Game Theory In Marketing
Group 7
Derryl George
Manoj Pathak
Santosh Shetty
Sudham Shetty
Santosh Singh
Rasesh Shah
05
35
44
45
48
60
Game Theory
• The study of rational behavior among interdependent
players.
• The players have conflicting interest.
•The outcome of strategy of a player depends upon the
particular pair of strategy chosen by the other player.
• The objective of Game theory is to determine the best
decision for each player involved.
Prisoner’s Dilemma
Prisoner 2
Confess
Don’t Confess
Prisoner 1
Confess
Don’t Confess
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Prisoner 2
Don’t Confess
Confess
Prisoner 1
Confess
Don’t Confess
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Prisoner 2
Confess
Don’t Confess
Prisoner 1
Confess
Don’t Confess
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Conclusion:
The Prisoner 1 will confess.
And Prisoner 2?
Prisoner’s Dilemma
Prisoner 2
Confess
Don’t Confess
Prisoner 1
Confess
Don’t Confess
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Prisoner 2
Confess
Don’t Confess
Prisoner 1
Confess
Don’t Confess
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Prisoner 2
Confess
Don’t Confess
Prisoner 1
Confess
Don’t Confess
Equilibrium
( -8,
-8)
( -15, 0)
( 0, -15)
( -1, -1)
Prisoner’s Dilemma
Conclusion:
Prisoner 2 confesses also
Both get 8 years, even though if they cooperated,
they could get off with one year each
For both, confession is a dominant strategy: a
strategy that yields a better outcome regardless of
the opponent’s choice
Prisoner’s Dilemma
What would the Prisoner 1 and Prisoner 2 decide if
they could negotiate?
They could both become better off if they reached
the cooperative solution.
Equilibrium need not be efficient. Non - cooperative
equilibrium in the Prisoner’s dilemma results in a
solution that is not the best possible outcome for the
parties.
Equilibrium
Nash Equilibrium: Neither player has an
incentive to change strategy, given the other
player’s choice
Both confess is a Nash Equilibrium.
Conflict Vs Cooperation
• Case of Cournot Ltd and Bertrand ltd
(In Mineral Water Business).
– Competing by choosing one of two possible
prices, low or high.
– Each firm’s profits depends not only on its own
prices, but also on the price of its rival.
Conflict Vs Cooperation
Cont.
• Situation one: Cournot believes that Bertnard
charges high.
Bertrand
Cournot
High price
Low Price
High price
(10, 10)
(1, 15)
Low price
(15, 1)
(4, 4)
Conflict Vs Cooperation
Cont.
• Situation two: Cournot believes that Bertnard
charges low.
Bertrand
Cournot
High price
Low Price
High price
(10, 10)
(1, 15)
Low price
(15, 1)
(4, 4)
Conflict Vs Cooperation
Cont.
• Equilibrium of this game, the outcome of
simultaneous rational decision by both players, has
both charging the low price.
Bertrand
Cournot
High price
Low Price
High price
(10, 10)
(1, 15)
Low price
(15, 1)
(4, 4)
Cases
• “Advanced Micro Devices (AMD) has slashed prices of its desktop
and mobile Athlon processors just days after a similar move by
rival Intel. ‘We’re going to do what it takes to stay competitive’ on
prices, said an AMD representative. AMD’s aggressive pricechopping means the company doesn’t want to give up market
share gains, even at the cost of losses on the bottom line, analysts
said.” (CNet News.com, May 30,2002.)
• Dell Computer is known for ruthlessly driving down PC prices, but
competitors are working hard this week to catch up with the
worldwide market leader. Possibly sparked by a 10 percent price
cut on Dell corporate desktops earlier in the week, Compaq and
Hewlett-Packard have fought back with sizable cuts of their own.
HP announced Thursday that it would cut prices on corporate
desktop PCs by as much as 28 percent. Compaq Computer
reduced PC prices by as much as 31 percent Tuesday.” (CNet
News.com News, May 3, 2001)
AMD – Game theory case
• In this example, the companies compete on price in order to gain market
share. Interestingly, the product under question is not a commodity, it is
highly specialized, requiring a significant amount of innovation. As a result
of price cuts, during the first quarter of 2002, AMD increased processor
shipments from the fourth quarter of 2001, topping 8 million, but
processor revenue declined by 3%.
• In effect, the company sold more chips for less money than in the fourth
quarter. Competing companies who go into such price wars do rarely, if
ever, benefit from such competition. Clearly, rather than engaging in
mutual price cuts, both Intel and AMD would have done better if they
kept their prices higher. Cutting prices slightly might increase the overall
market potential, i.e., the “pie” might get bigger. But decreasing the prices
beyond a certain limit has a diminishing impact on the market potential.
• Hence, eventually the size of the pie does not increase anymore and firms
have to fight even harder to get a bigger portion of the pie by slashing
prices, and profits. Why do firms behave this way? In this situation, and in
many others, firms are caught in what is known as the “prisoner’s
dilemma,”
Cases
• “Burger King Corp. will put its flagship Whopper hamburger
on sale for 99 cents. The move is likely to intensify and
prolong the burger price wars that have been roiling the U.S.
fast-food industry in recent months. Burger King officials had
said earlier that while they were reluctant to discount the
Whopper, they had little choice given a $1 menu at archrival
McDonald’s Corp. that included a Whopper-like hamburger,
called the Big ’N Tasty.” (Chicago Sun-Times, January 3, 2003)
• “Tesco announced plans to slash £80 million from prices of
more than 1,000 products,with some prices falling by more
than 30%. The cuts came as rival Asda also said it was slashing
selected prices.The cuts echo memories of the supermarket
price wars played out in 1999 as stores fought to capture
more customers and increased market share.” (Sunday
Telegraph, January 5, 2003)
Dominant Firm Game
This game is also know as “Rational Pigs”
Case: Two firms, one large and one small.
Either firm can announce an output level
(lead) or else wait to see what the rival does
and then produce an amount that does not
saturate the market.
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Conclusion:
Dominant Firm will always lead…..
But what about the Subordinate firm?
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Conclusion:
No dominant strategy for the Subordinate firm.
Does this mean we cannot predict what they
will do?
Dominant Firm Game
Dominant
Lead
Follow
Subordinate
Lead
Follow
( 0.5,
4)
( 1, 8)
( 3, 2)
( 0.5, 1)
Dominant Firm Game
Conclusion:
Subordinate firm will always follow, because
dominant firm will always lead.
Equilibrium
Nash Equilibrium: Neither player has an
incentive to change strategy, given the other
player’s choice
Dominant: Lead & Subordinate Follow is a Nash
Equilibrium
A player’s best option may be dictated by
anticipating the rival’s best option
Battle of the networks
• Two television networks are battling for viewer
shares.
• The networks make their programming decisions
independently and simultaneously.
• Each network can show either sports or a sitcom.
• What should they do???
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Conclusion
• In Network 1's point of view, it is better to show a
sitcom, irrespective of Network 2’s strategy.
• The strategy “Show a Sitcom" is said to dominate the
strategy “Show Sports" for Network 1.
So Network 1 will show a sitcom.
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Battle of the networks
• Network 2 is better of showing sports, irrespective of
Network 1’s strategy.
• In other words, Network 2 also has a dominating
strategy.
• So Network 2 shows sports.
Battle of the networks
Network 2
Network 1
Sitcom
Sports
Sitcom
(56%, 44%)
(51%, 49%)
Sports
(50%, 50%)
(46%,54%)
Conclusion
• The resulting outcome, namely 51% viewer share to Network
1 and 49% to Network 2, is an equilibrium, since neither of
the two players in this game can unilaterally improve their
outcome.
• If Network 1 were to switch from sitcom to sports, its viewer
share would drop 5%, from 51% to 46%.
&
If Network 2 were to switch from sports to sitcom, its viewer
share would also drop, from 49% to 44%.(Nash equilibrium)
• Each network is getting the best viewer share it can, given the
competition it is up against.
A Sequential Game
Migros
Normal
Aggressive
Wal-Mart
Wal-Mart
Enter
Enter
Stay out
Stay out
680
730
700
800
-50
0
400
0
Assumptions
• All players are rational.
• Players move sequentially. (Therefore, also called
sequential games)
• Players have complete and perfect information
– Players can see the full game tree including the payoffs
– Players can observe and recall all previous moves
Solution of a sequential game
• Subgame Perfect Equilibrium: For an
equilibrium to be subgame perfect, it has to
be a NE for all the subgames as well as for the
entire game.
– A subgame is a decision node from the original
game along with the decision nodes and end
nodes.
– Backward induction is used to find SPE
Advertising Example:
3 proper subgames
Migros
Wal-Mart
Wal-Mart
680
730
700
800
-50
0
400
0
Solution of the Advertising Game
Subgame 1
Subgame 2
Wal-Mart
Wal-Mart
Enter
Enter
Stay out
Stay out
680
730
700
800
-50
0
400
0
Solution of the Advertising Game
(cont.)
Migros
Aggressive
Normal
730
700
0
400
SPE of the game is the strategy profile: {aggressive, (stay out, enter)}
Properties of SPE
• The outcome that is selected by the backward
induction procedure is always a NE of the
game with perfect information.
• SPE is a stronger equilibrium concept than NE
• SPE eliminates NE that involve incredible
threats.
Cases
• Coca-Cola is developing a vanilla-flavored version of its bestselling flagship cola, a report says, extending the company’s
palette of flavorings from Cherry Coke and Diet Coke with
lemon. But don’t expect to see a vanilla-flavored Pepsi anytime
soon. ‘It’s not something we’re looking at,’ said spokesman
Larry Jabbonsky of Pepsi. ‘We think it’s a bit vanilla.’ ” (USA
Today, April 01, 2002)
• “PepsiCo is launching Pepsi Vanilla and its diet version in stores
across the country this weekend. Coke came out with Vanilla
Coke in May 2002 and it was a resounding success, selling 90
million cases, according to trade publication Beverage Digest.
‘We’re a little surprised that Pepsi decided to enter the vanilla
segment,’ said Mart Martin, spokesman for Coca-Cola. ‘When
we came out with Vanilla Coke, Pepsi originally said the idea
sounded ‘a bit vanilla.’ But, whatever.’ ”(CNN/Money, August 8,
2003)
Thank you.
The E.U. Airbus Subsidies
• When Airbus Industries got its start, it was believed that there
would not be enough total demand for two major aircraft
manufacturers (viz., Airbus and Boeing) to both turn a profit
developing a new mid‐size aircraft line (roughly 4000mi range
with 150‐200 passengers).
• Rather, because aircraft development involves such high fixed
costs, world demand would make it economical for only one
firm to produce a new aircraft in this size range.
•
The inter‐dependence of the two firms’ profit and decisions
in this product line can be represented by the payoffs of the
following game (payoffs in billion $):
Airbus
Boeing
Produce
Don’t Produce
Produce
(-10, –10)
(100, 0)
Don’t Produce
(0, 100)
(0, 0)
If Boeing has a head start in the development process for this line of aircraft,
then what would be the outcome of this game? If Boeing does not have a head
start, then what (if any) outcome of this game would you expect?
• If Boeing has a head start in the development
process for this line of aircraft, then what
would be the outcome of this game?
• If Boeing does not have a head start, then
what (if any) outcome of this game would you
expect?
• Airbus is partially owned by four nations (France,
Germany, Britain, and Spain), and they would prefer
that Airbus produce the new aircraft.
• Suppose that these governments, through the E.U.,
commit to a subsidy of $20 billion before Boeing has
committed itself to produce.
• Regardless of what Boeing decides to do, this subsidy
would raise Airbus’ payoff by 20 (billion $) if Airbus
decides to produce the new aircraft (however, Airbus
would not receive the subsidy if it decides not to
produce the new aircraft).