Competitive exams form an integral part of our lives. It’s what segregates the objective? He or she wants people who understand the problem to get the winners from the mediocre, the dedicated from day dreamers, the hungry answer right and those who don’t to get it wrong. It seems likely that he has hunters from those who just want to have some fun. It’s what schools and chosen the wrong answers carefully so as to be appealing to folks who don’t companies use to judge your mettle. And it’s what brought you and me here in quite know the answer. For example, in response to the question: What is the the first place! Regardless of which year you are in, the memories of one’s JEE number of rings in the Olympic flag, an option of “1000” or “square root of 2 ” days are bound to stay fresh in everyone’s 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! IT’S 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 32Π is right? Not many. I mean, you can’t just add Π to following question from GMAT (the test for MBA aspirants). +10 for the right anything that’s supposed to be rational ! “Have you met my new answer -5 for wrong. Here we go! boyfriend—He bought me a ring worth 5678Π bucks!!” Thus we can truly rule

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

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

2formula for the area of a circle is Πr . However, the person who didn’t quite 2 2

a. 4π cm b.8π cm remember the formula might have mixed it up with the formula for the 2 2 2 c. 32 cm d. 16π cm e.32π cm circumference i.e .2Πr. (we assume that someone so uninformed wouldn’t

bother to check the units) Note that if r = 4, then 2Πr is 8Π, and that would lead So! What’s 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 2Πr and hence

Okay, we recognize that you’re at a bit of a disadvantage of not having the believe that 32Π or(e) was the right answer. The person could leave off the Π 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 to Still, we think that by putting on your strategic hats you should be able to figure square the radius and simply use Πr as the area, leading to 4Π or (a). In it out. summary, if 16Π 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 wrong Found it yet? No? Well then, let’s do this together. answers for the old bugger.

stLet’s 1 state what most of us have already done thanks to the hard and fast Now, what if 4Π, the other option with square and Π is the correct solution (so elimination 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 with probably not right. At this stage some of us may start thinking that the answer area. If the student used the wrong formula, 2Πr, he or she would still get 4Π

2 is (e) i.e. 32π cm . Why? Perhaps because it is similar to the odd answer regardless of units. There is nothing more frustrating from a test maker’s numerically and our past experience tells us that whenever you have 2 options perspective, than allowing the person to get the right answer for the wrong with similar digits one of them is likely to be the answer. reason. Hence 4Π would be a terrible right answer, as it would allow too many people who didn’t 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 4Π or 16Π. It is at this stage that --------------------------------------------------------------------------------------------------you need to put on your strategic hats. Think of the game that the old bugger who set the question is trying to play with you! What is that person’s

Π

The StrategistThe KGPian Game Theory Society Second EditionAugust, 2012

Lets Play a Game

PRISONERS’DILEMMA

RACK YOURBRAINS!

THREATS AND PROMISES

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 mathematical Sgame theory. The existence of the world wide web and the Algorithmic Game Theory is an area in the intersection of Game Theory and

omnipresence 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 foreigner’s 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 game an entirely new perspective when computation met with game theory. theory, give AGT its distinct character and relevance.We can see Algorithmic Game Theory from two perspectives:Introduction

The primary role of a computer evolved from a stand-alone, well-understood Analysis: Analyze current implemented using Game Theory tools: calculate machine 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 phase transition were inevitable: theoretical computer science would respond by Design: design games that have both good game-theoretical and algorithmic formulating 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 beautiful study of interaction between competing or cooperating individuals, would play a crucial role. Research on the interface of theoretical computer science and 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 for risoner’s 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 it Phelps 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

Prisoner’s Dilemma.

Commissioner James Gordon catches two men for a crime but doesn’t have A would be to sufficient 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 similar If B betrays (we are constrained to column 3 now) then the best strategy for A deal – if one testifies against his partner and the other remains silent then the should 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 prison words 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 minor Thus 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 opponent’s strategy. Since convictions but because they cooperated with the police they shall get an early the 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 his strategic 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 of Let us see this more clearly using a pay off matrix. Payoff is nothing but the equilibrium. Here if A decides to deviate his strategy from betrayal to utility or the outcome that each player gets. A payoff matrix is a elegant way of cooperation, then his payoff would become -5 worse than his current payoff of presenting 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 he is a specification of strategies for every player) as the input and yields a decides to cooperate then his payoff would become -5 (bottom left cell of the representation of payoff for each player as its output. In each cell, the first matrix). Thus none of the players would individually like to deviate from the number represents the payoff to the row player (in this case convict A), and the betrayal, 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 the Art of Game Theory Society (KGTS). In this endeavour of ours we try to bring to you some Strategy project, 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 Talk last 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.KGTSplayers 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

The KGPian Game Theory Society The Strategist 3

Prisoners’ Dilemmas of KGP !

their bosses and not comrades looking for them. Thus each soldier has spent he brief introduction to Nash Equilibrium and prisoner’s dilemma would 5.5 hours to complete a 4 hour task, that too inefficiently. This carries on till the probably have raised some questions in your mind? Is this mere end, leading to heavy wastage of time and energy and poor academic theoretical humbug or do these number filled boxes actually make a Tperformance.difference to my life? Well, actually, it does! Read on to find out the

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

The payoff values are assigned using following logic: If A comes on time and B down your posterior, nothing can overpower the age old tradition of GPL. GPL- doesn’t then A has additional burden of finding B. B gets more leverage time to an event that reminds us of the soft patting we received on the posterior from complete other personal work. Thus for both A and B “Don’t come on time” the pretty hospital nurse while being held upside down, soon after we were seems to be the dominant strategy, even though both would have benefited by born. 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 event In reality only about half the soldiers do the work. If all soldiers had agreed to where the predators swing their footwear with satanic conviction and the prey do their part the work could be completed in 2 hours saving them all 3.5 hours yells for his life, clinging on the pillar as if begging it to strengthen his of time!fragmenting backside.

Clearly, GPL is fun only as long as you are not the victim. And given a choice TO BUNK OR NOT TO BUNK?most of us would rather not go through it. Now let us consider the case of two Come October and the thought on everyone’s mind is ‘frust KGPians’- A and B who are faced with a choice of whether or not to GPL “Only 4 days off for Durga Puja? And I thought I was i.e. whether to Score or not to Score. It is B’s 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 mummy’s 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 that

Taking 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 merely score 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 from follow suit when it’s 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 afford of +3 with sadistic pleasure. However if he doesn’t score there is every chance to fail everyone who did not appear for the test? Can he really afford to let one that he’ll 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, most instincts and takes a swing. B faces a similar situation when it’s his turn and of us would fear to bunk a lab or test. In fact almost all plans of mass bunking in does 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 of Score 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 of To Illu or not to Illu? us give in to the fear of “that someone who may spoil the party”. That’s Illumination and rangoli is without doubt the most spectacular event of the because we are all trapped in the following prisoner’s dilemma: Assume the KGP 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 that students that their “not so voluntary” participation in Illu is the main reason if Maggus and Semi-maggus make their decisions independently (for they for 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 to hall of residence is the gathering of ‘junta’ to do the work. Ask any 2 year what they think the Maggus and semimaggus will do.student why he doesn’t 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,

stlet us keep in mind that Illu is here to stay and the work will be done by 1 and nd2 years- referred to hereafter as the ‘soldiers’. Let’s assume that a working

time of 8:00 pm – 12 am has been announced for each day. What happens in stthe 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 to The payoff’s 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 these home, 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 goes the 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 doesn’t. They will both benefit partially already been done by the 20 present on field from 8:00am). Thus every soldier on 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 other rescheduled 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 prisoner’s dilemma form of Nash Equilibrium is well group commanders (read HCMs) now take up the task of pulling the soldiers demonstrated here! We leave the reader to ponder over the solution to this out 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 Don’t Score

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

Don’t Score (3,-3) (1,1)

B->/A Come on time Don’t come on time

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

Don’t 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)

->

President seems the most sought-after choice in this case to remove the above ackward 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 your B

perspective 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 are significant. It proceeds by first considering the last time a decision might be made and supposed to get a perfect Jan Lokpal. But WAIT!! Did we consider, what effects choosing 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 the involves another person, to make your plan count, you have to go all the way back to points which might benefit the corrupt politicians will be vetoed out. In this case, will the opponent's side of situation and come back to the action part of the plan. Only the government be willing to pass-on the modified bill to President?? This changes the after 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 it stget 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 thei ndlevel 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, guessing rejecting). 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 one take-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 propose We 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 showed Parliament'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 of have 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

The KGPian Game Theory Society The Strategist 4

Look forward and reason backward

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 can’t even believe a threat from God, whose threat can we believe? The main Tthe right time can work wonders for a player. It can solve cases and deter problem with God’s threat was that it was too big to be credible especially for

nuclear wars. It can help you win companies and command loyalty. It can put someone with God’s sanity. The destruction of his most prized creation is you 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 often absolutely 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 to promises on the other hand are safer moves but do not guarantee immediate someone on the dining table, “Pass me the salt or I’ll break your jaw”. Your action. dining table neighbors may be the obstinate kind who revolts at any prospect To 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 to Threats and promises are more complex conditional moves that are meant to comply, you must either go through with thethreatened action or back down force 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 Bal robbery- The conman forces the staff to follow his orders at gunpoint, “Don’t Thackeray contrary to his usual practices, cannot directly threaten Sachin move, or I’ll blow your head off”. This undoubtedly eases the process of getting Tendulkar despite his obvious dislike for Sachin’s anti Shiv-Sena remarks. what he wants but there’s an added danger- that of getting arrested for not 1 Sachin is too popular among the masses and damage to him will infuriate even but 2 crimes- robbery and attempt to murder. That’s where the dangerous side Thackeray’s followers. of threats comes into picture. It is a response that punishes the other player for non-compliance with your wants but at some cost to oneself. Because threats Very often when you don’t know the exact size of a threat that is needed to and 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 as credibility 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 the loopholes if present. And without credibility, they will not be influenced by size of the threat. This is the delicate strategy of brinkmanship, the first of the mere words. Children who know that their parents get pleasure from giving two methods of making credible threats that I want to discuss here, the second them toys are not influenced by threats to with hold toys unless the parents being “Burning your bridges”. Brinkmanship can be very well understood from take 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 long When 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 each by 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 and instantly 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 ‘don’t swerve’. But in reality side actions that make this plan credible. It’s a decision making process so the choice is not whether to swerve but when to swerve. The longer the two delicate 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 the the 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 a collision. Bachchan eventually won this battle of minds and Hrithik Roshan The “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 Bachchan universe and mankind in agreement with Jewish and Christian beliefs.

th during his fall). For obvious reasons this game is popularly called the game of According 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 of

Eden surrounded by everything he could need. In chapter 2 God warns Adam against 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 options the 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!” It’s what Abhimanyu did when he entered the Chakravyuh . The knowledge Think 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 of instant 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 - assume And 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 the suggests 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 has won 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 it Brinkmanship and Burning of bridges are strategies that if used carefully can do your 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, thus As 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 to them. According to the threat God should destroy them and start all over be handled with extreme care, for even the best of plans may fail. You may after again. Now put yourself in God’s position! Can he really afford to carry out the all 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 same all of the 6 day’s work would be undone. He would have to recreate man and time? The consequences could be disastrous! So chose these paths at your feed him with every line instruction, all over again! So God came up with a less own risk.drastic punishment. Adam was banished from the Garden of Eden, forced to till There are numerous other techniques that can help you make credible barren 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 knowledge and now they had wisdom! The snake was right- God’s threat had no credibility well.attached to it. It was a mere bluff! A cheap strategy!

The KGPian Game Theory Society The Strategist 5

Threats , Promises , Chicken and God !

The KGPian Game Theory Society The Strategist 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 Alicia’s proposal and reject being that instead of a 2 party interaction we have a 3

his wife Alicia White. It’s 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 law’s 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 Tim nd

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? rddecided to spend the holiday in office for extra hour’s 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 the mixture of both their and the other person’s 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 him are 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 or kitty 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 keep The White house rule of decision making requires following!!Daughter in law to make a proposal, which the Mom in PS: Don’t try googling the question, it’s original!.law can accept or reject. However she cannot Give us your valuable fedback on the above given selectively 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 White’s 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 a nd

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

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Mom in law Daughter in law

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 prefers going 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!"

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Abhishek Pal

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