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1. Presentation on
Game theory
Presented to Presented by
Dr. Hulas Pathak Navin Chandra Das
Professor M.Sc.(Ag.) Pre. Year
Deptt. Of Agril. Economics Deptt. Of Agril. Economics
 College of Agriculture Raipur (C.G.)

2. Game Theory
 Game theory is the study of how people interact
and make decisions.
 This broad definition applies to most of the social sciences,
but game theory applies mathematical models to this
interaction under the assumption that each person's behavior
impacts the well-being of all other participants in the game.
These models are often quite simplified abstractions of real-
world interactions.

3. History of Game Theory
 Game theoretic notions go back thousands of
years
– Talmud and Sun Tzu's writings.
 Modern theory credited to John von Neumann
and Oskar Morgenstern 1944.
– Theory of Games and Economic Behavior. In the early
1950s,
 John Nash (“A Beautiful Mind” fame)
generalized these results and provided the basis
of the modern field.

4. Meaning of game theory
 Game theory is the study of the strategic
interaction among rational players.
 The games studied can be quite serious and are
studied in many areas of the natural and social
sciences: military, political and marketing
campaign strategy can be modeled with game
theory, also phenomena in natural science, for
example, in the study of evolutionary biology.

5. Definition of game:-
 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
 In a competitive situation the course of action
(alternatives) for each competitor may be either
finite or infinite .A competitive situation will be
called ‘’Game’’ .

6. Basic terms related to game theory
1. Players
2.Strategy.
a. Pure strategy
b. mixed strategy
3. Optimum strategy
4. Value of game
5.Payoff matrix

7. 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.

8. Assumption con…
 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

9. Use Of Game Theory
 Economists
 innovated antitrust policy
 auctions of radio spectrum licenses for cell phone
 program that matches medical residents to hospitals.
 Computer scientists
 new software algorithms and routing protocols
 Game AI
 Military strategists
 nuclear policy and notions of strategic deterrence.
 Sports coaching staffs
 run versus pass or pitch fast balls versus sliders.
 Biologists
 what species have the greatest likelihood of extinction.

10. Game Theory
 For Game Theory, our focus is on games where:
– There are 2 or more players.
– There is some choice of action where strategy matters.
– The game has one or more outcomes, e.g. someone wins,
someone loses.
– The outcome depends on the strategies chosen by all players;
there is strategic interaction.
 What does this rule out?
– Games of pure chance, e.g. lotteries, slot machines. (Strategies
don't matter).
– Games without strategic interaction between players, e.g.
Solitaire.

11. Elements of a Game
1. The players
• how many players are there?
• does nature/chance play a role?
2. A complete description of what the players can do –
the set of all possible actions.
3. The information that players have available when
choosing their actions
4. A description of the payoff consequences for each
player for every possible combination of actions
chosen by all players playing the game.
5. A description of all players’ preferences over
payoffs.

12. 12
Types of Game Theory
1. Two-person constant sum game theory
3. Two-person zero sum game theory (e.g., prisoner’s dilemma)
Saddle point
4. Mixed strategy
5. The rectangular game as linear progamming

13. Zero-Sum vs. Non-zero-Sum
 In a zero-sum game, a player’s gain is equal
to another player’s loss.
 In a non-zero-sum game, a player’s gain is
not necessarily equal to another player’s
loss.

14. Two-Person Zero-Sum Game
 Payoff/penalty table (zero-sum table):
– shows “offensive” strategies (in rows) versus
“defensive” strategies (in columns);
 gives the gain of row player (loss of column
player), of each poTwo decision makers’ benefits
are completely opposite
i.e., one person’s gain is another person’s loss
– ssible strategy encounter

15. Example 1 (payoff/penalty table
Athlete Manager’s Strategies
Strategies (Column Strategies)
(row strat.) A B C
1 $50,000 $35,000 $30,000
2 $60,000 $40,000 $20,000

16. Two-Person Constant-Sum Game
 For any strategy encounter, the row
player’s payoff and the column player’s
payoff add up to a constant C.
 It can be converted to a two-person zero-
sum game by subtracting half of the
constant (i.e. 0.5C) from each payoff

17. Example 2 (2-person, constant-sum
During the 8-9pm time slot, two
broadcasting networks are vying for an
audience of 100 million viewers, who
would watch either of the two networks.

18. Payoffs of NW1 for the constant-sum
of 100(million
Network 1 Network 2 (NW2)
(NW1) western Soap Comedy
western 35 15 60
soap 45 58 50
comedy 38 14 70

19. An equivalent zero-sum table
Network 2
Network 1 western Soap Comedy
western -15 -35 10
soap - 5 8 0
comedy -12 -36 20

20. Equilibrium point
• In a two-person zero-sum
game, if there is a payoff value
P such that
P = max{row minimums}
= min{column maximums}
then P is called the equilibrium point, or
saddle point, of the game

21. The Prisoners' Dilemma Game
 Two players, prisoners 1, 2.
 Each prisoner has two possible actions.
– Prisoner 1: Don't Confess, Confess
– Prisoner 2: Don't Confess, Confess
 Players choose actions simultaneously without
knowing the action chosen by the other.
 Payoff consequences quantified in prison years.
– If neither confesses, each gets 1 year
– If both confess, each gets 5 years
– If 1 confesses, he goes free and other gets 15 years
 Fewer years=greater satisfaction=>higher payoff.
– Prisoner 1 payoff first, followed by prisoner 2 payoff.

22. Prisoners’ Dilemma in “Normal”
or “Strategic” Form
Don’t
Confess
Confess
Don’t
Confess
1,1 15,0
Confess 0,15 5,5

23. Prisoner’s Dilema
Prisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” FormPrisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic

24. Prisoners' Dilemma :
Example of Non-Zero Sum Game
 A zero-sum game is one in which the players'
interests are in direct conflict, e.g. in football, one
team wins and the other loses; payoffs sum to
zero.
 A game is non-zero-sum, if players interests are
not always in direct conflict, so that there are
opportunities for both to gain.
 For example, when both players choose Don't
Confess in the Prisoners' Dilemma

25. Prisoners' Dilemma :
Application to other areas
 Nuclear arms races.
 Dispute Resolution and the decision to hire
a lawyer.
 Corruption/political contributions between
contractors and politicians.
 Can you think of other applications?