Game Theory In Marketing

Game Theory In Marketing

Group 7

Derryl George 05Manoj Pathak 35Santosh Shetty 44Sudham Shetty 45Santosh Singh 48Rasesh Shah 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

Confess Don’t ConfessPrisoner 1

Prisoner 2

Confess

Don’t Confess

( -8, -8)

( -15, 0)

( 0, -15)

( -1, -1)


Conclusion:

The Prisoner 1 will confess.

And Prisoner 2?


Confess Don’t ConfessPrisoner 1

Prisoner 2Prisoner 2

Confess

Don’t Confess

( -8, -8)

( -15, 0)

( 0, -15)

( -1, -1)


ConfessConfess Don’t ConfessPrisoner 1


Confess

Don’t Confess

( -8, -8)

( -15, 0)

( 0, -15)

( -1, -1)


ConfessConfess Don’t ConfessPrisoner 1


Confess

Don’t Confess

( -8, -8)

( -15, 0)

( 0, -15)

( -1, -1)

Equilibrium


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 DilemmaWhat 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

High price Low Price

Cournot High price (10, 10) (1, 15)

Low price (15, 1) (4, 4)


• Situation two: Cournot believes that Bertnard charges low.

Bertrand



Low price (15, 1) (4, 4)


Bertrand



Low price (15, 1) (4, 4)

• Equilibrium of this game, the outcome of simultaneous rational decision by both players, has both charging the low price.

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 price-chopping 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,”

• “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)

Cases

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

Lead FollowSubordinate

Dominant

Lead

Follow

( 0.5, 4)

( 1, 8)

( 3, 2)

( 0.5, 1)

Dominant Firm Game

Lead FollowSubordinate

DominantDominant

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

Lead FollowSubordinateSubordinate

Dominant

Lead

Follow

( 0.5, 4)

( 1, 8)

( 3, 2)

( 0.5, 1)

Dominant Firm Game


Dominant

Lead

Follow

( 0.5, 4)

( 11, 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


DominantDominant

Lead

Follow

( 0.5, 4)

( 11, 88)

( 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

Sitcom Sports

Network 1 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.


Network 2

Sitcom Sports

Network 1 Sitcom (56%, 44%) (51%, 49%)

Sports (50%, 50%) (46%,54%)


• 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.


Network 2

Sitcom Sports

Network 1 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

Wal-Mart

Aggressive Normal

Wal-Mart

EnterStay out

Enter

Stay out

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

Migros

Wal-Mart

Wal-Mart

Advertising Example: 3 proper subgames

Wal-Mart

Wal-Mart

EnterStay out

EnterStay out

Subgame 1 Subgame 2

Solution of the Advertising Game

Aggressive Normal

Migros

Solution of the Advertising Game (cont.)

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 best-

selling 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

Produce Don’t Produce

Boeing 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 headstart, 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).

Game Theory In Marketing

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