The Strategist August2012

7/31/2019 The Strategist August2012

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Competitive exams form an integral part of our lives. Its what segregates the objective? He or she wants people who understand the problem to get thewinners from the mediocre, the dedicated from day dreamers, the hungry answer right and those who dont to get it wrong. It seems likely that he hashunters from those who just want to have some fun. Its what schools and chosen the wrong answers carefully so as to be appealing to folks who dontcompanies use to judge your mettle. And its what brought you and me here in quite know the answer. For example, in response to the question: What is thethe first place! Regardless of which year you are in, the memories of ones JEE number of rings in the Olympic flag, an option of 1000 or square root of 2

days are bound to stay fresh in everyones mind. And today we challenge you is unlikely to lure any candidates. But an option like 6 seems more alluring.2to put your MCQ skills to use once again! ITS TIME TO PLAY A GAME! Turning this around, imagine that the odd answer 32 cm really is the right

2answer. What kind of question might have 32 cm as the answer but would lead

The rules of the game are simple. All you need to do is to find the answer to the someone to think 32 is right? Not many. I mean, you cant just add tofollowing question from GMAT (the test for MBA aspirants). +10 for the right anything thats supposed to be rational ! Have you met my newanswer -5 for wrong. Here we go! boyfriendHe bought me a ring worth 5678 bucks!! Thus we can truly rule

out 32 as being the correct solution.(Q)FHGkhlkjsdklvmfmveopudfhtrewrupoewrpfo***fnejh$%%&&@FJ,LJLJF()(FGJGJ!@#^FHJG Lets now turn to the two perfect squares, 4 and 16. Assume for a moment

2XHEHhdndncndvba^%*()$#@%&*gdjkhfvd that 16 cm is the correct solution. A and a perfect square suggest that thefjvlkjka ? question could be asking about the area of a circle with radius. The correct

2formula for the area of a circle is r . However, the person who didnt quite

2 2

a. 4cm b.8cm remember the formula might have mixed it up with the formula for the2 2 2

c. 32 cm d. 16cm e.32cm circumference i.e .2r. (we assume that someone so uninformed wouldntbother to check the units) Note that if r = 4, then 2r is 8, and that would lead

So! Whats your answer? the person to the wrong answer of (b) A dream come true for any examiner!2The person could also mix and match and use the formula 2r and hence

Okay, we recognize that youre at a bit of a disadvantage of not having the believe that 32 or(e) was the right answer. The person could leave off the Question. Unfortunately copyright laws prevented us from reproducing it. and come up with 32 or (c) as it appears unique! Or the person could forget toStill, we think that by putting on your strategic hats you should be able to figure square the radius and simply use r as the area, leading to 4 or (a). Init out. summary, if 16 is the correct answer, then we can tell a plausible story about

how each of the other answers might be chosen. They are all good wrongFound it yet? No? Well then, lets do this together. answers for the old bugger.

stLets 1 state what most of us have already done thanks to the hard and fast Now, what if 4, the other option with square and is the correct solution (soelimination methods taught in JEE coaching factories of our country. The odd that r = 2)?answer in the series is c. Since it is so different from the other answers, it is Think now about the most common mistake, mixing up circumference withprobably not right. At this stage some of us may start thinking that the answer area. If the student used the wrong formula, 2r, he or she would still get 4

2is (e) i.e. 32 cm . Why? Perhaps because it is similar to the odd answer regardless of units. There is nothing more frustrating from a test makersnumerically and our past experience tells us that whenever you have 2 options perspective, than allowing the person to get the right answer for the wrongwith similar digits one of them is likely to be the answer. reason. Hence 4 would be a terrible right answer, as it would allow too many

people who didnt know what they were doing to get full marks!So is that your final answer? If it is, then we present to you a -5.

At this point we are done!Think further! The fact that the units are in square centimeters suggests an So, now! What was your initial answer? (d)? Take a +10 mate!answer that has a perfect square in it, such as 4 or 16. It is at this stage that --------------------------------------------------------------------------------------------------you need to put on your strategic hats. Think of the game that the old buggerwho set the question is trying to play with you! What is that persons

The StrategistThe KGPian Game Theory Society Second EditionAugust, 2012

Lets Play a Game

PRISONERS

DILEMMA

RACK YOUR

BRAINS!

THREATS AND

PROMISES


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The KGPian Game Theory Society The Strategist 2

Prisoners Dilemma

trategic thinking has long been an object of study in economic theory and exploded phenomenally over the past ten years.

related areas, and is most purely expressed in classical mathematicalSgame theory. The existence of the world wide web and the Algorithmic Game Theory is an area in the intersection of Game Theory andomnipresence of computers make strategic behavior an everyday concern for Algorithm Design, whose objective is to design algorithms in environments.

both, man and machine: How should I bet in a web auction? According to The central research themes in AGT differ from those in classical

which rules should ads show up in a web search result? Why should a computer microeconomics and game theory in important, albeit predictable, respects.

forward a foreigners internet packets? Ibility results, upper and lower bounds on feasible approximation guarantees,

Well, in the past five years, Algorithmic Game Theory emerged as a field with and so on.These themes, which have played only a peripheral role in traditional gamean entirely new perspective when computation met with game theory.theory, give AGT its distinct character and relevance.We can see AlgorithmicGame Theory from two perspectives:Introduction

The primary role of a computer evolved from a stand-alone, well-understoodAnalysis: Analyze current implemented using Game Theory tools: calculatemachine for executing software to a conduit for global communication,

and prove properties on their Nash Equilibria, Price of Anarchy.content-dissemination, and commerce. Two consequences of this phasetransition were inevitable: theoretical computer science would respond by Design: design games that have both good game-theoretical and algorithmicformulating novel problems, goals, and design and analysis techniques properties. This area is called Algorithmic Mechanism Design.relevant for Internet applications; and game theory, with its deep and beautifulstudy of interaction between competing or cooperating individuals, wouldplay a crucial role. Research on the interface of theoretical computer scienceand game theory, an area now known as algorithmic game theory (AGT), has

Simulations of games in real-time often hint a lot of things and brings

out the Equilibria in games easily.

Have a look at Gambit!!!! http://www.gambit-project.org/doc/index.html

Algorithmic Game Theory

If B cooperates (we are constrained to column 2 now) then the best strategy forrisoners Dilemma is a classic game of strategy which depicts how in

certain situations individual players might not cooperate even if it is in

their best interest to do so and this makes it quite interesting. Further itPhelps in developing the understanding of what governs the balance between

cooperation and competition in any social setting.

Now let us get acquainted with the best known game of strategy - The

Prisoners Dilemma.

Commissioner James Gordon catches two men for a crime but doesnt have A would be tosufficient evidence to convict them for their crimes. So he puts them in betray (since a payoff of 0 is better than a payoff of -1, or in other words not

going to jail is better than serving 1 year in jail).separate cells in isolation to each other and offers each of the men a similarIf B betrays (we are constrained to column 3 now) then the best strategy for Adeal if one testifies against his partner and the other remains silent then theshould be to betray (since a payoff of -3 is better than a payoff of -5 or in other

one who testifies shall go free and who remains silent gets a five year prisonwords serving 3 years in jail is better than serving 5 years in jail).

term. If both remain silent then both will get a minor term of one year for minorThus no matter what B chooses it is better for A to Betray. This is called a

charges (say possession of firearms but shall not be convicted for the actual dominant strategy in technical terms which means that no matter what your

crime). If both rat out each other then the commissioner shall have two opponent chooses it is better for you to choose a particular strategy only or in

other words your strategy is independent of your opponents strategy. Sinceconvictions but because they cooperated with the police they shall get an earlythe above matrix is symmetric because the choices given two the convicts are

parole thus a jail time of 3 years each.same we can easily see that for B also the best strategy would be to betray.

What should the convicts do -testify against their partner (betrayal) or remain Check that for yourselves if you are not sure!silent (cooperate)? Thus each would decide to betray the other and get a payoff of -3 each; even

though they both would have been better off if they had chosen to cooperate (-Think for a while what would be your strategy had you been one of the

1,-1).convicts.Betray, betray is also the Nash equilibrium of this game. Nash equilibrium is a

It is rational to assume that each convict is only concerned with lessening hisstrategic profile from which a deviation by any one player would hurt the

time in jail. The interesting symmetry of this problem is that the logical decision payoff of that player and hence that player shall not deviate from that position.would leave each one betraying the other, even though their individual payoff Thus it is a position of equilibrium; we shall not observe deviation from that

strategic profile.would be greater had they cooperated.Let us see what happens if one of the convicts deviate from the position ofLet us see this more clearly using a pay off matrix. Payoff is nothing but theequilibrium. Here if A decides to deviate his strategy from betrayal toutility or the outcome that each player gets. A payoff matrix is a elegant way ofcooperation, then his payoff would become -5 worse than his current payoff ofpresenting the outcomes of a strategic game. It takes the strategy profile (that-3 (top right cell of the matrix). Similarly if B decides to deviate that is heis a specification of strategies for every player) as the input and yields adecides to cooperate then his payoff would become -5 (bottom left cell of therepresentation of payoff for each player as its output. In each cell, the firstmatrix). Thus none of the players would individually like to deviate from thenumber represents the payoff to the row player (in this case convict A), and thebetrayal, betrayal strategic profile.second number represents the payoff to the column player (in this case convict

B).

What is the dilemma here? It is left to the reader to figure out the dilemma.Now let us analyze the options of each of the convicts. Lets us put ourselves in

the shoes of convict A. What are his options?

A/B Cooperation(B) Betrayal(B)

Cooperation(A) (-1,-1) (-5,0)

Betrayal(A) (0,-5) (-3,-3)

Hello everyone! game theory in the field of biology too.

We are back with our second edition of The Strategist. For those who are going to We incorporate some mind boggling puzzles in each of our papers that uses the

read The Strategist for the first time, let us briefly introduce ourselves and The concepts of game theory, which we are sure will interest you.

Strategist. We started last year when our founder Manoj Gadia took this initiative. In this

The Strategist, a monthly paper on game theory is an initiative by The Kgpian small span of time we have started publishing The Strategist, working on theArt of

Game Theory Society (KGTS). In this endeavour of ours we try to bring to you some Strategyproject, conducted sessions of Strategia Hub- fortnightly discussions on

very interesting articles and developments in the field of Game Theory . Game game theory and also a Finance Talklast year. To know more about us follow us on our

theory is the study of strategic decision making, that is, whenever two or more facebook page https://www.facebook.com/The.KGTS

players are involved in any cooperation or conflict situation game theory can come After reading the above section if you are curious to know more about Game

handy. Game theory is mainly used in the field of economics, business, political Theory and strategic thinking then dive in and read the remaining paper, you are

science, psychology and logic. There have been some fascinating developments of gonna love it! Team KGTS

Welcome


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Prisoners Dilemmas of KGP !

their bosses and not comrades looking for them. Thus each soldier has spenthe brief introduction to Nash Equilibrium and prisoners dilemma would5.5 hours to complete a 4 hour task, that too inefficiently. This carries on till theprobably have raised some questions in your mind? Is this mereend, leading to heavy wastage of time and energy and poor academictheoretical humbug or do these number filled boxes actually make aTperformance.difference to my life? Well, actually, it does! Read on to find out the

various prisoners dilemmas that every KGPian faces during his day. The * But why does this happen? Because each soldier is caught in a prisoners

marked sections will especially appeal to the more experienced KGPians. So dilemma as shown below for two soldiers A and B:here we go.!

To GPL or not to GPL?

From hostel rooms that remind you of Mohenjo-

daro to obnoxious room-mates who refuse to buy a

toothpaste, mess food that tastes like fevicol to

proud professors obsessed with attendance,

pestering drams secys to clingy girlfriends KGP is

full of things that are nothing less than pain in the

ass. But when it comes to sending true shiversThe payoff values are assigned using following logic: If A comes on time and Bdown your posterior, nothing can overpower the age old tradition of GPL. GPL-doesnt then A has additional burden of finding B. B gets more leverage time toan event that reminds us of the soft patting we received on the posterior fromcomplete other personal work. Thus for both A and B Dont come on timethe pretty hospital nurse while being held upside down, soon after we wereseems to be the dominant strategy, even though both would have benefited byborn. An event where dozens leave their work and gather around to witness

coming on time and getting the work done.the dramatic transformation of firm leather to mellow gelatina. An eventIn reality only about half the soldiers do the work. If all soldiers had agreed towhere the predators swing their footwear with satanic conviction and the preydo their part the work could be completed in 2 hours saving them all 3.5 hoursyells for his life, clinging on the pillar as if begging it to strengthen hisof time!fragmenting backside.

Clearly, GPL is fun only as long as you are not the victim. And given a choiceTO BUNK OR NOT TO BUNK?most of us would rather not go through it. Now let us consider the case of twoCome October and the thought on everyones mind isfrust KGPians- A and B who are faced with a choice of whether or not to GPLOnly 4 days off for Durga Puja? And I thought I wasi.e. whether to Score or not to Score. It is Bs GPL day.studying in Bengal!. Typically students respond to

this situation by bunking the Thursday and Friday

classes to extend their stay at home. However if one

of these days is marked by a lab period or a class test,

most students would be compelled to cancel their

bunking plans and make do without mummys food

for 2 more days. But what if none of the students of

that department turn up for the lab or the test? It may be mentioned here thatTaking into account the sentiments of a true frust KGPian, A would prefer to we do not intend to encourage mass bunking among students but are merelyscore and yet not be sored upon. He may choose to not score and hope for B to providing a logical explanation to a common phenomenon. Now, think fromfollow suit when its his turn yielding both a payoff of (1,1). Or he may score the professors point of view. They are responsible for your academic growth.and hope for B to try and set an example of righteousness yielding him a payoff Your performance reflects on their performance. Can a professor really affordof +3 with sadistic pleasure. However if he doesnt score there is every chance to fail everyone who did not appear for the test? Can he really afford to let onethat hell end up with a payoff of -3. Hence A chooses to go with his predatory missed lab affect the whole class grades? The answer is obvious. And yet, mostinstincts and takes a swing. B faces a similar situation when its his turn and of us would fear to bunk a lab or test. In fact almost all plans of mass bunking indoes the same, giving both a payoff of -1 and a blue posterior! Here Score- such situations turn out to be a failure. There is always someone/group ofScore is a Nash Equilibrium. QED: GPL is here to stay! people who cannot resist the wonderful aroma of a chemicals, machinery and

blank papers and this someone ends up getting better grades than rest of the

class. Clearly, all would benefit by spending that extra day at home. Yet most ofTo Illu or not to Illu?us give in to the fear of that someone who may spoil the party. ThatsIllumination and rangoli is without doubt the most spectacular event of thebecause we are all trapped in the following prisoners dilemma: Assume theKGP calendar. An event that stands for unity and team spirit and highlights the

st nd class to be divided into 4 groups- Maggu, Semi Maggu, Non maggu , Peace-uniqueness of IIT Kharagpur. There is a often a complaint by 1 and 2 year

maru. We consider the dilemma of Maggu and Semi-maggus. We assume thatstudents that their not so voluntary participation in Illu is the main reasonif Maggus and Semi-maggus make their decisions independently (for theyfor their beautiful panjis. In fact a common problem during Illu in almost every

nd would rather not trust each other), and the others will respond according tohall of residence is the gathering of junta to do the work. Ask any 2 yearwhat they think the Maggus and semimaggus will do.student why he doesnt turn up at the declared time do start the work and you

are bound to get a reply like No one else turns up on time! If I reach on time, I

will be assigned the annoying task of dragging my batch mates out of the

rooms and toilets- as if I have nothing better to do. Before analyzing further,st

let us keep in mind that Illu is here to stay and the work will be done by 1 andnd

2 years- referred to hereafter as the soldiers. Lets assume that a working

time of 8:00 pm 12 am has been announced for each day. What happens inst

the 1 week? Out of a batch of around 200 soldiers, at most 30 turn up on time.

Among these, 10 are now assigned the task of assembling the remaining

battalion. The folks who do not turn up on time use this leverage time toThe payoffs are described as follows. Both magus and semi-maggus want to go

complete records or carry out other leisure activities. And by the time all thesehome, however they also want to top the class. They would prefer to not write

prisoners of war are captured, its 11.00 pm! Consequently the work now goesthe test provided the other follows suit. The best case possible for them would

on till 2:00 am to make up for the time lost (not till 2:30 am as some work has be if they write the test and the other doesnt. They will both benefit partiallyalready been done by the 20 present on field from 8:00am). Thus every soldieron bunking the test as they will have an equal chance of performing in the

who came on time has spent 6 hours to complete a 3.5 hour task. On the otherrescheduled test or exams. However the temptation to write the test is too

hand the late comers had to work for only 3 hours!high and they both end up getting a low payoff of (-1,-1). The ironic

What happens the following week? Practically no one turns up on time! The consequence of the prisoners dilemma form of Nash Equilibrium is wellgroup commanders (read HCMs) now take up the task of pulling the soldiers demonstrated here! We leave the reader to ponder over the solution to thisout of their burrows. The soldiers are captured in 2 hours and the work again dilemma.. ;-)goes on till 2:00 am. However, unlike before, the soldiers spend most of these 2

hours hiding and get at most half hour to complete records- as this time, it was

A / B-> Score Dont Score

Score (-1,-1)=NASH EQM (3,-3)

Dont Score (3,-3) (1,1)

B->/A Come on time Dont come on time

Come on time (-2,-2) {4 hours each} (-4,-1) {6 hours, 3hours}

Dont come on time (-1,-4) {3 hours, 6hours} (-3,-3) {5.5 hours each}=

NASH EQM

->

->Maggu->/Semi Maggu Write the test Bunk the test

Write the test (-1,-1)=NASH EQM (5,-5)

Bunk the test (-5,5) (2,2)

->


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President seems the most sought-after choice in this case to remove the aboveackward reasoning is an important aspect of Game Theory. This statement arises

m o d i f i c a t i o n s . .from the fact that the outcome of your actions isn't solely dependent upon yourBperspective of the situation. Remember, a coin has two sides with both being equally

So, this new power seems to be as a perfect tool in favour of the bill and we aresignificant. It proceeds by first considering the last time a decision might be made andsupposed to get a perfect Jan Lokpal. But WAIT!! Did we consider, what effectschoosing what to do in any situation at that time. Using this information, one can then

implementing this line-item veto will have on the parliament?? The government,determine what to do at the second-to-last time of decision. But, when the situation aware of the fact that President is a supporter of the bill will know for sure that theinvolves another person, to make your plan count, you have to go all the way back topoints which might benefit the corrupt politicians will be vetoed out. In this case, willthe opponent's side of situation and come back to the action part of the plan. Onlythe government be willing to pass-on the modified bill to President?? This changes theafter that, your part of the plan will be truly meaningful.perspective of entire situation. The bill which was about to be passed in a slightly

modified form, won't be passed at all. The following diagram justifies our hypothesis:Let's look at an example of how backward reasoning changes the viewpoint of a

situation which seemed positive in a thinking forward fashion. In the Indian law

making procedure, the president has a power to return or pocket veto the bills

passed by the Parliament i.e if the president doesn't feel the entire bill or parts of

bill to be befitting, he/she can either reject the bill and resend it to the parliament

or take no action, in effect suspending the bill. However, the president can't

sanction the bill partially. He either has to sanction the complete bill or reject the

same. Now let's assume hypothetically that due to public pressure the Lokpal Bill if

finally passed by the Lok Sabha and Rajya Sabha but certain modifications are

made to the ideal image projected by Anna Hazare and group to preserve some if

not all interests of the top politicians. Here we assume that sufficient negotiations

have already occurred b/n the 2 houses and thus they are grouped under the

common term parliament. Assume that the President is a staunch opposer of

corruption who is tired of the situation in his country and for once, wants to

actually use his powers. Let the Lok Pal bill that is passes by the parliament have 2

facets : G being the part that controls the activities of all government officials

regardless of what post they hold and B being the part that exempts some top

politicians from such control. The president wants only G, the parties want only B.

The following table gives the payoff values (i.e the satisfaction that each party will

get, expressed in terms of numbers if the given event was to take place) for the 2

parties- the parliament and the president, 4 being the highest payoff (when both Clearly the payoffs received by the Parliament is same whether or not itstget exactly what they want) and 1 being the lowest (when they get only what the passes the bill in form B. So it doesn't make any sense to pass it in the 1 place. Thus

other wants). Since even element G benefits the society partially i.e at least the low both parties have received their2nd lowest payoff when they could have received theindlevel corruption is taken care of the payoff is 1 and not 0 or negative. 2 highest. The country of course, loses much more that just pride.

This situation illustrates an important general conceptual point. In single-person

decisions, greater freedom of action can never hurt. But in mutual decisions, it can

hurt because its existence can influence other players' actions. Note that the pocket

veto power has only been used once in Indian history. Also although the president is

bound to give his assent if the bill is sent unchanged to him for the 2nd time, this

hardly happens in the Indian parliament. Most politicians are bent on maintaining a

false respect for their seniors. They have the urge to score political points and some

desired modifications are always made before passing the bill for the 2nd time. Thus

not giving the president a line item veto helps bring about some desired

improvements, if not all. Also, it prevents the rise of a dictatorial head of state.Obviously the president will sign a bill containing the elements of G and B, or one with The question may arise; there are a thousand ways your opponent may think, which

G alone, but will veto one with B alone ( as he has only the option of signing or way to follow? There are complexities, but if you know your opponent well, guessingrejecting). Knowing the President's bold and yet rational behavious, the Congress what step they are most likely to take shouldn't be a difficult task.chooses the package as can be seen from the tree below.

WHAT IF YOUR OPPONENT IS A COMPLETE STRANGER?

Game theorists and experts have been working on such a situation via the

ULTIMATUM game. This is the simplest possible negotiation game: there is just onetake-it-or-leave-it offer. The ultimatum game has two players, a proposer, say A, a

responder, say B, and a sum of money, say 100 rupees. Player A begins the game by

proposing a division of the 100 rupees between the two. Then B decides whether to

agree to A's proposal. If B agrees, the proposal is implemented; each player gets what

Aproposed and the game ends. If B refuses, then neither player gets anything, and the

game ends. The twist comes from the fact that both A and B are complete strangers, so

that they can't judge their decision based on the opponent's instincts.Pause a minute

and think. If you were playing this game in the A role, what division would you proposeWe show the selections at each point by thickening the chosen. We do this for all the

points where the president might conceivably be called upon to choose, even though Ideally one may think that A will propose 99:1 and B has no option but to take it. But,some of these are not likely to be part of the Parliament's choice. The reason is that pause again and think, would you have accepted the offer? The experiment showedParliament's actual choice is affected by its calculation of what the president would results which were far from ideal with 50:50 divisions in some cases and rejection ofhave done if Congress had counterfactually made a different choice; to show this logic e v e n 8 0 : 2 0 d i v i s i o n s b y B i n s o m e c a s e .must show the president's actions in all logically conceivable situations.

Our analysis of the game yields an outcome in which both sides get their second best So, be careful dealing with strangers. Ideal notions of human behaviour don't apply to

preference i.e the Lok Pal bill is passed to combat corruption but with some conditions everyone.that favour top ministers.

.

It has been suggested by many concerned citizens that the President should be given

more powers, for e.g he should have the power to line item veto the bill i.e pass only

the parts of the bill he feels are correct. Let us assume that the President has finally

been given these powers. Thus, implementing line-item veto in powers of the


Look forward and reason backward


5/6

hreats and promises are very important tools in making competitive This is perhaps genesis of the problem of making credible strategies. I mean, if

strategies in Game Theory. The right threat, made to the right person at cant even believe a threat from God, whose threat can we believe? The mainTthe right time can work wonders for a player. It can solve cases and deter problem with Gods threat was that it was too big to be credible especially fornuclear wars. It can help you win companies and command loyalty. It can put someone with Gods sanity. The destruction of his most prized creation isyou in history books or destroy your image forever! Threat making is an art and something that you do not expect from the creator.overuse of it can spoil your image permanently. So beware: Do not use it unless In fact large threats made on small issues or to the wrong person can oftenabsolutely necessary and be prepared for the side effects. Commitments and make you look like a fool. That is the reason why you simply cannot say topromises on the other hand are safer moves but do not guarantee immediate someone on the dining table, Pass me the salt or Ill break your jaw. Youraction. dining table neighbors may be the obstinate kind who revolts at any prospectTo define technically a commitment is an unconditional strategic move. of bullying, or a tough guy who enjoys an opportunity for a fight. If he refuses toThreats and promises are more complex conditional moves that are meant to comply, you must either go through with thethreatened action or back downforce your opponent into doing what you desire. Consider the case of a bank and face the humiliation and loss of reputation. This is also the reason why Balrobbery- The conman forces the staff to follow his orders at gunpoint, Dont Thackeray contrary to his usual practices, cannot directly threaten Sachinmove, or Ill blow your head off. This undoubtedly eases the process of getting Tendulkar despite his obvious dislike for Sachins anti Shiv-Sena remarks.what he wants but theres an added danger- that of getting arrested for not 1 Sachin is too popular among the masses and damage to him will infuriate evenbut 2 crimes- robbery and attempt to murder. Thats where the dangerous side Thackerays followers.of threats comes into picture. It is a response that punishes the other player fornon-compliance with your wants but at some cost to oneself. Because threats Very often when you dont know the exact size of a threat that is needed toand promises indicate that you will act against your own interest, their deter or compel your adversary you would want to keep the size as low ascredibility becomes the key issue. After others have moved, you have an possible to minimize the cost to you in the event that things go wrong and you

incentive to break your threat or promise. The other players can sense these have to go through with the action. So you start small and gradually raise theloopholes if present. And without credibility, they will not be influenced by size of the threat. This is the delicate strategy ofbrinkmanship, the first of themere words. Children who know that their parents get pleasure from giving two methods of making credible threats that I want to discuss here, the secondthem toys are not influenced by threats to with hold toys unless the parents being Burning your bridges. Brinkmanship can be very well understood fromtake some prior action to make the threat credible. the climax of the movie Dhoom 2. Abhishek Bachchan, the supercop is

determined to catch Hrithik Roshan, the master thief. They enter into a longWhen the US proclaims that it does not negotiate with terrorists, it backs it up chase which ends at the edge of a cliff and they are compelled to take eachby giving orders of blowing up a plane carrying its own citizens. This is the other head on. They start their bikes and speed towards each other knowing

streason why the CIA is able to get the information out of terrorists almost that the 1 to swerve from the track will lose balance and may also fall off andinstantly and the CBI fails to do so even after spending crores on their get injured. However there is a greater risk involved that of a head on collision.accommodation. Strategic moves thus require a planned course of action and At first the choice appears to be that of swerve or dont swerve. But in realityside actions that make this plan credible. Its a decision making process so the choice is not whether to swerve but when to swerve. The longer the twodelicate that even God has failed to master it completely as can be seen from keep on going straight, the greater the risk of a head on collision. Eventually thethe following example: bikes may get so close to each other that even if one of the rider decides that

the danger is too high and even if one swerves, it may be too late to avoid acollision. Bachchan eventually won this battle of minds and Hrithik RoshanThe Book of Genesis is an ancient book that describes the origin of the

swerved just in time only to fall off the cliff (and then being caught by Bachchanuniverse and mankind in agreement with Jewish and Christian beliefs.th

during his fall). For obvious reasons this game is popularly called the game ofAccording to it, God created the universe in 6 days and rested on the 7 day.th

chicken!Man was his last creation, created on the 6 day and placed in the Garden ofEden surrounded by everything he could need. In chapter 2 God warns Adamagainst eating from the tree of knowledge- You are free to eat from any tree in Burning your bridges refers to the act of deliberately eliminating your optionsthe garden, but you must not eat from the tree of knowledge of good and evil, of retreat so that you have no choice but to go with the threat or commitment.for when you eat of it, you will surely die! Its what Abhimanyu did when he entered the Chakravyuh . The knowledgeThink for a second. Would you eat the apple? Would you be ready to trade that he could not back off made him more determined to achieve his goal ofinstant death for knowledge that you will not be able to use in your lifetime? keeping the kauravas busy. In the game of chicken mentioned above - assumeAnd yet the wily serpent was able to lure Eve into having a taste. The serpent that we have cars instead of bikes. What if the thief while heading towards thesuggests that God was faking it: cop takes out his steering wheel and throws it out of the window in a manner

that is visible to the cop? The cop has no option but to swerve! The thief haswon the battle by eliminating his escape route and his threat is very credible!You will surely not die! the serpent said, For God knows that when you eat itBrinkmanship and Burning of bridges are strategies that if used carefully can doyour eyes will open and you will become like him, knowing good and evil.wonders for the society. It is brinkmanship that made the Soviets back off after

the US threat of nuclear attack during the Cuban missile crises, thusAs we all know, Adam and Eve do give in to the temptation and God does catch eliminating the possibility of an actual nuclear war. However these are tools tothem. According to the threat God should destroy them and start all overbe handled with extreme care, for even the best of plans may fail. You may afteragain. Now put yourself in Gods position! Can he really afford to carry out theall be facing a mad man, or an irrational player, or someone equally smart!threat? If he destroyed his most wonderful creation created in his own image

th What if both the drivers were to remove their steering wheels at the sameall of the 6 days work would be undone. He would have to recreate man andtime? The consequences could be disastrous! So chose these paths at yourfeed him with every line instruction, all over again! So God came up with a lessown risk.drastic punishment. Adam was banished from the Garden of Eden, forced to tillThere are numerous other techniques that can help you make crediblebarren lands. For Eve, Childbirth was made painful. But they were both alive,strategies and not all of them are good for the society. So use this knowledgeand now they had wisdom! The snake was right- Gods threat had no credibilitywell.attached to it. It was a mere bluff! A cheap strategy!


Threats , Promises , Chicken and God !


6/6


1.At No.7, Bird Street lives a family of 4. Mr.White, change the White-house rules so that the she gets to (This too follows the previous concept, only difference

Mrs.White, their newly married son Tim White and selectively accept a part of Alicias proposal and reject being that instead of a 2 party interaction we have a 3

his wife Alicia White. Its a holiday and each member the other if needed. Now what is the likely result of party interaction here, and thus an extra set of nodes is

of the family wants to celebrate the day- the problem daughter in laws proposal? needed)

being that they all want to do it their way. Mom in law A. The mother in law gets her best payoff.

wants to go to Church and daughter in law wants a B. The daughter in law gets her best payoff. 3.What is the most likely proposal made by Timnd

kitty party. The males, sensing a nagging session have C. Both get their 2 best payoff. White to his wife AND what is the FINAL result?rd

decided to spend the holiday in office for extra hours D. Both get their 3 best payoff. A. K and M. The proposal is accepted.

wage. The White- house rule says that whatever the B. KMC. The proposal is accepted.

members at home do, they have to do it together. So Now suppose while travelling to his office Tim White C. C and M. The proposal is rejected.the women must decide on what they want to do. decides to return home and spend the day with his D. K and C. The proposal is accepted.They have limited time and an obvious dislike for wife and mother. He prefers to go to cinema hall to

each other. However, they would rather have a watch a movie. He loves both these women and his 4)Now suppose the Son argues that as the man in themixture of both their and the other persons choice main priority is to go out and spend time with them house, he should have the chance to decide and hence

stthan sitting at home and doing nothing. The following rather than sitting at home and be a witness to a in the 1 step his wife should make a proposal to himare their payoffs for each possible decision. Denoting domestic war of taunts. The following are their payoffs which he may accept and forward to his mother orkitty party by K and Church by C for each possible decision. Denoting kitty party by K , reject completely. In such a case what is the likely

proposal made by the wife AND the FINAL result?

A. K and M. The proposal is accepted.

B. KMC. The proposal is accepted.

C. C and M. The proposal is accepted

D. K and C. The proposal is accepted.

Submit your answers with explanation to

by 8th September 2012. The

best answer gets a reward and a mention in the next

edition of The Strategist. The solution will be posted

on our facebook page

http://www.facebook.com/The.KGTS. So keepThe White house rule of decision making requiresfollowing!!Daughter in law to make a proposal, which the Mom inPS: Dont try googling the question, its original!.law can accept or reject. However she cannotGive us your valuable fedback on the above givenselectively accept a part of the proposal.email id or on our facebook page(NOTE THAT THE FOLLOWING QUESTIONS ARE BASED

ON BACKWARD INTERPOLATION, IF YOU HAVE

UNDERSTOOD THE RELEVANT ARTICLE IN THIS

EDITION, YOU SHALL HAVE NO PROBLEM CRACKING

THIS ONE)

1). Assuming rational behavior what is the likely result

of Alicia Whites proposal?

A. The mother in law gets her best payoff.Church by C and Movie by M.

B. The daughter in law gets her best payoff.The White house rule requires the Son to make and

C. Both get their 2 best payoff.proposal to his wife who may accept or reject it (Theyr d

D . B o t h g e t t h e i r 3 b e s t p a y o f f.behave rationally). If the wife accepts the proposal

reaches Mom in law who may accept or reject it.2.Now suppose Mrs. White convinces Mr. White to

[email protected]

Mom in law Daughter inlaw

Son

K 1 8 1

M 1 1 8

C 8 1 1

KM 1 6 6

MC 6 6 1

CK 6 1 6

KMC 4 4 1

None 2 2 0 prefersgoing out

Rack your Brains!

Mom in law Daughter in law

K only 1 8

C only 8 1

Both C and K 6 6

None 2(ego) 2(ego)

The KGPian Game Theory society will soon conduct selections for its Literary (The Strategist), design

and web teams. So all you writers, cartoonists, designers and coders out there- keep your eyes and

ears open!"

Manoj Saurabh

Deepant HarikaSahil ShipraAkshat DastagiriVaibhav Srikar AyushAnurag SachinPoorva UditVibhor

Abhishek Pal

TeamKGTS

The Strategist August2012

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Transcript of The Strategist August2012