Lecture 3 Oil-Price Negotiation - MIT OpenCourseWare

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Lecture 3Salt Harbor, Prisoners’Dilemmas & Oil Price Game

Debrief Salt Harbor Overview of Prisoners’ Dilemma Situations– The first PD example– Analysis of static game Iterative Prisoners’ Dilemma– Holdup (if time)– Oil Price Game

Hard Hat or Soft Hat?What Should it be?

Which is Better? Black Hat/White Hat: Few earlyconcessions, followed by increasingly largerconcessions White Hat/Black Hat: Generous earlyconcessions, followed by increasinglysmaller concessions Hilty and Carnevale found that BH/WH ismore effective

Prisoners’ DilemmasF

ADAM SMITH(The Wealth of the Nations, 1776)“An individual who intends only his own gain, is, asit were, led by an invisible hand to promote thepublic interest.”(1, 3)(5, 4)(4, 1)(6, 8)

Prisoners’ DilemmaA striking example of howindividual rationality and grouprationality may diverge

“The Drosophila of thesocial sciences”

The Prisoner’s DilemmaAn important class of non-strictlycompetitive situations where the bestoutcome results when the players refrainfrom trying to maximize his/her ownpayoff.

Each player has a dominantstrategy and the use of thesedominant strategies leads to a“bad” outcome (i.e., Non-ParetoOptimal)

TWO SUSPECTS ARE TAKEN INTO CUSTODY AND SEPARATED. THE DISTRICTATTORNEY IS CERTAIN THAT THEY ARE GUILTY OF A SPECIFIC CRIME, BUT HEDOES NOT HAVE ADEQUATE EVIDENCE TO CONVICT THEM AT A TRIAL.HE POINTS OUT TO EACH PRISONER THAT EACH HAS TWO ALTERNATIVES:TO CONFESS TO THE CRIME THE POLICE ARE SURE THEY HAVE DONE, OR NOTTO CONFESS.IF THEY BOTH DO NOT CONFESS, THEN THE DISTRICT ATTORNEY STATESHE WILL BOOK THEM ON SOME VERY MINOR PUNISHMENT.IF THEY BOTH CONFESS THEY WILL BE PROSECUTED, BUT HE WILLRECOMMEND LESS THAN THE MOST SEVERE SENTENCE.BUT IF ONE CONFESSES AND THE OTHER DOES NOT, THEN THE CONFESSORWILL RECEIVE LENIENT TREATMENT FOR TURNING STATE'S EVIDENCEWHEREAS THE LATTER WILL GET "THE BOOK" SLAPPED AT HIM.

Prisoner’s Dilemma Problem StatementTwo suspects: A BTwo Alternatives: Confess C Don’t Confess DC

Prisoner’s Dilemma Payoff TableBCC(8, 8)DC(10, 1/2)ADC(1/2, 10)(1,1)This is a non-zero sum gameNo matter what A does, B comes out ahead confessing.No matter what B does, A comes out ahead confessing.For A, strategy C dominates DC strategyFor B, strategy C dominates DC strategyIf each prisoner chooses his/her dominant strategy, they both lose.Both players would be better off if neither confess

Pareto OptimalityAn outcome that is not dominated by any other outcome is calledPareto optimal.Pareto optimal strategy pairs are (DC,DC) (DC,C) and (C,DC)(1/2, 10)(8,8)(1,1)(10, 1/2)

What if Prisoners Could Communicate?Prisoners might choose strategy (DC,DC). This, however, is not an equilibrium pair, since A and B caneach do better by making a unilateral change of choice. There is incentive to defect, but if both defect, then we areback where we started from. Pre-choice communication cannot help in solving thedilemma unless there is some binding force (legal, moral,etc.) that holds the players to their agreement.

Prisoners and ParadoxesIt is “rational” for each player to confess.There is no strategy that is best in all circumstances.Problems such as this confuse our notion(s) ofrationality.— Collective or group rationality vs. individualrationalityForces us to resort to “Extra-rational” or “Meta-rational”notions (e.g., trust, conscience, etc.)

Applying the Prisoner’s DilemmaEconomists use Prisoner’s Dilemma-type problems in analyzingmarket structures and competitive strategy.PD-type problems are common in the real world.PD creates price rigidity in oligopolistic markets.— Firms may be reluctant to change prices for fear of settingoff a price war.Price leadership as a way around the PD.

Iterative Prisoner’s DilemmaRemoves the static nature of the problem.Allows players to:– Develop reputations– Study competitor’s behavior

When Individuals Meet Often:AxelrodStrategy: A rule that determines the probability of “cooperate” or“defect” as a function of history of interaction.WHAT STRATEGIES ARE:Initially viable?Robust?Stable?

One Possible Strategy: “Tit for Tat”“Tit for Tat”:First move is to cooperate.Thereafter, mimic the last move of opponent.Infinite vs. Finite Trials:In the infinite case, it always pays to cooperate.Cooperative behavior is profitable in expected valueterms, but depends upon the time horizon inquestion.

Why Does “Tit for Tat” Work?Because it is nice (!)Zero-sum myopia, i.e., score envyQuick to anger, quick to forgiveValue of provocabilityValue of clear and consistent strategies

Axelrod’s Genetic AlgorithmSimulation of evolutionComputer tournament Round Robin (14 entries) 2nd round (62 entries)WHAT HAPPENED?TIT FOR TATDOMINATED!Don’t rock the boat!“C” follows CCCBe provocable! “D” follows CCDForget & forgive!“C” after DCCAccept a rut!“D” after DDD(1985)

“Distinguishing Best and Strategic Practices”Keith Allred (2000)Moves to claim value tend to block moves aimed atcreating valueClaiming is competitive and assertiveThe downside of pursuing a cooperative strategyaimed creating value is that it often exposes you toexploitation

Best versus Strategic PracticesBEST PRACTICES:– Those that work well irrespective of what yournegotiating counterparts doSTRATEGIC PRACTICES:– Practices that work well in particular situationswith some counterpart responses and poorly inother situations with other responses

In a formal game-theoretic framework,equilibrium strategies are often, but not always“Best Practice”– Stud Poker bluffing strategiesPrisoners’ Dilemma games are an example of caseswhere equilibrium strategy choice may not be a“Best Practice”– Dominance leads to poor outcomes for bothparties– Holdup!

HoldupRepeated Prisoner’s Dilemma andMonopoly PowerFrom “Repeated Interaction”By Adam BrandenburgerHBS 9-793-116 (1992)Brandenburger op. cit

Holdup Investor A must first decide whether or not tomake an investment of 1 If made, 3 (gross) of economic value iscreated. B then decides how to divide the 3– Divide the NET pie of 2 equally: then each gets 1– Grab the 3 so A is 1 out of pocketBrandenburger op. cit.27

Holdup TreePayoffsSplit the PieInvest 111 1300BGrab the PieADon’t What is likely if the game is played once? Ad infinitum?Brandenburger op. cit.

Time Value of MoneySuppose that future payoffs are discounted forthe time value of money– r is the discount rate– w 1/(1 r) is the discount factorA constant stream of 1 per time period then hasa present value of 1/(1-w) 1/rBrandenburger op. cit.29

A’s BEST STRATEGY:Begin by investing every timeIf B ever takes this whole pie, refuse toinvest thereafter.Brandenburger op. cit.I

Split the pie yields 1(1 w w2 . . . ) 1/(1-w) Take the whole pie once and getnothing after yields 3. A jointly beneficial outcome issustainable if12 3 or w 1 w3

What happens if B splits the pie n times, then grabs? A gets 1 (1 w w2 . . . wn) 1 wn 1The game stops at n 1. B gets 1 (1 w w2 . . . wn) 3 wn 1 This strategy pays for B 1 wn 11 3 wn 1 1 w1 w12oror 3w 1 w3The same as “Take the Whole Pie!”Brandenburger op. cit.

Ways Around This DilemmaCoca Cola facilitated investment in bottling plants byawarding bottlers fixed-price contracts forconcentrateA computer is designed around a specific microprocessor, adoption of a new chip may bejeopardized by a computer manufacturer’s fears ofbeing held up– Intel licensed a new design to a second company (up tointro of 80386 micro-processorBrandenburger op. cit.33

Holdup: Factors that Facilitate CooperationSize of pie– The greater the value to be divided, the greater theincentive to play “tough” BUT future losses fromnon-cooperation are also greater!Discount factor (factor not “rate”):– A higher discount factor w 1/(1 r) means futurelosses from non-cooperation loom largerBrandenburger op. cit.34

Frequency of interaction:– More frequent interaction is equivalent to alarger discount factor– “Maintenance of an exclusive relationshipbetween buyer and seller can increaseinteraction frequency”, an argument for dealingonly with a few longer term suppliers, forexample.– Break down a large transaction into smallerones to achieve more frequent interactionBrandenburger op. cit.35

Observation lags:– If choices are observed with a time lag, futurelosses from non-cooperation are delayed,making cooperation harder!Noise:– Noisy signals make it harder to distinguishtough from cooperative behavior, inhibitingcooperation.Brandenburger op. cit.36

Oil Price GameAnalysis of Payoff Table& Instructions

Price Charged byBATIA 30 20 10A: 2A: 2 30 A: 11B: 11B: 18B: 15A: 8A: 3ALBA 20 A: 18B: 2B: 8B: 15A: 15A: 5 10 A: 15B: 2B: 3B: 5

Iterative Dominance For Alba 20 preferred to 30 For Batia 20 preferred to 30 20 Dominates 30Price Charged byBATIA 30 20 10 30 A: 11A: 2A: 2B: 11B: 18B: 15ALBA 20 A: 18A: 8A: 3B: 2B: 8B: 15 10 A: 15A: 15A: 5B: 2B: 3B: 5

Now, for Alba, 10 is preferred to 20 Now, for Batia 10 is preferred to 20 10 Dominates 20Price Charged byBATIA 30 20 10 30 A: 11A: 2A: 2B: 11B: 18B: 15ALBA 20 A: 18A: 8A: 3B: 2B: 8B: 15 10 A: 15A: 15A: 5B: 2B: 3B: 5

MIT OpenCourseWarehttp://ocw.mit.edu15.067 Competitive Decision-Making and NegotiationSpring 2011For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

Coca Cola facilitated investment in bottling plants by awarding bottlers fixed-price contracts for concentrate A computer is designed around a specific micro-processor, adoption of a new chip may be jeopardized by a computer manufacturer’s fears of being held up – Intel licensed a new design to a second company (up to