consistently in a pursuit of his own objectives.
In a game, two or more individuals make decisions that
inuence each others expected utility.
The decision makers are called the players.
The decision objects of players are generally called
strategies.

4. Game theory uses two basic tools
Models offers two games.
There is a variety of models that represent dierent
scenarios that might show up in real-life situations-
Solution concepts.
Solution concepts are predictions about what rational intelligen
players should play.

5. History of game theory
 Von Neumann wrote a key paper in 1928
 1944:”Theory of games and Economic Behaviour
"by von Neumann and Morgenstern
 1950:Nash invent concepts of Nash equilibrium
 Game theory booms after this….
 1944:Harsani,Nash and Selten win Nobel prize in
economics for game theory work

6. Application of Game Theory
 Mathematics  Psychology
 Computer science  Law
 Biology  Military Strategy
 Economics  Sports
 Political science  Game Playing
 International Relation
 Philosophy

7. Key elements of a Game
 Players: Who is interacting?
 Strategies: What are their options?
 Payoffs: What are their incentives?
 Information: What do they work?
 Rationality: How do they think?

8. Types of games
 Cooperative or non-cooperztive
 Zero sum and non –zero sum
 Simultaneous and sequential
 Perfect information and imperfect information
 Finite and Infinite Strategies

9. Pure Strategies
 The upper value of the game is equel to the
minimum of the maximum values in the columns
 The lower value of the game is equalto the
maximum of the minimum values in the rows.

10. An Example
A
B Y1 Y2 Minimum
X1 10 6 6
X2 -12 7 -12
Maximum 10 6 6
7

11. Mixed Strategies
 A mixed strategy game exists when there is no
saddle point. Each player will then optimize their
expected gain by determining the percent of time
to use each strategy

12. Nash Eqilibrium(NE)
 A player’s best strategy is that strategy that
maximizes that player’s payoff(utility)’knowing
the strategy’s of the other players.

13. Penny Matching:
 Each of the two players has a penny.
 2 players must simultaneously choose whwther to show the
Head or the Tail.
 Both players know the following rules:
 If two pennies match (both heads or both tails ) then
players 2 wins payer1’s penny.
 Otherwise,player 1 wins player 2’s penny
Player 2
Head Tail
Head
-1 , 1 1 , -1
Player 1
Tail
1 , -1 -1 , 1

14. Prisoner’s Dilemma
 No communication:
 Strategies must be undertaken without the full
knowledge of what the the other players
(prisoners)will do.
 Players (prisoners) develop dominant strategies
but are not necessarily the best one.

15. Payoff Matrix for Prisoner’s
Dilemma Ted
Confess Not confess
Confess
Both get 5 years 1 year for Bill
10 years for ted
Bill
10 years for Bill Both get 3 years
Not Confess 1 year for Ted

16. An Example of Mixed Startegy
game
A
B believes B doesn’t believe
B
A bluffs 1 0
A doesn’t bluff 0 0.5

17. Nash Equilibrium
 This equilibrium occurswhen player’s strategy
is optimal,knowing the strategy’s of the other
player’s.
 A player’s best strategy is thet startegy that
maximize that player’s payoff(utility),
knowing the strategy’s of the other players.
 So when each player within a game follows
their best strategy, a Nash Equilibrium will
occur.