2. Basic concepts
• The payoff matrix
• Nash equilibrium
• Dominant strategies
• Maximin strategies
• Mixed strategies

3. Game Theory And Oligopoly
• Non cooperative games the prisoner dilemma
• Cooperative games dealing with cheaters
• Sequential games the ad of being first

4. Introduction
Introduced by
• In 1950s , By John von Neumann and Oskar
Morgenstern
• Application –
1. political, courtship, economic issues
2. It could be used to analyze the bargaining
• process between two parties : Wage rate
• negotiation: unions and firms Peace talks:
• between 2 countries.

5. Assumptions
• Assumptions Finite sets of possible action
• Awareness of availability competitors
strategies too Intelligent and rational
• Maximize gain and minimize loss If a’s gain is
b’s loss,its 0-sum game (amt of gain=amt of
loss) Players act; select their stategies
simultaneously

6. Types of games
Cooperative
Non-cooperative
when players can when game is not
negotiate a binding cooperative it is said to
contract to play joint be non-cooperative
strategies. game.

7. The Payoff Matrix
It is a course of action taken by 1 of
the participants in a game
Mixed strategies-
Pure strategies don’t selects the
Selects the same strategy same stategy Payoff:
It is the result or
outcome of the
strategy
Example: 2 children engaged in coin-flipping 2
competing firms whose objective is to increse their
profits by price changes

8. Payoff matrix
Consider the competition between two
department stores, each of which must what
kind of clothing to promote
Store 2
Promote girl’s Promote women’s
cloth cloth
Promote girl’s
cloth
0,0 4,2
Store 1
Promote 2,2 2,4
women’s cloth
Profit in millions

9. NASH EQUILIBRIUM
A Nash Equilibrium is defined as a set of strategies such that none of the participants in the game can
improve their payoff (profits), given the strategies of the other participants.
Dominant Strategies :
Dominant Strategies The dominant strategy is the optimal choice
for a player no matter what the opponent does. One firm will be in
dominant position in terms of change in strategy.
Dominant Strategy(in millions)
Firm Firm 2
Firm 1 Strategy No Price Change Price Change
No Price Change 10,10 100,-30
Price Change -20,30 140,25

10. Max min Strategy
Firm Firm 2
Firm 1 Strategy No New Product New Product
No New Product 4,6 3,6
New Product
6,3 2,2

11. Maxmin Strategy
Firm 2
Strategy No New Product New Product
4, 6 3 ,6
No New
Firm 1 Product
New Product 6, 3 2 ,2
Equilibrium
Nash

12. Maxmin Strategy
Firm 2
Strategy No New Product New Product Maximum
Minimum
4, 6 3 ,6 6
3
No New
Firm 1 Product
New Product 6, 3 2 ,2 6
2
Maximum
Minimum 3
6 6
2
Profit in millions

13. Nash Equilibrium & Maximin Point
Isn't Same
• Decision Criterion is not
Profit-Maximisation
Why So? • Its for avoiding highly
unfavourable outcome
• Its for avoidance of risks

14. Just Remember that its 2 Step Process
1.Find Minimum(Least) Profit
2.Select maximum Out of Minimum
Profit
Mixed Strategy
Why We Should Study This?

16. Game Table
• The Game of Tennis 1. For Striker:
Striker chooses to serve • Best response to defend
either left or right left is to Strike right
Receiver defends either • Best response to defend
left or right right is to Strike left
• Better chance to get a 2. For receiver: Just the
good return if you opposite
defend in the area the
striker is serving to

17. Receiver - 70-30
Striker - 60-40
Percent of
Payoff Chances of
Expects Throws Receiver Striker Probability Matrix Success
Left Left 0.70 0.60 0.42 75% 0.315
Left Right 0.30 0.40 0.12 25% 0.030
Right Left 0.70 0.60 0.42 25% 0.105
Right Right 0.30 0.40 0.12 75% 0.090
Total
Success 0.540

18. Receiver – 50-50
Striker - 70-30
Percent
of Chances
Receive Probabli Payoff of
Expects Throws r Striker ty Matrix Success
Left Left 0.50 0.70 0.35 75% 0.263
Left Right 0.50 0.30 0.15 25% 0.038
Right Left 0.50 0.70 0.35 25% 0.088
Right Right 0.50 0.30 0.15 75% 0.113
Total
Success 0.500

19. Receiver – 50-50
Striker - 40-60
Percent Chances
Probabli of Payoff of
Expects Throws Receiver Striker ty Matrix Success
Left Left 0.50 0.60 0.3 75% 0.225
Left Right 0.50 0.40 0.2 25% 0.050
Right Left 0.50 0.60 0.3 25% 0.075
Right Right 0.50 0.40 0.2 75% 0.150
Total
Success 0.500

20. Mixed Strategy Equilibrium
•A mixed strategy equilibrium is a pair of mixed
strategies that are mutual best responses.
• In the tennis example, this occurred when any
player chose a 50-50 mixture of left and right.

21. Receiver’s Best Response
Suppose p is the probability of Strikers Serving
towards left Clearly
•If p = 1, then the receiver should defend to the left
•If p = 0, the receiver should defend to the right.

22. Left
Right
1/2 P

23. Best Response
Suppose that the receiver goes left with probability
q. Clearly,
•if q = 1, the server should serve right
•If q = 0, the server should serve left Server’s

24. q
1/2
Right Left

25. Putting Things Together
q
Mutually best
R’s best response response
1/2
S’s best response
1/2 p

26. Noncooperative Games
A game is considered non cooperative if it not possible to
negotiate with other participants and enter into some form of
binding agreement.
Example : Prisoner's Dilemma
Prisoner Prisoner 2
Prisoner 1 Strategy Don’t Confess Confess
Don’t Confess 0,0 15,5
Confess
5,15 5,5

27. Prisoner Prisoner 2
Remain Silent
Prisoner 1 Strategy Confess
Confess 5,5 0,20
Remain Silent 20,0 1,1

28. cooperative Games
A game is considered cooperative if it possible to
negotiate with other participants and enter into
some form of binding agreement.
Firm Firm 2
Firm 1 Strategy No New New Product
Product
No New 30,30 10,40
Product
New Product
40,10 20.20
Profit in millions

29. Repeated Games
•A repeated game is a game that the same
players play more than once In repeated games
• the sequential nature of the relationship
allows for the adoption of strategies that are
contingent on the actions chosen in previous
plays of the game

30. Firm Firm 2
Firm 1 Strategy Low-level
Advertising High-level
Advertising
30,30 10,40
Low-level
Advertising
High-level 40,10 20.20
Advertising
Profit in millions

31. • Any 1 Firm breaks the agreement
• Adopts High-Level Advertising
• Temporary Loss to other firm due to cheating
• In next period, Other firm will do the same (Tit-
For-Tat)
• If One Firm Cuts price-Other firm will cuts price in
next period.
• If One firm Raise Price-Other firm will do so in
next period.
• Tit-For-Tat is Win-Win Situation

32. Advantages
•Easy to understand
•Never initiates cheating
•Never rewards cheating cause it punish in some
way
•Its about forgiving because cooperation is quickly
restored

33. Sequential Games
•One Player acts First & Then other responds.
•Games where players choose actions in a
particular sequence are sequential move
games.
Examples: Chess, Bargaining/Negotiations.
•Must look ahead in order to know what action
to choose now

34. Benifits to the one Who acts first
Firm Firm 2
Strategy Low-level High-level
Advertising Advertising
2,2 -5,10
Low-level
Firm 1 Advertising
High-level 10,-5 -7,7
Advertising
Profit in millions

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