1. GAME
THEORY
The Complete Strategyst
By
J . D. William

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4. 4
Why We Selected The Book
“The complete Strategyst by J.D. William”
Evolutionary
Not as a set of theorems
but
a box of tools
Stunning
Interplay
Cooperation and Conflict
strengths and weaknesses of market
economy

5. 5
Definition, History and Significance of Game
Theory
Arif Hussain
Types of Games
Basic Concepts of Game Theory
Kinds of Strategies
Nash Equilibrium and Prisoners Dilemma
Examples of Application of Game Theory
In real World
Sequence of Presentation

6. 6
What is Game Theory?
Mathematical
analysis of a
conflict of
interest
To
find optimal
choices
will lead to a
desired outcome
under given
conditions
That

7. 7
Game Theory
Actually
becoming a field
of major interest
economics sociology
political military

8. 8
A study of ways to win in a situation
under
the given the conditions of the situation

9. 9
Game Theory is a set of tools and
techniques for decisions
in which each
opponent
aspires to
optimize his
own decision.
involving two or
more intelligent
opponents
under uncertainty
at the expense
of the other
opponents
Formal Definition

10. Ideas underlying game theory
Apparent
in
Bible
Charles
Darwin
Talmud
The works
of
Descrates
Sun
Tzu
History Of Game Theory
10

11. Game Theory
Outgrowth of Three Seminal Works
Augustin Cournot
Emile Borel,
Francis Ysidro
Edgeworth
History Of Game Theory
11

12. Systematic and Modern Analysis
1944
“Theory of Games and
Economic Behavior”
1950
Modern methodological
framework
by John Nash
World War -II
British Naval Officers first
applied
game theory
History Of Game Theory
12

13. 1994
Johns Nash
J.C.Harsanyi
R. Selton
Noble Prizes Shared
1996
William Vickery
James Mirrlees
History Of Game Theory
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14. 14
Flexible Decision Structure
Correct
solutions no
matter what
happens
Constant
reassessment of
the planning
process
Analyze
through other
players' eyes
Don't just play
the game,
change the rules
look beyond the
traditional roles
Significance of Game Theory

15. Elements of Game
The essential elements of a game are:
 Players. The individuals who make decisions.
 Rules of The Game. Who moves when? What can they
do?
 Outcomes. What do the various combinations of
actions produce?
 Payoffs. What are the players’ preferences over the
outcomes?
 Information. What do players know when they make
decisions?
 Chance. Probability distribution over chance events, if any
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16. Basic Concepts of Game Theory
 Game
 Move
 Information
 Strategy
 Payoffs
 Extensive Form
 Normal Form
 Equilibria
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17. Game
 A conflict in interest among players (individuals or
groups)
 There exists a set of rules that define the terms of
exchange of information and pieces
 The conditions under which the game begins, and the
possible legal exchanges in particular conditions
 The entirety of the game is defined by all the moves to
that point, leading to an outcome.
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18. Move
 The way in which the game progresses between states
through exchange of information and pieces
 Moves are defined by the rules of the game
 Moves can be made in either alternating fashion, occur
simultaneously for all players, or continuously for a single
player until he reaches a certain state or declines to move
further
 Moves may be choice or by chance. For example, choosing
a card from a deck or rolling a die is a chance move with
known probabilities
 On the other hand, asking for cards in blackjack is a choice
move.
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19. Information
 A state of perfect information is when all moves
are known to all players in a game
 Games without chance elements like chess are
games of perfect information
 While games with chance involved like blackjack
are games of imperfect information.
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20. Strategy
 A strategy is the set of best choices for a player for an
entire game
 It is an overlying plan that cannot be upset by
occurrences in the game itself.
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21. Difference Between
 A Move is a single step a
player can take during the
game.
 A strategy is a complete set of
actions, which a player takes
into account while playing
the game throughout
Move Strategy
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22. Cont …..
Example
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23.  Pure strategy
 Mixed Strategy
 Totally mixed strategy.
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Kinds of Strategies

24. Pure Strategy
 A pure strategy provides a complete definition of
how a player will play a game. In particular, it
determines the move a player will make for any
situation he or she could face.
 A player‘s strategy set is the set of pure strategies
available to that player.
 select a single action and play it
 Each row or column of a payoff matrix represents both
an action and a pure strategy
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25. Mixed Strategy
 A strategy consisting of possible moves and a
probability distribution (collection of weights)
which corresponds to how frequently each move is
to be played. A player would only use a mixed
strategy when she is indifferent between several
pure strategies, and when keeping the opponent
guessing is desirable - that is, when the opponent
can benefit from knowing the next move.
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26. Totally Mixed Strategy.
 A mixed strategy in which the player assigns strictly
positive probability to every pure strategy
 In a non-cooperative game, a totally mixed strategy of
a player is a mixed strategy giving positive probability
weight to every pure strategy available to the player.
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27. Payoff
 The payoff or outcome is the state of the game at
it's conclusion
 In games such as chess, payoff is defined as win or
a loss
 In other situations the payoff may be material (i.e.
money) or a ranking as in a game with many
players.
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28. Extensive and Normal Form
Extensive Form
The extensive form of a game is a complete
description of:
- The set of players
- Who moves when and what their choices are
- What players know when they move
- The players’ payoffs as a function of the choices
that are made.
- In simple words we also say it is a graphical
representation (tree form) of a sequential game.
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29. The Normal Form
 The normal form is a matrix representation of
a simultaneous game
 For two players, one is the "row" player, and the other, the
"column" player
 Each rows or column represents a strategy and each box
represents the payoffs to each player for every
combination of strategies
 Generally, such games are solved using the concept of a
Nash equilibrium. .
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30. Equilibrium
 Equilibrium is fundamentally very complex and subtle
 The goal to is to derive the outcome when the agents
described in a model complete their process of
maximizing behaviour
 Determining when that process is complete, in the
short run and in the long run, is an elusive goal as
successive generations of economists rethink the
strategies that agents might pursue.
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31. Nash Equilibrium
 Defined as a set of strategies such that none of the
participants in the game can improve their payoff,
given the strategies of the other participants.
 Identify equilibrium conditions where the rates of
output allowed the firms to maximize profits and
hence no need to change.
 No price change is an equilibrium because neither
firm can benefit by increasing its prices if the other
firm does not
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32. Limitations of Nash Equilibrium
 For some games, there may be no Nash equilibrium;
continuously switch from one strategy to another
 There can be more than one equilibrium
10, 10 100, -30
-20, 30 140, 25
Firm 2
Firm
1
No Price
Change
No Price
Change
Price
Increase
Price
Increase
Both firms increasing their price is also a
Nash equilibrium
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33. Dominant Strategies
 One firm’s best strategy may not depend on the choice
made by the other participants in the game
 Leads to Nash equilibrium because the player will use
the dominant strategy and the other will respond with
its best alternative
 Firm 2’s dominant strategy is not to change price
regardless of what Firm 1 does
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34. Dominated Strategies
 An alternative that yields a lower payoff than some
other strategies
 a strategy is dominated if it is always better to play
some other strategy, regardless of what opponents
may do
 It simplifies the game because they are options
available to players which may be safely discarded
as a result of being strictly inferior to other
options.
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35. Continued….
 A strategy s¡ in set S is strictly dominated for
player i if there exists another strategy, s¡’ in S such
that,
Πi(s¡’) > Πi(s¡)
 In this case, we say that s¡’ strictly dominates s¡
 In the previous example for Firm 2 no price change is
a dominant strategy and price change is a dominated
strategy
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36. Maxim in Strategies
 Highly competitive situations (oligopoly)
 Risk-averse strategy – worst possible outcome is as
beneficial as possible, regardless of other players
 Select option that maximizes the minimum possible
profit
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37.  Each firm first determines the minimum profit that could
result from each strategy
 Second, selects the maximum of the minimums
 Hence, neither firm should introduce a new product
because guaranteed a profit of at least $3 million
 Maxim in outcome not Nash equilibrium- loss avoidance
rather than profit maximization
4, 4 3, 6
6, 3 2, 2
Firm
1
Firm
2
Firm 2
Minimum
Firm 1
Minimum
New
Product
No New
Product
No New
Product
New
Product
3
2
23
37

38. Mixed Strategies
 Pure strategy – Each participant selects one course of
action
 Mixed strategy requires randomly mixing different
alternatives
 Every finite game will have at least one equilibrium
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40. Example
Battle of the Sexes
 Two agents need to coordinate their actions, but they have
different preferences
 Original scenario:
• husband prefers football
• wife prefers opera
 Another scenario:
• Two nations must act together to deal with an
international crisis
• They prefer different solutions
 This game has two pure-strategy Nash equilibrium and one
mixed-strategy Nash equilibrium
 How to find the mixed-strategy Nash equilibrium?
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41. Nash Equilibrium
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42. Types of Games
 One-Person Games
 Zero-Sum Games
 Non zero sum game
 Two-Person Games
 Repeated Games
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43. One-Person Games
 A one-person games has no real conflict of interest
 Only the interest of the player in achieving a
particular state of the game exists
 Single-person games are not interesting from a game-
theory perspective because there is no adversary
making conscious choices that the player must deal
with

44. Zero-Sum Games
 A zero-sum game is one in which no wealth is created or
destroyed
 Whatever one player wins, the other loses
 Therefore, the player share no common interests
 There are two general types of zero-sum games: with and
without perfect information
 If the total gains of the participants are added up, and the
total losses are subtracted, they will sum to zero
 Example
a. Rock, Paper, Scissors
b. Poker game

45. Example of poker game
 Let’s there are three players, Aslam, Akram and Saleem
each starting with Rs 100, in a total of Rs 300.
 They meet at Akram’s house and play for a couple of
hours. At the end of the evening Aslam has Rs 200,
Akram has Rs 60 and Saleem has Rs 40. The total
amount of money between them is still Rs 300.
 Aslam has a increase of Rs 100, Akram is down Rs 40
and Saleem is down Rs 60.
 The total of these three numbers is zero (100-40-60),
so it is a zero-sum game.

46. Example
 In non-zero-sum games, one player's gain needn't be
bad news for the other(s)
 Indeed, in highly non-zero-sum games the players'
interests overlap entirely
 In 1970, when the three Apollo 13 astronauts were
trying to figure out how to get their stranded spaceship
back to earth, they were playing an utterly non-zero-
sum game, because the outcome would be either
equally good for all of them or equally bad.

47. Non Zero Sum Game
 In game theory, situation where
one decision maker's gain (or loss) does not
necessarily result in the other decision makers' loss
(or gain). In other words, where the winnings and
losses of all players do not add up to zero and
everyone can gain: a win-win game.
 Example
 Prisoner's dilemma

48. Two-Person Games
 Two-person games are the largest category of familiar
games
 A more complicated game derived from 2-person
games is the n-person game
 These games are extensively analyzed by game
theorists
 However, in extending these theories to n-person
games a difficulty arises in predicting the interaction
possible among players since opportunities arise for
cooperation and collusion.

49. Repeated Games
 In repeated games, some game
G is played multiple times by
the same set of agents
 G is called the stage game
 Each occurrence of G is called
an iteration or a round
 Usually each agent knows what
all the agents did in the
previous iterations, but not
what they’re doing in the
current iteration
 Usually each agent’s payoff
function is additive
 Examples
1. Iterated Prisoner’s
Dilemma
2. Repeated
Ultimatum Game
3. Repeated
Matching Pennies
4. Repeated Stag
Hunt

50. Sequential Games
 A game where one player chooses his action before the
others choose theirs
 Importantly, the later players must have some
information of the first's choice, otherwise the
difference in time would have no strategic effect
 Extensive form representations are usually used for
sequential games, since they explicitly illustrate the
sequential aspects of a game.
 Combinatorial games are usually sequential games.
 Sequential games are often solved by backward
induction.

51. Simultaneous Games
 A game where each player chooses his action
without knowledge of the actions chosen by other
players
 Normal form representations are usually used for
simultaneous games.
 Example
 Prisoner dilemma .

52. Application of Game Theory
 Philosophy
 Resource Allocation and Networking
 Biology
 Artificial Intelligence
 Economics
 Politics
 Warfare

53. Non Cooperative Games
Because the two participants are interrogated
separately, they have no idea whether the other person
will confess or not
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54. Co-operative Games
 Possibility of negotiations between participants for a
particular strategy
 If prisoners jointly decide on not confessing, they
would avoid spending any time in jail
 Such games are a way to avoid prisoner’s dilemma
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55. Sequential Games
 One player acts first & then the other responds
 2 firms contemplating the introduction of an identical
product in the market
 1st firm- develop brand loyalties, associate product
with the firm in minds of consumers
 Thus, first mover advantage
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56. An example for sequential games
Firm 2
No new product
Introduce new
product
Firm 1
No new product $2, $2 $-5, $10
Introduce new
product
$10, $-5 $-7, $-7
• Assume firms use maximum criterion, so
neither should introduce a new product and
earn $2 mn each
• Firm 1 introduces a new product, firm 2 will
still decide to stay out because right now it is
losing $5 mn, opposed to $7 mn otherwise.
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57. Conclusion
 By using simple methods of game theory, we can
solve for what would be a confusing array of
outcomes in a real-world situation
 Using game theory as a tool for financial analysis
can be very helpful in sorting out potentially
messy real-world situations, from mergers to
product releases.