Introduction to practical Game Theory Introduction to practical Game Theory and its corporate applicationsand its corporate applications

Prepared by Manbo LiPrepared by Manbo LiMay 8, 2002May 8, 2002

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Opening ExperimentOpening Experiment

• Each of you give me one buck;Each of you give me one buck;

• Each of you pick one number between 1 and 100. Each of you pick one number between 1 and 100. Then we take the average of all the numbers you Then we take the average of all the numbers you pick, and multiple it by 60% and get number X;pick, and multiple it by 60% and get number X;

• Whoever picks the number that is closest to this Whoever picks the number that is closest to this number X will get all the money.number X will get all the money.

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An example of irrationality in realityAn example of irrationality in reality

• Rationality is a foundation assumption for Game TheoryRationality is a foundation assumption for Game Theory

• If one is rational, he would assume everyone start with 50, If one is rational, he would assume everyone start with 50, the average between 1 and 100. So he will further reason that the average between 1 and 100. So he will further reason that the final number will be 30 - however, if every one is thinking the final number will be 30 - however, if every one is thinking the same way, everyone will pick 30, so the final number the same way, everyone will pick 30, so the final number should be 18… then he continue to think in this way again should be 18… then he continue to think in this way again and again until he picks zero - the equilibrium point!and again until he picks zero - the equilibrium point!

• However, that’s never the case in reality - in group However, that’s never the case in reality - in group experiments, the final number that appears most often is experiments, the final number that appears most often is around 17, given a large enough sample size.around 17, given a large enough sample size.

• Actual outcome depends on how smart the group is, or how Actual outcome depends on how smart the group is, or how smart (stupid) the group thinks their peers are;smart (stupid) the group thinks their peers are;

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AgendaAgenda

• Game Theory in DefinitionGame Theory in Definition

• Game Theory in IllustrationGame Theory in Illustration

• Game Theory in ApplicationGame Theory in Application

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AgendaAgenda

• Game Theory in DefinitionGame Theory in Definition

• Game Theory in IllustrationGame Theory in Illustration

• Game Theory in ApplicationGame Theory in Application

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What is Game theory? - many definitions, but What is Game theory? - many definitions, but you got the pointyou got the point

• Study of rational behavior in situations involving Study of rational behavior in situations involving interdependence. (McMillan, economist)interdependence. (McMillan, economist)

• A formal way to analyze interactions among a A formal way to analyze interactions among a group of rational agents who behave strategically group of rational agents who behave strategically (Dutta, economist)(Dutta, economist)

• In war the will is directed at an animate object that In war the will is directed at an animate object that reacts (Karl von Clausewitz, general)reacts (Karl von Clausewitz, general)

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Key elements of a game we will visit many Key elements of a game we will visit many times in today’s discussiontimes in today’s discussion

• Assumption for playersAssumption for players– Rationality (not doing crazy things)Rationality (not doing crazy things)– Self-interested (to maximize own utilities)Self-interested (to maximize own utilities)

• The strategic environmentThe strategic environment– Who are the players? (decision makers)Who are the players? (decision makers)– What actions are available? (strategic options)What actions are available? (strategic options)– What are the payoffs? (objectives)What are the payoffs? (objectives)

• Rules of the gameRules of the game– What is the time frame? (Repeat game vs. one-shot What is the time frame? (Repeat game vs. one-shot

interaction)interaction)– What is the nature of the interaction? (sequential vs. What is the nature of the interaction? (sequential vs.

simultaneous)simultaneous)– What information are available? (symmetric vs. asymmetric)What information are available? (symmetric vs. asymmetric)– What’s the nature of the conflict? (seriousness and players’ What’s the nature of the conflict? (seriousness and players’

posture)posture)

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Game theory is everywhere - Economics & Game theory is everywhere - Economics & BusinessBusiness

• ““Game theory is hot!” - Game theory is hot!” - Wall Street JournalWall Street Journal, 13 , 13 February 1995, P. A14February 1995, P. A14– Auctioneer and bidders, such as in FCC Spectrum Auctioneer and bidders, such as in FCC Spectrum

auctions in 1993 where government employed a game auctions in 1993 where government employed a game

theory professor to design auction methods ;theory professor to design auction methods ;– Labor union negotiation with employer & repeated game;Labor union negotiation with employer & repeated game;– Negotiation between buyer and seller;Negotiation between buyer and seller;– Airlines’ price wars & tacit collusion;Airlines’ price wars & tacit collusion;– Timing of launch of new products in IT industry;Timing of launch of new products in IT industry;– Evaluation in merger and acquisitions & winner’s curse;Evaluation in merger and acquisitions & winner’s curse;– Insurance companies vs. the insured & asymmetric Insurance companies vs. the insured & asymmetric

information;information;– Others ...Others ...

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Game theory is everywhere - Beyond Game theory is everywhere - Beyond Economics & BusinessEconomics & Business

• Presidential electionPresidential election• International relationsInternational relations• Office politicsOffice politics• Dating strategiesDating strategies• WarWar• Sports gamesSports games• RecruitingRecruiting• Everything...Everything...

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Game theory is everywhere - Even hot in Pop Game theory is everywhere - Even hot in Pop Culture these daysCulture these days

• John Nash & John Nash & Nash equilibriumNash equilibrium

• 20012001 • Prisoner’s Prisoner’s dilemmadilemma

• 20022002• Game of Game of

chickenchicken• 20002000

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AgendaAgenda

• Game Theory in DefinitionGame Theory in Definition

• Game Theory in IllustrationGame Theory in Illustration

• Game Theory in ApplicationGame Theory in Application

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Prisoner’s dilemma - the classic game as a Prisoner’s dilemma - the classic game as a example throughout our discussionexample throughout our discussion

ConfessConfessDon’tDon’t

Don’tDon’t

ConfessConfess

AA

BB

3, 33, 3

0, 00, 0

5, -55, -5

-5, 5-5, 5

• Player: A & B;Player: A & B;• Payoffs: (a, b);Payoffs: (a, b);• Strategies: (don’t confess, confess)Strategies: (don’t confess, confess)

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Nash EquilibriumNash Equilibrium

• Nash equilibriumNash equilibrium– For every game, there exists at least one set of For every game, there exists at least one set of

strategies, one for each player, such that each strategies, one for each player, such that each player’s strategy is best for her given that all other player’s strategy is best for her given that all other players are playing their equilibrium strategiesplayers are playing their equilibrium strategies

• key conditionkey condition– No incentive to unilaterally change my strategyNo incentive to unilaterally change my strategy– The strategies employed can be mixed strategiesThe strategies employed can be mixed strategies

• A byproduct theorem by Nash in his proof using A byproduct theorem by Nash in his proof using TopologyTopology– For every human head, there exists at least one For every human head, there exists at least one

swirl.swirl.

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Prisoner’s dilemma - the equilibrium is not Prisoner’s dilemma - the equilibrium is not necessarily the best payoffsnecessarily the best payoffs

ConfessConfessDon’tDon’t

Don’tDon’t

ConfessConfess

Person APerson A

Person BPerson B

3, 33, 3

0, 00, 0

5, -55, -5

-5, 5-5, 5EquilibriaEquilibria

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AgendaAgenda

• Game Theory in DefinitionGame Theory in Definition

• Game Theory in IllustrationGame Theory in Illustration

• Game Theory in ApplicationGame Theory in Application

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Conventional business strategy focuses on Conventional business strategy focuses on understanding the static environmentunderstanding the static environment

• Who are the players?Who are the players?• What strategic options are available?What strategic options are available?• Who are the payoffs and objectives?Who are the payoffs and objectives?

““3 Cs”3 Cs”““Porter’sPorter’s5 forces”5 forces”

““CoreCoreCompetence”Competence”

Others...Others...

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Game theory driven strategy formulation Game theory driven strategy formulation focuses on focuses on Dynamics Dynamics and and Change the RulesChange the Rules

– What’s the nature of the conflict? What’s the nature of the conflict? (seriousness and players’ posture)(seriousness and players’ posture)

– What is the nature of the interaction? What is the nature of the interaction? (sequential vs. simultaneous)(sequential vs. simultaneous)

– What is the time frame?What is the time frame?(Repeat game vs. one-shot interaction)(Repeat game vs. one-shot interaction)

– What information are available? What information are available? (symmetric vs. asymmetric)(symmetric vs. asymmetric)

Good news: all of these rules can be changed, Good news: all of these rules can be changed, manipulated or influenced to our advantagemanipulated or influenced to our advantage

– Game of ChickenGame of Chicken

– Game of AssuranceGame of Assurance

– Game of CollusionGame of Collusion

– Winner’s CurseWinner’s Curse

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I. Change the nature of the conflict - Game of I. Change the nature of the conflict - Game of ChickenChicken

FightFightAccommodateAccommodate

Don’t EnterDon’t Enter

EnterEnter

IncumbentIncumbent

Potential Potential entrantentrant

10, 010, 0

-5, -5-5, -5

10, 010, 0

5, 55, 5EquilibriaEquilibria

EquilibriaEquilibria

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Commitment and posture matters – Commitment and posture matters – Perception Is RealityPerception Is Reality

• Two Equilibria exist - but incumbent wants the Two Equilibria exist - but incumbent wants the equilibrium of (10, 0)equilibrium of (10, 0)

• To achieve this Equilibria, incumbent needs to To achieve this Equilibria, incumbent needs to convince that he convince that he willwill fight to death if entrant enters fight to death if entrant enters

• Ways of convincing the rival:Ways of convincing the rival:– Serious commitment such as preemptively building Serious commitment such as preemptively building

extra capacity in manufacturing and airline industry;extra capacity in manufacturing and airline industry;– Perception of being “tough” - bluff, PR, advertising, Perception of being “tough” - bluff, PR, advertising,

and etc;and etc;– Historical behaves to make credible threatsHistorical behaves to make credible threats

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A real event...A real event...

Radio conversation released by the Chief of Naval Operations, 10-10-95.

#1: Please divert your course 15 degrees to the North to avoid a collision.

#2: Recommend you divert YOUR course 15 degrees to South to avoid a collision.

#1: This is the Captain of a US Navy ship. I say again, divert YOUR course.

#2: No. I say again, you divert YOUR course.

#1: THIS IS THE AIRCRAFT CARRIER ENTERPRISE, WE ARE A LARGE WARSHIP OF THE US NAVY. DIVERT YOUR COURSE NOW!

#2: This is a lighthouse. Your call.

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II. Change the timing of the conflict - Game of II. Change the timing of the conflict - Game of AssuranceAssurance

Promote/Invest new standard/productPromote/Invest new standard/productDon’tDon’t

Don’tDon’t

PromotePromote

Firm AFirm A(Market Leader)(Market Leader)

Firm BFirm B

5, 55, 5

10, 1010, 10

0, 50, 5

5, 05, 0

EquilibriaEquilibria

EquilibriaEquilibria

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Leadership and first move matters – snowball Leadership and first move matters – snowball effect in industry standardizationeffect in industry standardization

• Two Equilibria exist – “Invest & promote” is best Two Equilibria exist – “Invest & promote” is best for all but very riskyfor all but very risky

• Ways of getting to the ideal equilibrium (10,10):Ways of getting to the ideal equilibrium (10,10):– Market leader must commit first and make the initial Market leader must commit first and make the initial

move, rather than waiting for everything to happen move, rather than waiting for everything to happen at the same time;at the same time;

– Turn simultaneous game into sequential game, and Turn simultaneous game into sequential game, and minimize uncertaintyminimize uncertainty

Example: IP over voice, Java based banking and etc – Example: IP over voice, Java based banking and etc – all are new standards and risky today given still all are new standards and risky today given still

premature technology and services; premature technology and services; Do you have the right to influence the equilibrium?Do you have the right to influence the equilibrium?

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Game in extensive form to demonstrate a Game in extensive form to demonstrate a sequential movesequential move

AALeaderLeader

InvestInvest

Don’tDon’t

BB

BB

InvestInvest

Don’tDon’t

InvestInvest

Don’tDon’t

(10, 10)(10, 10)

(0, 5)(0, 5)

(5, 0)(5, 0)

(5, 5)(5, 5)

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III. Change the interaction of the conflict - III. Change the interaction of the conflict - Game of CollusionGame of Collusion

Airline AAirline A

AirlineAirlineBB

cut pricecut pricedon’tdon’t

don’tdon’t

cutcutpriceprice

(5,5)(5,5)

(0,0)(0,0)(-5,10)(-5,10)

(10,-5)(10,-5)

EquilibriaEquilibria

Airline AAirline A

AirlineAirlineBB

cut pricecut pricedon’tdon’t

don’tdon’t

cutcutpriceprice

(5,5)(5,5)

(0,0)(0,0)(-5,10)(-5,10)

(10,-5)(10,-5)StableStablePointPoint

Repeated learning and Repeated learning and cooperation processcooperation process

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Repeatability and punishment matters – tacit Repeatability and punishment matters – tacit collusion in industry “co-petition”collusion in industry “co-petition”

• A variation of prisoner’s dilemmaA variation of prisoner’s dilemma• One mutually damaging Equilibria existsOne mutually damaging Equilibria exists• How to avoid it?How to avoid it?

• Ways of getting to the optimal equilibrium (5,5):Ways of getting to the optimal equilibrium (5,5):– Signaling: announce commitment of price level through Signaling: announce commitment of price level through

press and advertising; press and advertising; – Punishment: if A cuts price in period 1, B will cut prices Punishment: if A cuts price in period 1, B will cut prices

in the next 3 periods in a row no matter what A does;in the next 3 periods in a row no matter what A does;

Example: card issuers undercut each other Example: card issuers undercut each other though 0% APR, fee waiving and other though 0% APR, fee waiving and other

measures - are there any ways that you can measures - are there any ways that you can slow down this path to non-profitability??slow down this path to non-profitability??

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IV. Change information flow of the game - IV. Change information flow of the game - Winner’s CurseWinner’s Curse

• What is winner’s curse?What is winner’s curse?– Lack of information or asymmetry of existing Lack of information or asymmetry of existing

information on the bidder or buyer side make the information on the bidder or buyer side make the winner actually a loserwinner actually a loser

• ExamplesExamples– Auction Auction – Merge & AcquisitionMerge & Acquisition– LBOLBO– OthersOthers

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Winner’s Curse in action - one example in Winner’s Curse in action - one example in biddingbidding

• In dotcom heydays, brick & mortar A, as one of the bidders, In dotcom heydays, brick & mortar A, as one of the bidders, wants to acquire Internet startup B of the same industry, with wants to acquire Internet startup B of the same industry, with assumed 50% added synergy generation;assumed 50% added synergy generation;

• You know, accurate evaluation is almost impossible here: in You know, accurate evaluation is almost impossible here: in A’s assessment, the highest potential value is $100MM and A’s assessment, the highest potential value is $100MM and the actual outcome could be evenly spread between 0 and the actual outcome could be evenly spread between 0 and $100MM;$100MM;

• So A bid $50MM and won -- a perceived total value of So A bid $50MM and won -- a perceived total value of $50MM*(1+50%)=$75MM;$50MM*(1+50%)=$75MM;

• But in fact B wouldn’t sell itself unless offer is equal to the But in fact B wouldn’t sell itself unless offer is equal to the highest potential it feel it can reach; So the highest actual highest potential it feel it can reach; So the highest actual value of the acquisition is $25MM*(1+50%)=$37.5MM, far value of the acquisition is $25MM*(1+50%)=$37.5MM, far below the prices A pays for!below the prices A pays for!

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An example of how to avoid Winner’s CurseAn example of how to avoid Winner’s Curse

• Before 1960s, American oil companies who won the drilling Before 1960s, American oil companies who won the drilling right in certain area always later found themselves in the right in certain area always later found themselves in the business of losing money;business of losing money;

• After 1960s, American oil companies who participated in After 1960s, American oil companies who participated in bidding:bidding:– always only offer a fraction (0.65 ~ 0.75) of their estimated always only offer a fraction (0.65 ~ 0.75) of their estimated

value in bidding for overseas drilling rightsvalue in bidding for overseas drilling rights– spend money in testing in adjacent fields;spend money in testing in adjacent fields;– those who see critical strategic benefit in certain fields took those who see critical strategic benefit in certain fields took

out full-page ads to signal their intention so others stayed out;out full-page ads to signal their intention so others stayed out;

Example: how should we gather and benchmark Example: how should we gather and benchmark information to make right decision in acquisition information to make right decision in acquisition

and vendor selection?and vendor selection?

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Q&AQ&A