The Strategist August, 2012 by The Kgpian Game Theory Society

The Strategist The KGPian Game Theory Society

August, 2012

PRISONERS’ DILEMMA

THREATS AND PROMISES

Second Edition

RACK YOUR BRAINS!

Lets Play a Game Competitive exams form an integral part of our lives. It’s what segregates the winners from the mediocre, the dedicated from day dreamers, the hungry hunters from those who just want to have some fun. It’s what schools and companies use to judge your mettle. And it’s what brought you and me here in the first place! Regardless of which year you are in, the memories of one’s JEE days are bound to stay fresh in everyone’s mind. And today we challenge you to put your MCQ skills to use once again! IT’S TIME TO PLAY A GAME! The rules of the game are simple. All you need to do is to find the answer to the following question from GMAT (the test for MBA aspirants). +10 for the right answer -5 for wrong. Here we go! (Q)FHGkhlkjsdklvmfmveopudfhtrewrupoewrpfo ***fnejh$%%&&@FJ,LJLJF()(FGJGJ!@#^FHJG XHEHhdndncndvba^%*()$#@%&*gdjkhfvd fjvlkjka ? 2

a. 4π cm c. 32 cm2

b. 8π cm d. 16π cm2

e.32π cm2

So! What’s your answer? Okay, we recognize that you’re at a bit of a disadvantage of not having the Question. Unfortunately copyright laws prevented us from reproducing it. Still, we think that by putting on your strategic hats you should be able to figure it out. Found it yet? No? Well then, let’s do this together. Let’s 1st state what most of us have already done thanks to the hard and fast elimination methods taught in JEE coaching factories of our country. The odd answer in the series is c. Since it is so different from the other answers, it is probably not right. At this stage some of us may start thinking that the answer is (e) i.e. 32π cm2 . Why? Perhaps because it is similar to the odd answer numerically and our past experience tells us that whenever you have 2 options with similar digits one of them is likely to be the answer.

objective? He or she wants people who understand the problem to get the answer right and those who don’t to get it wrong. It seems likely that he has chosen the wrong answers carefully so as to be appealing to folks who don’t quite know the answer. For example, in response to the question: What is the number of rings in the Olympic flag, an option of “1000” or “square root of 2 ” is unlikely to lure any candidates. But an option like ‘6’ seems more alluring. 2 Turning this around, imagine that the odd answer 32 cm really is the right answer. What kind of question might have 32 cm2 as the answer but would lead someone to think 32Π is right? Not many. I mean, you can’t just add Π to anything that’s supposed to be rational ! “Have you met my new boyfriend—He bought me a ring worth 5678Π bucks!!” Thus we can truly rule out 32 Π as being the correct solution. Let’s now turn to the two perfect squares, 4Π and 16Π. Assume for a moment that 16π cm2 is the correct solution. A Π and a perfect square suggest that the question could be asking about the area of a circle with radius. The correct formula for the area of a circle is Πr2. However, the person who didn’t quite remember the formula might have mixed it up with the formula for the 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 the person to the wrong answer of (b) A dream come true for any examiner! 2 The person could also mix and match and use the formula 2Πr and hence believe that 32Π or(e) was the right answer. The person could leave off the Π and come up with 32 or (c) as it appears unique! Or the person could forget to square the radius and simply use Πr as the area, leading to 4Π or (a). In 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 answers for the old bugger. Now, what if 4Π, the other option with square and Π is the correct solution (so that r = 2)? Think now about the most common mistake, mixing up circumference with area. If the student used the wrong formula, 2Πr, he or she would still get 4Π regardless of units. There is nothing more frustrating from a test maker’s perspective, than allowing the person to get the right answer for the wrong 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. Think further! The fact that the units are in square centimeters suggests an 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

At this point we are done! So, now! What was your initial answer? (d)? Take a +10 mate! --------------------------------------------------------------------------------------------------

The Strategist 2

The KGPian Game Theory Society

Welcome Hello everyone! We are back with our second edition of “The Strategist”. For those who are going to read The Strategist for the first time, let us briefly introduce ourselves and The Strategist. The Strategist, a monthly paper on game theory is an initiative by The Kgpian Game Theory Society (KGTS). In this endeavour of ours we try to bring to you some very interesting articles and developments in the field of “Game Theory” . Game theory is the study of strategic decision making, that is, whenever two or more players are involved in any cooperation or conflict situation game theory can come handy. Game theory is mainly used in the field of economics, business, political science, psychology and logic. There have been some fascinating developments of

game theory in the field of biology too. We incorporate some mind boggling puzzles in each of our papers that uses the concepts of game theory, which we are sure will interest you. We started last year when our founder Manoj Gadia took this initiative. In this small span of time we have started publishing The Strategist, working on the Art of Strategy project, conducted sessions of Strategia Hub- fortnightly discussions on game theory and also a Finance Talk last year. To know more about us follow us on our facebook page https://www.facebook.com/The.KGTS After reading the above section if you are curious to know more about Game Theory and strategic thinking then dive in and read the remaining paper, you are gonna love it! Team KGTS

Prisoners’ Dilemma

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 helps 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 sufficient evidence to convict them for their crimes. So he puts them in separate cells in isolation to each other and offers each of the men a similar deal – if one testifies against his partner and the other remains silent then the one who testifies shall go free and who remains silent gets a five year prison term. If both remain silent then both will get a minor term of one year for minor charges (say possession of firearms but shall not be convicted for the actual crime). If both rat out each other then the commissioner shall have two convictions but because they cooperated with the police they shall get an early parole thus a jail time of 3 years each. What should the convicts do -testify against their partner (betrayal) or remain silent (cooperate)? Think for a while what would be your strategy had you been one of the convicts. It is rational to assume that each convict is only concerned with lessening his time in jail. The interesting symmetry of this problem is that the logical decision would leave each one betraying the other, even though their individual payoff would be greater had they cooperated. Let us see this more clearly using a pay off matrix. Payoff is nothing but the utility or the outcome that each player gets. A payoff matrix is a elegant way of presenting the outcomes of a strategic game. It takes the strategy profile (that is a specification of strategies for every player) as the input and yields a representation of payoff for each player as its output. In each cell, the first number represents the payoff to the row player (in this case convict A), and the second number represents the payoff to the column player (in this case convict B). 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?

If B cooperates (we are constrained to column 2 now) then the best strategy for A/B

Cooperation(B)

Betrayal(B)

Cooperation(A)

(-1,-1)

(-5,0)

Betrayal(A)

(0,-5)

(-3,-3)

A would be to 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). If B betrays (we are constrained to column 3 now) then the best strategy for A should be to betray (since a payoff of -3 is better than a payoff of -5 or in other words serving 3 years in jail is better than serving 5 years in jail). Thus no matter what B chooses it is better for A to Betray. This is called a dominant strategy in technical terms which means that no matter what your 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 the above matrix is symmetric because the choices given two the convicts are same we can easily see that for B also the best strategy would be to betray. Check that for yourselves if you are not sure! 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 (1,-1). Betray, betray is also the Nash equilibrium of this game. Nash equilibrium is a strategic profile from which a deviation by any one player would hurt the payoff of that player and hence that player shall not deviate from that position. Thus it is a position of equilibrium; we shall not observe deviation from that strategic profile. Let us see what happens if one of the convicts deviate from the position of equilibrium. Here if A decides to deviate his strategy from betrayal to cooperation, then his payoff would become -5 worse than his current payoff of -3 (top right cell of the matrix). Similarly if B decides to deviate that is he decides to cooperate then his payoff would become -5 (bottom left cell of the matrix). Thus none of the players would individually like to deviate from the betrayal, betrayal strategic profile. What is the dilemma here? It is left to the reader to figure out the dilemma.

Algorithmic Game Theory

trategic thinking has long been an object of study in economic theory and related areas, and is most purely expressed in classical mathematical game theory. The existence of the world wide web and the omnipresence of computers make strategic behavior an everyday concern for both, man and machine: How should I bet in a web auction? According to which rules should ads show up in a web search result? Why should a computer forward a foreigner’s internet packets? Well, in the past five years, Algorithmic Game Theory emerged as a field with an entirely new perspective when computation met with game theory.

Introduction The primary role of a computer evolved from a stand-alone, well-understood machine for executing software to a conduit for global communication, content-dissemination, and commerce. Two consequences of this phase transition were inevitable: theoretical computer science would respond by formulating novel problems, goals, and design and analysis techniques 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

exploded phenomenally over the past ten years. Algorithmic Game Theory is an area in the intersection of Game Theory and Algorithm Design, whose objective is to design algorithms in environments. The central research themes in AGT differ from those in classical microeconomics and game theory in important, albeit predictable, respects. Ibility results, upper and lower bounds on feasible approximation guarantees, and so on. These themes, which have played only a peripheral role in traditional game theory, give AGT its distinct character and relevance.We can see Algorithmic Game Theory from two perspectives: Analysis: Analyze current implemented using Game Theory tools: calculate and prove properties on their Nash Equilibria, Price of Anarchy. Design: design games that have both good game-theoretical and algorithmic properties. This area is called Algorithmic Mechanism Design. 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

The Strategist 3

The KGPian Game Theory Society

Prisoners’ Dilemmas of KGP !

he brief introduction to Nash Equilibrium and prisoner’s dilemma would probably have raised some questions in your mind? Is this mere theoretical humbug or do these number filled boxes actually make a 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 * marked sections will especially appeal to the more experienced KGPians. So here we go….!

Don’t Score

Score

(-1,-1)=NASH EQM

(3,-3)

Don’t Score

(3,-3)

(1,1)

Score

/ B->

Taking into account the sentiments of a true frust KGPian, A would prefer to score and yet not be sored upon. He may choose to not score and hope for B to follow suit when it’s his turn yielding both a payoff of (1,1). Or he may score and hope for B to try and set an example of righteousness yielding him a payoff of +3 with sadistic pleasure. However if he doesn’t score there is every chance that he’ll end up with a payoff of -3. Hence A chooses to go with his predatory instincts and takes a swing. B faces a similar situation when it’s his turn and does the same, giving both a payoff of -1 and a blue posterior! Here ScoreScore is a Nash Equilibrium. QED: GPL is here to stay!

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

The payoff values are assigned using following logic: If A comes on time and B doesn’t then A has additional burden of finding B. B gets more leverage time to complete other personal work. Thus for both A and B “Don’t come on time” seems to be the dominant strategy, even though both would have benefited by coming on time and getting the work done. In reality only about half the soldiers do the work. If all soldiers had agreed to do their part the work could be completed in 2 hours saving them all 3.5 hours of time! TO BUNK OR NOT TO BUNK? Come October and the thought on everyone’s mind is “Only 4 days off for Durga Puja? And I thought I was 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 we do not intend to encourage mass bunking among students but are merely providing a logical explanation to a common phenomenon. Now, think from the professors’ point of view. They are responsible for your academic growth. Your performance reflects on their performance. Can a professor really afford to fail everyone who did not appear for the test? Can he really afford to let one missed lab affect the whole class’ grades? The answer is obvious. And yet, most of us would fear to bunk a lab or test. In fact almost all plans of mass bunking in such situations turn out to be a failure. There is always someone/group of 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 us give in to the fear of “that someone who may spoil the party”. That’s because we are all trapped in the following prisoner’s dilemma: Assume the class to be divided into 4 groups- Maggu, Semi Maggu, Non maggu , Peacemaru. We consider the dilemma of Maggu and Semi-maggus. We assume that if Maggus and Semi-maggus make their decisions independently (for they would rather not trust each other), and the others will respond according to what they think the Maggus and semimaggus will do. 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)

To Illu or not to Illu? Illumination and rangoli is without doubt the most spectacular event of the KGP calendar. An event that stands for unity and team spirit and highlights the uniqueness of IIT Kharagpur. There is a often a complaint by 1st and 2nd year students that their “not so voluntary” participation in Illu is the main reason for their beautiful panjis. In fact a common problem during Illu in almost every hall of residence is the gathering of ‘junta’ to do the work. Ask any 2nd year 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, let us keep in mind that Illu is here to stay and the work will be done by 1st and 2nd 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 st 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 to complete records or carry out other leisure activities. And by the time all these prisoners of war are captured, its 11.00 pm! Consequently the work now goes on till 2:00 am to make up for the time lost (not till 2:30 am as some work has already been done by the 20 present on field from 8:00am). Thus every soldier who came on time has spent 6 hours to complete a 3.5 hour task. On the other hand the late comers had to work for only 3 hours! What happens the following week? Practically no one turns up on time! The group commanders (read HCMs) now take up the task of pulling the soldiers out of their burrows. The soldiers are captured in 2 hours and the work again 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

B->/A

To GPL or not to GPL? From hostel rooms that remind you of Mohenjodaro 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 down your posterior, nothing can overpower the age old tradition of GPL. GPLan event that reminds us of the soft patting we received on the posterior from the pretty hospital nurse while being held upside down, soon after we were born. An event where dozens leave their work and gather around to witness the dramatic transformation of firm leather to mellow gelatina. An event where the predators swing their footwear with satanic conviction and the prey yells for his life, clinging on the pillar as if begging it to strengthen his fragmenting backside. Clearly, GPL is fun only as long as you are not the victim. And given a choice most of us would rather not go through it. Now let us consider the case of two ‘frust KGPians’- A and B who are faced with a choice of whether or not to GPL i.e. whether to Score or not to Score. It is B’s GPL day.

their bosses and not comrades looking for them. Thus each soldier has spent 5.5 hours to complete a 4 hour task, that too inefficiently. This carries on till the end, leading to heavy wastage of time and energy and poor academic performance. But why does this happen? Because each soldier is caught in a prisoner’s dilemma as shown below for two soldiers A and B:

The payoff’s are described as follows. Both magus and semi-maggus want to go home, however they also want to top the class. They would prefer to not write the test provided the other follows suit. The best case possible for them would be if they write the test and the other doesn’t. They will both benefit partially on bunking the test as they will have an equal chance of performing in the rescheduled test or exams. However the temptation to write the test is too high and they both end up getting a low payoff of (-1,-1). The ironic consequence of the prisoner’s dilemma form of Nash Equilibrium is well demonstrated here! We leave the reader to ponder over the solution to this dilemma…….. ;-)

The Strategist 4

The KGPian Game Theory Society

Look forward and reason backward

ackward reasoning is an important aspect of Game Theory. This statement arises from the fact that the outcome of your actions isn't solely dependent upon your perspective of the situation. Remember, a coin has two sides with both being equally significant. It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time. Using this information, one can then determine what to do at the second-to-last time of decision. But, when the situation involves another person, to make your plan count, you have to go all the way back to the opponent's side of situation and come back to the action part of the plan. Only after that, your part of the plan will be truly meaningful. 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 get exactly what they want) and 1 being the lowest (when they get only what the other wants). Since even element G benefits the society partially i.e at least the low level corruption is taken care of the payoff is 1 and not 0 or negative.

Obviously the president will sign a bill containing the elements of G and B, or one with G alone, but will veto one with B alone ( as he has only the option of signing or rejecting). Knowing the President's bold and yet rational behavious, the Congress chooses the package as can be seen from the tree below.

President seems the most sought-after choice in this case to remove the above m o d i f i c a t i o n s . . So, this new power seems to be as a perfect tool in favour of the bill and we are supposed to get a perfect Jan Lokpal. But WAIT!! Did we consider, what effects implementing this line-item veto will have on the parliament?? The government, aware of the fact that President is a supporter of the bill will know for sure that the points which might benefit the corrupt politicians will be vetoed out. In this case, will the government be willing to pass-on the modified bill to President?? This changes the 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:

Clearly the payoffs received by the Parliament is same whether or not it passes the bill in form B. So it doesn't make any sense to pass it in the 1st place. Thus both parties have received their2nd lowest payoff when they could have received thei 2 nd 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. The question may arise; there are a thousand ways your opponent may think, which way to follow? There are complexities, but if you know your opponent well, guessing what step they are most likely to take shouldn't be a difficult task. 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 some of these are not likely to be part of the Parliament's choice. The reason is that Parliament's actual choice is affected by its calculation of what the president would have done if Congress had counterfactually made a different choice; to show this logic 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 preference i.e the Lok Pal bill is passed to combat corruption but with some conditions 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

Ideally one may think that A will propose 99:1 and B has no option but to take it. But, pause again and think, would you have accepted the offer? The experiment showed results which were far from ideal with 50:50 divisions in some cases and rejection of 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 . So, be careful dealing with strangers. Ideal notions of human behaviour don't apply to everyone.

The Strategist 5

The KGPian Game Theory Society

Threats , Promises , Chicken and God !

hreats and promises are very important tools in making competitive strategies in Game Theory. The right threat, made to the right person at the right time can work wonders for a player. It can solve cases and deter nuclear wars. It can help you win companies and command loyalty. It can put you in history books or destroy your image forever! Threat making is an art and overuse of it can spoil your image permanently. So beware: Do not use it unless absolutely necessary and be prepared for the side effects. Commitments and promises on the other hand are safer moves but do not guarantee immediate action. To define technically a commitment is an unconditional strategic move. Threats and promises are more complex conditional moves that are meant to force your opponent into doing what you desire. Consider the case of a bank robbery- The conman forces the staff to follow his orders at gunpoint, “Don’t move, or I’ll blow your head off”. This undoubtedly eases the process of getting what he wants but there’s an added danger- that of getting arrested for not 1 but 2 crimes- robbery and attempt to murder. That’s where the dangerous side 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 and promises indicate that you will act against your own interest, their credibility becomes the key issue. After others have moved, you have an incentive to break your threat or promise. The other players can sense these loopholes if present. And without credibility, they will not be influenced by mere words. Children who know that their parents get pleasure from giving them toys are not influenced by threats to with hold toys unless the parents take some prior action to make the threat credible. When the US proclaims that it does not negotiate with terrorists, it backs it up by giving orders of blowing up a plane carrying its own citizens. This is the reason why the CIA is able to get the information out of terrorists almost instantly and the CBI fails to do so even after spending crores on their accommodation. Strategic moves thus require a planned course of action and side actions that make this plan credible. It’s a decision making process so delicate that even God has failed to master it completely as can be seen from the following example: The “Book of Genesis” is an ancient book that describes the origin of the universe and mankind in agreement with Jewish and Christian beliefs. According to it, God created the universe in 6 days and rested on the 7th day. Man was his last creation, created on the 6th 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 the garden, but you must not eat from the tree of knowledge of good and evil, for when you eat of it, you will surely die!” Think for a second. Would you eat the apple? Would you be ready to trade instant death for knowledge that you will not be able to use in your lifetime? And yet the wily serpent was able to lure Eve into having a taste. The serpent suggests that God was faking it: “You will surely not die!” the serpent said, “For God knows that when you eat it your eyes will open and you will become like him, knowing good and evil”. As we all know, Adam and Eve do give in to the temptation and God does catch them. According to the threat God should destroy them and start all over again. Now put yourself in God’s position! Can he really afford to carry out the threat? If he destroyed his most wonderful creation “created in his own image” all of the 6th day’s work would be undone. He would have to recreate man and feed him with every line instruction, all over again! So God came up with a less drastic punishment. Adam was banished from the Garden of Eden, forced to till barren lands. For Eve, Childbirth was made painful. But they were both alive, and now they had wisdom! The snake was right- God’s threat had no credibility attached to it. It was a mere bluff! A cheap strategy!

This is perhaps genesis of the problem of making credible strategies. I mean, if can’t even believe a threat from God, whose threat can we believe? The main problem with God’s threat was that it was too big to be credible especially for someone with God’s sanity. The destruction of his most prized creation is something that you do not expect from the creator. In fact large threats made on small issues or to the wrong person can often make you look like a fool. That is the reason why you simply cannot say to someone on the dining table, “Pass me the salt or I’ll break your jaw”. Your dining table neighbors may be the obstinate kind who revolts at any prospect of bullying, or a tough guy who enjoys an opportunity for a fight. If he refuses to comply, you must either go through with thethreatened action or back down and face the humiliation and loss of reputation. This is also the reason why Bal Thackeray contrary to his usual practices, cannot directly threaten Sachin Tendulkar despite his obvious dislike for Sachin’s anti Shiv-Sena remarks. Sachin is too popular among the masses and damage to him will infuriate even Thackeray’s followers. Very often when you don’t know the exact size of a threat that is needed to deter or compel your adversary you would want to keep the size as low as possible to minimize the cost to you in the event that things go wrong and you have to go through with the action. So you start small and gradually raise the size of the threat. This is the delicate strategy of brinkmanship, the first of the two methods of making credible threats that I want to discuss here, the second being “Burning your bridges”. Brinkmanship can be very well understood from 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 chase which ends at the edge of a cliff and they are compelled to take each other head on. They start their bikes and speed towards each other knowing that the 1st to swerve from the track will lose balance and may also fall off and get injured. However there is a greater risk involved that of a head on collision. At first the choice appears to be that of ‘swerve’ or ‘don’t swerve’. But in reality the choice is not whether to swerve but when to swerve. The longer the two keep on going straight, the greater the risk of a head on collision. Eventually the 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 swerved just in time only to fall off the cliff (and then being caught by Bachchan during his fall). For obvious reasons this game is popularly called the game of chicken! Burning your bridges refers to the act of deliberately eliminating your options of retreat so that you have no choice but to go with the threat or commitment. It’s what Abhimanyu did when he entered the Chakravyuh . The knowledge that he could not back off made him more determined to achieve his goal of keeping the kauravas busy. In the game of chicken mentioned above - assume that we have cars instead of bikes. What if the thief while heading towards the 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! Brinkmanship and Burning of bridges are strategies that if used carefully can do 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 eliminating the possibility of an actual nuclear war. However these are tools to be handled with extreme care, for even the best of plans may fail. You may after all be facing a mad man, or an irrational player, or someone equally smart! What if both the drivers were to remove their steering wheels at the same time? The consequences could be disastrous! So chose these paths at your own risk. There are numerous other techniques that can help you make credible strategies and not all of them are good for the society. So use this knowledge well.

The Strategist 6

The KGPian Game Theory Society

Rack your Brains! 1.At No.7, Bird Street lives a family of 4. Mr.White, Mrs.White, their newly married son Tim White and his wife Alicia White. It’s a holiday and each member of the family wants to celebrate the day- the problem being that they all want to do it their way. Mom in law wants to go to Church and daughter in law wants a kitty party. The males, sensing a nagging session have decided to spend the holiday in office for extra hour’s wage. The White- house rule says that whatever the members at home do, they have to do it together. So the women must decide on what they want to do. They have limited time and an obvious dislike for each other. However, they would rather have a mixture of both their and the other person’s choice than sitting at home and doing nothing. The following are their payoffs for each possible decision. Denoting kitty party by K and Church by C

Mom in law

Daughter in law

K only

C only

Both C and K

None

2(ego)

The White house rule of decision making requires Daughter in law to make a proposal, which the Mom in law can accept or reject. However she cannot selectively accept a part of the proposal. (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. B. The daughter in law gets her best payoff. nd C. Both get their 2 best payoff. r d D. Both get their 3 b e s t p a y o f f. 2.Now suppose Mrs. White convinces Mr. White to

change the White-house rules so that the she gets to selectively accept a part of Alicia’s proposal and reject the other if needed. Now what is the likely result of daughter in law’s proposal? A. The mother in law gets her best payoff. B. The daughter in law gets her best payoff. nd C. Both get their 2 best payoff. D. Both get their 3rd best payoff. Now suppose while travelling to his office Tim White decides to return home and spend the day with his wife and mother. He prefers to go to cinema hall to watch a movie. He loves both these women and his main priority is to go out and spend time with them rather than sitting at home and be a witness to a domestic war of taunts. The following are their payoffs for each possible decision. Denoting kitty party by K , Mom in law

Daughter in law

Son

KMC

None

(This too follows the previous concept, only difference being that instead of a 2 party interaction we have a 3 party interaction here, and thus an extra set of nodes is needed) 3.What is the most likely proposal made by Tim White to his wife AND what is the FINAL result?

A. B. C. D.

K and M. The proposal is accepted. KMC. The proposal is accepted. C and M. The proposal is rejected. K and C. The proposal is accepted.

4)Now suppose the Son argues that as the man in the house, he should have the chance to decide and hence in the 1st step his wife should make a proposal to him which he may accept and forward to his mother or reject completely. In such a case what is the likely proposal made by the wife AND the FINAL result?

A. B. C. D.

K and M. The proposal is accepted. KMC. The proposal is accepted. C and M. The proposal is accepted K and C. The proposal is accepted.

………………………………………………………………………………… Submit your answers with explanation to The.kgts@gmail.com 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 following!! PS: Don’t try googling the question, it’s original!. Give us your valuable fedback on the above given email id or on our facebook page

TeamKGTS prefers going out

Church by C and Movie by M. The White house rule requires the Son to make a proposal to his wife who may accept or reject it (They behave rationally). If the wife accepts the proposal reaches Mom in law who may accept or reject it.

Manoj Deepant Sahil Akshat Vaibhav Ayush Anurag Poorva Vibhor

Saurabh Harika Shipra Dastagiri Srikar Abhishek Pal Sachin Udit

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