Lecture 8

Game Theory

The Power to Constrain an Adversary Depends Upon the Power to Bind Oneself.- Thomas Schelling

Mike ShorLectures 7&8

Game Theory - Mike Shor

ReviewCooperation requires sacrificing immediate profits for a future relationship

The sacrifice is only made if the punishment is severe enough

Punishment that is too severe is not credible


Finite RepetitionUnraveling prevents cooperation if the number of periods is fixed and knownProbabilistic terminationThe game continues another round with some probability p:Equivalent to infinite game$1 next period is worth p todayValue of future ={ value if there is a future }

{ probability of a future } Effective interest rate: r = (1+r)/p 1


LessonsBe careful of finite games

Always a chance of another encounter

Balance severity of punishment!

Mild punishment may not deter cheatingSevere punishments may not be credible


Credibility & Commitment The difference between genius and stupidity is that genius has its limits.Albert Einstein

The difference between 'involvement' and 'commitment' is like an eggs-and-ham breakfast: the chicken was 'involved' - the pig 'committed'.Unknown


Talk is CheapPromises

Continental Airlines said yesterday that it would raise airfares on about two-thirds of its routes to take effect September 5. - The New York Times August 29, 1992

Continental Airlines has dropped its plan to raise domestic airfares by 5%. - USA Today September 4, 1992


Talk is Cheap Threats

On January 5, Boeing, the worlds top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever. Some in the industry suggest Boeings move is a bluff to preempt Airbus from going ahead with a similar plane. - Business Week, 1993


And Getting Cheaper Airbus announces commercial launch of the A3XX, the largest civil aircraft ever built.

Boeing has said that there is no market for such a large plane and has decided to modernize its trustworthy 747 family of planes rather than build its own megaseater. - Associated Press June 23, 2000


Conventional Wisdom

Dont burn bridges.Decrease downside risk.It is nice to have more options. While you may have money to burn, you shouldnt burn money


Strategic CommitmentYou are not credible if you propose to take suboptimal actions.

Specifically, if a rational actor proposes to play a strategy which earns less than maximal profit.

How to be credible?


CredibilityRemove strategiesfrom your own set of future choices the strategies that may tempt you in the futureGiving away your patent?Reduce payoffs from those strategies that may tempt youCustomers as hostages.Become irrationalRemove human meddling


A Non-credible ThreatTen suppliers each have two options:Deliver on time at a cost of $70,000Deliver a week late at a cost of $20,000Delivery results in $100,000 payment

I need at least nine suppliers and the suppliers know this


A Non-credible ThreatI threaten not to deal with a late supplier (at most one)

Two equilibria:All deliver on timeAll deliver late (the likely equilibrium)Even if only one other supplier delivers late, it is in my best interest to do so: (80) > 30


A Credible ThreatI number suppliers (110) and refuse delivery from the lowest numbered one among those who are late.Supplier 1 delivers on time (better than getting nothing)Thus, supplier 2 delivers on time


Removing Strategies IDelegation

In contract negotiation, can squabble over many detailsInstead, send an agent with power of attorney to sign as is or walk awayHaggling over prices in a department store

Learn from government bureaucracy: The rules wont allow me to do what you ask


Delegation ExamplesHuman resource departmentsShield from requests for higher salariesHR execs not compensated based on employer valueCollection agenciesshield from pleas or threats of the debtorreinforce repayment to protect reputationAccounting firms overseeing contestsAccountants payment not tied to outcomeConcerned with reputation for fairness


Removing Strategies IIBurning BridgesPower comes from not being able to retreatAllow opponent to retreat (Sun Tzu)

The PatchHunt for Red OctoberCortes upon arriving in Mexico


Burning Bridges(Example 1)Semiconductor patent sharing

Mosaid Technologies, a designer and licensor of semiconductor chips and technologies, just announced a patent sharing deal with Mitsubishi Electric

Share patent with another competing firmCommit to chip supply to production plantsCommit to no opportunistic behavior


Burning Bridges(Example 2)Capacity constraints

New entrant commits to low productionThe puppy-dog ploy

Puppy Dog PloyStay weak to avoid an aggressive response

Apple v. Microsoft


Removing Strategies IIIIrrationality

U.S. / U.S.S.R. nuclear deterrence Mutually Assured Destruction (MAD)like Grim Trigger Strategy Proportional Responselike Tit-for-TatWant a lot of deterrenceWant irrationality to be credibleDr. Strangelove & the Doomsday device


Dr. StrangeloveSeverity

Create fear in the mind of the enemyIrreversibility

Must be irreversibleIrrationality

Not something a sane man would doPracticality

Punishment shouldnt be too harshClarity

Tell the world


Use of ContractsPromises vs. Threats

Promises can sometimes be credible through a contract with the party to whom you are making the promiseNot always: Mario Puzos The GodfatherThreats can never become credible by use of a contract with the party you are threateningMust contract with third party


Reducing PayoffsContracting with customers to commit to competitors

Price-matchingMost Favored Customer clausesContracting with lenders to commit to a take-over

Interest-rate rise if loan amount increases


Example From Long Ago Two firms: Firm 1 and Firm 2Two prices: low ($4) or high ($5 )3000 captive consumers per firm4000 floating go to firm with lowest price

Firm 2LowHighFirm 1Low 20 , 20 28 , 15High 15 , 28 25 , 25


Contracting with CustomersThe game is a prisoners dilemmaBoth firms prefer:{High,High}Only equilibrium: {Low , Low}Cannot credibly promise to play HighEven if committed to High, other firm would still respond with LowHow to resolve this?Third party contracts with customers


Most Favored CustomerSay in period 1, the firms colluded and each sold to 5000 customers

In period 2, firms must refund to last periods customers $1 each if price is low

What is the impact on the game?


Most Favored Customer




Contracting with LendersTakeover offer: $200 millionYou can afford $20 million / yearFinance takeover for 20 years at 7%Add penalty: if amount greater than $200 million, +1.5 points on interest rateAnnual Payments:

$200 million:$18.6 million / year$210 million:$19.6 million / yearwith penalty: $21.9 million / year


Extravagance in Nature


Extravagance in Business


IrrationalityBurning money

Commit to long-term market planCommit to high quality productsFirm can produce high or low qualityCustomers cannot observe quality

Once customers buy a product the first time, observe quality, punish dishonest firms

QualityMarginal costValueHigh$8$50Low$4$20


Burning MoneyProducing high quality is more profitable

$50 - $8 = $42 > $16 = $20-$4Pretending you are high quality is best

$50 - $4 = $46Incentive to lie:

Customers do not believe in high qualityCustomers only pay for low qualityFirm only produces low quality INEFFICIENT AND UNPROFITABLE


Burning MoneyAnnounce high quality and burn $50

QualityProfitMoney BurnedNet ProfitHigh$42/year$50$8 loss this year, $42 in the futureLow$46 once$50$4 loss this yearNo Entry$0$0$0


Burning MoneyBy burning $50, convince customers of your high quality:

$8 loss this year, $42 profit in the futureWithout burning money, can only sell low quality:

$16 profit this year and in the futureGaining credibility by burning $50

Invest in future relationship with customers


Forcing Your OpponentSimilar tactics for making your opponent commit to strategies in your favorIncreasing his strategy space

Excluding bargaining agentsLowering his payoffs

Poison pillsRaising his payoffs

Reputation bolstering


Price MatchingIf one firm charges low, it does not gain any additional customers, since the competitor automatically matches it.

What is the effect on the game?

NASDAQ order preferencing?


Price Matching




Commitment Is Counterintuitive COMMANDMENT.

Reduce your strategy space and decrease your own payoffs to commit.

Increase your opponents strategy space and alter your opponents payoffs to preclude the rival from committing.Hurt yourself to help yourselfHelp your opponent to help yourself


CommitmentUnder UncertaintyAn offer you cant refuseAfter a seemingly successful interview, the interviewer asked where the firm ranks on your list of potential employeesBefore answering, you are told:

The firm only hires applicants who rank it firstIf the firm is in fact your first choice, then you must accept a job offer in advance, should one be made


Commitment Under UncertaintyWhat to do?

Binding early-decision college applications

Why make such proposals?

Take advantage of your uncertaintyTake advantage of your risk-aversionMake you commit before they do!


Flexibility vs. CommitmentFlexibility in light of uncertainty about eventual outcomes generates value

Keeping your options openMust be balanced against strategic value of commitmentOption Value:

The additional expected profit from remaining flexible above the expected profit earned from committing


ExampleOption Value of DelayA firm can spend $100 million on an investment to enter a new marketMarket demand uncertain:

High acceptance: revenues of $300m(Probability=0.5)Low acceptance: revenues of $50m(Probability=0.5)Two options:Invest today in the presence of uncertaintyWait a year for full revelation of information


Calculating Option Value Immediate investment:

E[]=(1/2)(300-100) + (1/2)(50-100)= $75 million Delayed investment:

Only invest if high acceptanceE[]=(1/2)(300-100) + (1/2)(0) = $100 million Option value:

$100 - $75 = $25 million

Countervailing force: by waiting, the firm risks having the opportunity pre-empted by competitors


Philips, N.V.Capacity commitment in CD introductionPhilips: innovators advantage

Initiate construction of plant ahead of competitorsDecision problem of Philips in 1982:

Build a disk-pressing plant in the U.S. And invest in a substantial amount of capacity to deter potentially entry (Sony, etc.)Delay decision until commercial appeal of CDs can be determined. Import CDs to the U.S. To test the waters.


Option Value: Three Casesq probability of mass acceptance of CDs

Monopoly Benchmark:

Philips should wait if q < 0.380Sony competition, equal information

Philips should wait if q < 0.006Sony competition, better information

Philips should wait if q < 0.130


SummaryPure option value

In the absence of competition, Philips would have been better off waiting and retaining flexibility if the probability of acceptance was 0.38 or lowerCommitment value

Faced with competitors who are as well informed, Philips would be better off building the U.S. plant right away even in the presence of uncertaintyInformational advantage

Given proprietary information through its CD operations in Europe, Philips should remain flexible if the probability of acceptance was 0.13 or lower


EvidencePhilips did not build a U.S. Plant in 1983

Its assessment of the likelihood of general acceptance did not meet the thresholdMarket realization (surprise!)Sony constructed a U.S. Plant in 1984

Terry Haute, IndianaPhilips attempted to compete

Increased capacity in Hanover, Germany plantPhilips decided to invest in a U.S. Plant

Only after the Sony plant was fully operational


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Lecture 8