game theory in economics

1. GAME THEORY

2. Game theory and Strategic behaviour under oligopoly
Game theory is a technique used to analyse situations
where individuals or organisations have conflicting
objectives. Three important concepts are often used in
game theory. (i)Players (ii)Strategy and (iii) Payoffs.
Players are the decision makers (mangers). A strategy is
a course of action to change price, develop new
products, adopt new advertising, etc. The payoff is the
outcome of the strategy. The players always try to
optimise their strategy. This theory was first developed
by Von Neuman (mathematician)and Oskar
Morgenstern(economist). It explains the strategic
interaction among the Oligopoly firms. Each player
needs to adopt dominant strategy to maximise profit.

3. Types of games
• Constant sum of game: In this case the total benefit of the
players given each strategy, is a constant and the players have to
share the profit
• Zero sum game: In this game the total benefit, given each
strategy, is equal to zero. Under this game the gain of one player
is the loss by the other player.
• Positive sum games: The total benefit of the players added
together, given each strategy, is more than zero(+ve).
• Negative sum game: When the total benefit , given the strategy,
is less than zero (-Ve)
• Co operative game: The games where the strategies of the
players are coordinated or joint action.
Q.14.2

4. • Role of Interdependence
The essence of game is the interdependence of
player strategies.
It may be sequential game or a simultaneous game.
In a sequential game, each player moves in
succession, and each player is aware of all prior
moves.
A simultaneous game is one in which all players
make decisions (or select a strategy) without
knowledge of the strategies that are being chosen by
other players. Even though the decisions may be
made at different points of time, the decisions are
made simultaneously. Simultaneous games are
solved using the concept of Nash equilibrium.

5. The nature of Problems faced by the Oligopoly firms is
best explained by the Prisoner’s Dilemma game.
Let two persons are involved with some illegal activities
say; match fixing; were arrested and kept separately so
that they cannot communicate each other. Four possible
options were kept before them:
(i) If both confess, each one will get 5 years of
imprisonment;
(ii) If Both deny, each one will be put in jail for 1 year;
(iii) If A confesses and B denies, A will go free and B will
get 10 years of imprisonment ;
(iv) If B confesses and A denies, B will go free and A will
get 10 years of imprisonment .

6. Prisoner’s Dilemma: The Pay-off matrix With much of
Individuals
Startegies Do not confess
Do not confess
Individual A
Individual B
Confess
Confess 5,5 0,10
10,0 1,1
uncertainty, no one
knows the action of each
other, there is dilemma
in taking a decision. The
dominant strategy for A
is to confess. The
dominant strategy for B is
also is to confess. Each
one will end up with 5
years of imprisonment.
It refers to a situation in
which each individual
firm adopts its dominant
strategy and earns
maximum profits.

7. Payoff Matrix for an advertising game
Individuals
Startegies Do not advertise
Do not advertise
Individual B
Advertise
Individual A
Advertise 4,3 5,1
2,5 3,2
Firm A’s profit is always greater if it advertises than not advertising regardless of what B
does and the dominant strategy for A is to advertise. The same is the case for B also.
This is the final equilibrium as it is the optimal choice of both the players.

8. • In oligopoly, the business firm chooses its
strategies to achieve equilibrium. There are
actions, reactions and interactions to increase
their prices to achieve the optimum profit.
• To analyse this type of situation, an American
mathematician (John Nash)developed a
technique which is known as Nash equilibrium. It
is defined as a situation where each player
chooses his/her optimal strategy, given the
strategy chosen by other players. A game may
have more than one Nash equilibrium.

9. Simple Two Persons, Zero Sum Game
ASSUMPTIONS
• Each player knows both
his and his opponent’s
alternatives
• Preferences of all
players are known
• Single period game
• Sum of payoffs are zero
• An Equilibrium (or
Nash Equilibrium) - if
none of the participants
can improve their
payoff
PLAYER 2
PLAYER 1
a
b
c d
1, -1 3, -3
-2, 2 0, 0
Player 1 is the first number in
each pair. We will get to {a,c}
which is an Equilibrium

10. Two Person Game, Non-Zero Sum Game:
ASSUMPTIONS
• Each player can invade the territory of
the other (no guard)or Guard his own
territory
• Pak’s payoff is given first.
• Inida always ranks Guard above no
guard, so India has a Dominant Strategy
• Knowing what India will do, Pak decides
to Guard as well.
• An Equilibrium--none of the participants
can improve their payoff
India
Guard
PAK
No guard
Guard no guard
Better, 1st Worst, 4th
Worse, 2nd Best, 3rd
We will get to {Guard, Guard}
which is an Equilibrium

11. Unstable Games:
No Equilibrium Is Found
• Suppose KIM thinks
that the solution is
going to be: {b, c}
• Then, KIM has an
incentive to switch to
strategy-a
• Then JOHN has an
incentive to switch to
strategy-d, etc., etc.
John
c d
KIM
a
b
3, - 3 1, - 1
2, - 2 4, - 4
There is no, single stable equilibrium
Each player may elect a random
strategy

12. Dominant strategy and domonated startegy
PLAYER 2
a
PLAYER 1
b
c d
1, -1 3, -3
-2, 2 0, 0
• For Player 1, strategy (a) is a
dominant strategy - an
action that maximizes the
decision maker’s welfare
independent of the actions
of the other players.
– Also, strategy (b) is a
dominated strategy,
which is worst regardless
of what others do
• Player 2 also has a
dominant strategy of (c).
• Dominant strategies make
games easy to solve.
With dominant strategies of (a)
for Player 1 and ( c) for Player
2, the solution will be {a, c},
which is an Equilibrium.

13. Individuals
Startegies Do not advertise
Do not advertise
Individual B
Advertise
Individual A
Advertise
4,3 5,1
2,5 8,2
•In real world the one player or both of them may not have a dominant strategy as shown
in the matrix. Here firm B has the dominant strategy is to advertise whether firm A
advertises or not, because the payoffs for B remain the same.
• Firm A has no dominant strategy now. Because if B advertises, A earns a profit of 4 if it
advertises and 2 if it does not. Thus if B advertises, firm A should advertise.
•A earns a profit of 5 if it advertises and 8 if it does not advertise. Here the assumption is
that A uses an expensive advertisement and it adds to its cost than revenue. It would shift
the burden of increased cost to its consumers and get the larger share. It indicates that if B
does not advertise, it is better for A not to advertise and get the larger share of the market.
Hence A does not have a dominant strategy.

14. Individuals
Startegies Do not advertise
Do not advertise
Individual B
Advertise
Individual A
Advertise
4,3 5,1
2,5 8,6
B gets better payoff by advertising than not advertising. But if A does not advertise,
B will not advertise as advertisement leads to lower payoffs to B than not advertising
when A does not advertise. Hence the decision of B to advertise or not depends on
whether A advertises or not. In other words, B does not have a dominant strategy
on his own. B gets a share of 6 if it does not advertise when A also does not
advertise.
No one can choose a dominant strategy independently of the other firm. When each
player chooses its optimal strategy given the strategy of the other player, we will
have a Nash equilibrium. Hence a dominant strategy equilibrium is always a Nash
equilibrium, but a Nash equilibrium is not necessarily a dominant strategy.
Problem 14.3 for assignment

15. • Every dominant strategy equilibrium
is also a Nash equilibrium.
• Nash equilibrium can exist where
there is no dominant strategy
equilibrium.
• In Nash bargaining, two competitors
or players "bargain" over some item
of value. In a simultaneous-move,
one-shot game, the players have
only one chance to reach an
agreement.

16. • A. Yes, the dominant strategy for firm A is “up.” If firm B chooses “left,”
the highest payoff of $5 million can be achieved if Firm A chooses “up.”
On the other hand, if firm B chooses “right,” the highest payoff of $7.5
million can be achieved if firm A again chooses “up.” No matter what firm
B chooses, the highest payoff results for firm A occurs if A chooses “up.”
Therefore, “up” is a dominant strategy for firm A.
B. No, there is no dominant strategy for firm B. If firm A chooses “up,”
the highest payoff of $10 million can be achieved if firm B chooses “left.”
On the other hand, if firm A chooses “down” the highest payoff of $5
million can be achieved if firm B chooses “right.” Therefore, there is no
dominant strategy for firm B. The profit-maximizing choice by firm B
depends upon the choice made by firm A.