Thinking strategically requires research, analysis, and forethought in order to and Managers. Thinking Strategically. ™. Syntesis Global 20/20 Leadership Series. Facilitator: Rick Hernandez. President & CEO. Syntesis Global, LLC [email protected] The Competitive Edge in Business, Politics, and Everyday Life Praise for Thinking Strategically “Machiavelli is brought up-to-date in this book by Dixit and .

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    The implication for organizations is that they must find ways to identify and cultivate future leaders with the capacity to think strategically. Recent research by authors Carroll and Mui underscore the importance of strategic thinking at the organizational level as well. The authors studied Thinking Strategically. The Competitive Edge in Business,. Politics, and Everyday Life. Avinash K. Dixit and Barry J. Nalebuff. W. W. Norton & Company.

    Search the history of over billion web pages on the Internet. Books by Language. They make strategic tools humorous, human, and effective. Dixit and Nalebuff provide the skeleton key. He has taught courses on games of strategy and has done research into strategic behavior in international trade policy. He earned his Ph.

    What are those critical skills? I offer the following list of critical skills that the best strategic thinkers possess and use every day.

    Critical Skill 1: Strategic thinkers have the ability to use the left logical and right creative sides of their brain. This skill takes practice as well as confidence and can be tremendously valuable. Critical Skill 2: They have the ability to develop a clearly defined and focused business vision and personal vision.

    They are skilled at both thinking with a strategic purpose as well as creating a visioning process. They have both skills and they use them to complement each other. Critical Skill 3: They have the ability to clearly define their objectives and develop a strategic action plan with each objective broken down into tasks and each task having a list of needed resources and a specific timeline.

    Critical Skill 4: They have the ability to design flexibility into their plans by creating some benchmarks in their thinking to review progress. Then they use those benchmarks to as a guide and to recognize the opportunity to revise their plans as needed. They have an innate ability to be proactive and anticipate change, rather than being reactive to changes after they occur.

    Critical Skill 5: They are amazingly aware and perceptive. They will recognize internal and external clues, often subtle, to help guide future direction and realize opportunities for them and their companies or organizations.

    Great strategic thinkers will listen, hear and understand what is said and will read and observe whatever they can so that they will have very helpful and strategic information to guide them.

    Critical Skill 6: They are committed lifelong learners and learn from each of their experiences. They use their experiences to enable them to think better on strategic issues.

    The science of game theory is far from being complete, and in some ways strategic thinking remains an art. We do provide guidance for translating the ideas into action. Chapter 1 offers several examples showing how strategic issues arise in a variety of decisions. We point out some effective strategies, some less effective ones, and even some downright bad ones.

    The subsequent chapters proceed to build these examples into a system or a framework of thought. In the later chapters, we take up several broad classes of strategic situations—brinkmanship, voting, incentives, and bargaining—where you can see the principles in action. The examples range from the familiar, trivial, or amusing— usually drawn from literature, sports, or movies—to the frightening —nuclear confrontation. The former are merely a nice and palatable vehicle for the game-theoretic ideas.

    As to the latter, at one point many readers would have thought the subject of nuclear war too horrible to permit rational analysis. But as the cold war winds down and the world is generally perceived to be a safer place, we hope that the game-theoretic aspects of the arms race and the Cuban missile crisis can be examined for their strategic logic in some detachment from their emotional content.

    The chapters are full of examples, but these serve primarily to develop or illustrate the particular principle being discussed, and many other details of reality that pertain to the example are set aside. Each case sets out a particular set of circumstances and invites you to apply the principles discussed in that chapter to find the right strategy for that situation. Some cases are open-ended; but that is also a feature of life.

    At times there is no clearly correct solution, only imperfect ways to cope with the problem.

    A serious effort to think each case through before reading our discussion is a better way to understand the ideas than any amount of reading of the text alone. For more practice, the final chapter is a collection of twenty three more cases, in roughly increasing order of difficulty. By the end of the book, we hope that you will emerge a more effective manager, negotiator, athlete, politician, or parent.

    We warn you that some of the strategies that are good for achieving these goals may not earn you the love of your defeated rivals. If you want to be fair, tell them about our book. Part I Ten Tales of Strategy We begin with ten tales of strategy from different aspects of life and offer preliminary thoughts on how best to play. Many of you will have faced similar problems in everyday life, and will have reached the correct solution after some thought or trial and error.

    For others, some of the answers may be surprising, but surprise is not the primary purpose of the examples. Our aim is to show that such situations are pervasive, that they amount to a coherent set of questions, and that methodical thinking about them is likely to be fruitful. In later chapters, we develop these systems of thought into prescriptions for effective strategy.

    Think of these tales as a taste of dessert before the main course. They are designed to whet your appetite, not fill you up. They point out that if you flip a coin long enough, you will find some very long series of consecutive heads. The psychologists suspect that sports commentators, short on insightful things to say, are just finding patterns in what amounts to a long series of coin tosses over a long playing season. They propose a more rigorous test. A similar calculation is made for the shots immediately following misses.

    If a basket is more likely to follow a basket than to follow a miss, then there really is something to the theory of the hot hand. They conducted this test on the Philadelphia 76ers basketball team. When a player made his last shot, he was less likely to make his next; when he missed his previous attempt, he was more likely to make his next. This was true even for Andrew Toney, a player with the reputation for being a streak shooter.

    Game theory suggests a different interpretation. The difference between streak shooting and a hot hand arises because of the interaction between the offensive and the defensive strategies. Suppose Andrew Toney does have a truly hot hand.

    Surely the other side would start to crowd him. This could easily lower his shooting percentage. That is not all. When the defense focuses on Toney, one of his teammates is left unguarded and is more likely to shoot successfully. Thus we might test for hot hands by looking for streaks in team success.

    Similar phenomena are observed in many other team sports. A brilliant running-back on a football team improves its passing game and a great pass-receiver helps the running game, as the opposition is forced to allocate more of its defensive resources to guard the stars.

    In the soccer World Cup final, the Argentine star Diego Maradona did not score a goal, but his passes through a ring of West German defenders led to two Argentine goals.

    In ice hockey, assists and goals are given equal weight for ranking individual performance. A player may even assist himself when one hot hand warms up the other. The Boston Celtics star, Larry Bird, prefers shooting with his right hand though his left hand is still better than most. The defense knows that Bird is right-handed, so they concentrate on defending against right-handed shots. What happens when Bird spends his off season working to improve his left-handed shooting?

    The defense responds by spending more time covering his left-handed shots. The result is that this frees his right hand more often. A better left-handed shot results in a more effective right-handed shot. Going one step further, in Chapter 7 we show that when the left hand is stronger it may even be used less often. Many of you will have experienced this seemingly strange phenomenon when playing tennis.

    If your backhand is much weaker than your forehand, your opponents will learn to play to your backhand. Eventually, as a result of all this backhand practice, your backhand will improve. As your two strokes become more equal, opponents can no longer exploit your weak backhand. They will play more evenly between forehands and backhands. You get to use your better forehand more often; this could be the real advantage of improving your backhand.

    At the start, Liberty got off to a second lead when Australia II jumped the gun and had to recross the starting line. The Australian skipper, John Bertrand, tried to catch up by sailing way over to the left of the course in the hopes of catching a wind shift. Dennis Conner chose to keep Liberty on the right-hand side of the course.

    Two races later, Australia II won the series. The leading sailboat usually copies the strategy of the trailing boat. When the follower tacks, so does the leader. The leader imitates the follower even when the follower is clearly pursuing a poor strategy. If you have the lead, the surest way to stay ahead is to play monkey see, monkey do. On the other hand, newcomers take the risky strategies: Usually they are wrong and are never heard of again, but now and again they are proven correct and move to the ranks of the famous.

    Industrial and technological competitions offer further evidence. In the personal-computer market, IBM is less known for its innovation than for its ability to bring standardized technology to the mass market.

    More new ideas have come from Apple, Sun, and other start-up companies. Risky innovations are their best and perhaps only chance of gaining market share. This is true not just of high- technology goods.

    There are two ways to move second. You can imitate as soon as the other has revealed his approach as in sailboat racing or wait longer until the success or failure of the approach is known as in computers. The longer wait is more advantageous in business because, unlike sports, the competition is usually not winner-take-all. As a result, market leaders will not follow the upstarts unless they also believe in the merits of their course.

    Go Directly to Jail The conductor of an orchestra in the Soviet Union during the Stalin era was traveling by train to his next engagement and was looking over the score of the music he was to conduct that night. Two KGB officers saw what he was reading and, thinking that the musical notation was some secret code, arrested him as a spy. We have caught your friend Tchaikovsky, and he is already talking. Let us develop the story to its logical conclusion.

    Suppose the KGB has actually arrested someone whose only offense is that he is called Tchaikovsky, and are separately subjecting him to the same kind of interrogation.

    Think Strategically | SpringerLink

    Of course, the tables will be turned if the conductor stands firm while Tchaikovsky gives in and implicates him. If both confess, then both will receive the standard sentence of 10 years. He knows that Tchaikovsky is either confessing or holding out. If Tchaikovsky confesses, the conductor gets 25 years by holding out and 10 years by confessing, so it is better for him to confess.

    If Tchaikovsky holds out, the conductor gets 3 years if he holds out, and only 1 if he confesses; again it is better for him to confess. In a separate cell in Dzerzhinsky Square, Tchaikovsky is doing a similar mental calculation and reaching the same conclusion. The result, of course, is that both of them confess. Later, when they meet in the Gulag Archipelago, they compare stories and realize that they have been had.

    If they both had stood firm, they both would have gotten away with much shorter sentences. If only they had had an opportunity to meet and talk things over before they were interrogated, they could have agreed that neither would give in. But they are quick to realize that in all probability such an agreement would not have done much good. Once again they would have met in the Gulag, there perhaps to settle the score of the betrayals not of the concerto.

    Can the two achieve enough mutual credibility to reach their jointly preferred solution? Look at the life-or-death issue of nuclear arms control. Therefore no matter what the other side did, each preferred to stay armed. However, they could join in agreeing that the outcome in which both disarm is better than the one in which both are armed.

    The problem is the interdependence of decisions: In this case it needed a fundamental change in Soviet thinking to get the world started on the road to nuclear disarmament.

    In Chapter 4 we look at some such avenues, and see when and how well they are likely to work. Football and poker are zero-sum games: Similarly, in employer-union bargaining, there is an opposition of interests in that one side prefers low wages and the other high ones, but there is agreement that a breakdown of negotiations leading to a strike would be more damaging for both sides.

    In fact such situations are the rule rather than the exception. Any useful analysis of games should be able to handle a mixture of conflict and concurrence of interests. Here I Stand When the Catholic Church demanded that Martin Luther repudiate his attack on the authority of popes and councils, he refused to recant: When defining what was right, there was no room for compromise.

    His firmness had profound long-term consequences; his attacks led to the Protestant Reformation and substantially altered the medieval Catholic Church. In what way did his intransigence give him power in bargaining? When de Gaulle took a truly irrevocable position, the other parties in the negotiation were left with just two options—to take it or to leave it.

    De Gaulle judged his position carefully to ensure that it would be accepted. But that often left the larger and unfair division of the spoils to France. In practice, this is easier said than done, for two kinds of reasons. The perception that you have been excessively greedy may make others less willing to negotiate with you in the future. Or, next time they may be more firm bargainers as they try to recapture some of their perceived losses. On a personal level, an unfair win may spoil business relations, or even personal relations.

    The second kind of problem lies in achieving the necessary degree of intransigence. Luther and de Gaulle achieved this through their personalities. But this entails a cost. An inflexible personality is not something you can just turn on and off. Although being inflexible can sometimes wear down an opponent and force him to make concessions, it can equally well allow small losses to grow into major disasters. Ferdinand de Lesseps was a mildly competent engineer with extraordinary vision and determination.

    He is famous for building the Suez Canal in what seemed almost impossible conditions. He did not recognize the impossible and thereby accomplished it. Later, he tried using the same technique to build the Panama Canal. It ended in disaster. The problem for de Lesseps was that his inflexible personality could not admit defeat even when the battle was lost. How can one achieve selective inflexibility? Although there is no ideal solution, there are various means by which commitment can be achieved and sustained; this is the topic for Chapter 6.

    The problem is, who will risk his life to bell the cat? This is a problem for both mice and men. How can relatively small armies of occupying powers or tyrants control very large populations for long periods? Why is a planeload of people powerless before a single hijacker with a gun? In both cases, a simultaneous move by the masses stands a very good chance of success.

    But the communication and coordination required for such action is difficult, and the oppressors, knowing the power of the masses, take special steps to keep it difficult. His reward may be posthumous glory or gratitude. There are people who are moved by considerations of duty or honor, but most find the costs exceed the benefits. After his dramatic speech, someone in the audience shouted out, asking what Khrushchev had been doing at the time.

    Khrushchev responded by asking the questioner to please stand up and identify himself. The audience remained silent. Khrushchev replied: Here we want to use this dilemma to make a different point—namely, the frequent superiority of punishment over reward. The dictator might keep the populace peaceful by providing it material and even spiritual comforts, but this can be a very costly proposition.

    There are many examples of this principle. In a large taxi fleet, cars are often assigned to drivers by a dispatcher. The fleet has some good cars and some clunkers. The dispatcher can use his assignment power to extract a small bribe from each of the drivers.

    Any driver who refuses to pay is sure to get a clunker, while those who cooperate are given the luck of the draw from the remainder. If the drivers acted in collusion, they probably could stop this practice. The problem lies in getting the movement organized. A similar story can be told about evicting tenants from rent- controlled apartments. If someone downloads such a building in New York, he has the right to evict one tenant so as to be able to live in his own building.

    But this translates into a power to clear the whole. A new landlord can try the following argument with the tenant in Apartment 1A: Therefore, I plan to evict you and move into your apartment. The landlord then offers the same deal to the tenant in IB, and so on. The United Auto Workers have a similar advantage when they negotiate with the auto manufacturers sequentially. A strike against Ford alone puts it at particular disadvantage when General Motors and Chrysler continue to operate; therefore Ford is more likely to settle quickly on terms favorable to the Union.

    Such a strike is also less costly to the Union as only one third of their members are out. After winning against Ford, the Union takes on GM and then Chrysler, using each previous success as precedent and fuel for their fire.

    In contrast, Japanese union incentives work the other way, since they are organized by company and have more profit sharing. We are not saying that any or all of these are good outcomes or desirable policies. In some cases there may be compelling arguments for trying to prevent the kinds of results we have described. This phenomenon arises again and again; but it can be countered, and we will show you how in Chapter 9.

    The Thin End of the Wedge Most countries use tariffs, quotas, and other measures to restrict import competition and protect domestic industries. Such policies raise prices, and hurt all domestic users of the protected product. The trick is to bring up the cases one at a time.

    First, 10, jobs in the shoe industry are at risk. Then along comes the garment industry, the steel industry, the auto industry, and so on. If we had foreseen the whole process, we might have thought the cost too high, and insisted that workers in each of these industries bear the risks of foreign trade just as they would have to bear any other economic risk.

    Decisions made case by case can lead to undesirable results overall. In fact, a sequence of majority votes can lead to an outcome that everyone regards as worse than the status quo. The income tax reform of almost collapsed because the Senate initially took a case-by-case approach. Yet the combination of these lobbyists could destroy the bill, and this would be worse than producing no legislation at all.

    So Senator Packwood, the committee chairman, made his own lobby: The reform was enacted. But special provisions are already staging a comeback, one or two at a time.

    Along similar lines, the line-item veto would allow the president to veto legislation selectively. If a bill authorized money for school lunches and a new space shuttle, the president would have the option of neither, either, or both, instead of the current neither or both.

    Although a first reaction is that this allows the president greater control over legislation, the opposite might end up happening as Congress would be more selective about which bills it passes.

    These problems arise because myopic decision-makers fail to look ahead and see the whole picture. In the case of tax reform, the Senate recovered its vision just in time; the issue of protectionism still suffers. Chapter 2 develops a system for better long-range strategic vision. Look before You Leap It is all too common for people to get themselves into situations that are difficult to get out of.

    Once you have a job in a particular city, it is expensive to resettle. Once you download a computer and learn its operating system, it becomes costly to learn another one and rewrite all your programs. Travelers who join the frequent-flyer program of one airline thereby raise their cost of using another. And, of course, marriage is expensive to escape. The problem is that once you make such a commitment, your bargaining position is weakened.

    Computer companies can charge higher prices for new, compatible peripheral equipment knowing that their customers cannot easily switch to a new, incompatible technology. Airlines, having established a large base of frequent flyers, will be less inclined to engage in fare wars.

    Strategists who foresee such consequences will use their bargaining power while it exists, namely, before they get into the commitment. Typically, this will take the form of a payment up front. Competition among the would-be exploiters can lead to the same result.

    Companies will have to offer more attractive initial salaries, computer manufacturers will have to charge sufficiently low prices for their central processing units CPUs , and airline frequent- flyer programs will have to offer larger signing-on mileage bonuses. As for married couples, exploitation may be a game that two can play.

    The same foresight is what prevents many curious but rational people from trying addictive drugs such as heroin. Mix Your Plays Let us return for a moment to the world of sports. In football, before each snap of the ball the offense chooses between passing and running while the defense organizes itself to counter one of these plays. In tennis, the server might go to the forehand or the backhand of the receiver, while the receiver, in turn, can try to return crosscourt or down the line. It will have a preference for the choice that exploits these weaknesses, but not exclusively.

    The point is that if you do the same thing all the time, the opposition will be able to counter you more effectively by concentrating its resources on the best response to your one strategy. Mixing your plays does not mean rotating your strategies in a predictable manner. Your opponent can observe and exploit any systematic pattern almost as easily as he can the unchanging repetition of a single strategy.

    It is unpredictability that is important when mixing. Imagine what would happen if there were some known formula that determined who would be audited by the IRS.

    Before you submitted a tax return, you could apply the formula to see if you would be audited. If an audit was unavoidable, you would choose to tell the truth. The result of the IRS being completely predictable is that it would audit exactly the wrong people. All those audited would have anticipated their fate and chosen to act honestly, while those spared an audit would have only their consciences to watch over them.

    When the IRS audit formula is somewhat fuzzy, everyone stands some risk of an audit; this gives an added incentive for honesty. There are similar phenomena in the business world. Think of competition in the market for razors. Imagine that Gillette runs a coupon promotion on a regular schedule—say, the first Sunday of every other month.

    Bic can preempt Gillette by running a competing coupon promotion the week before. This process leads to cutthroat competition and both make less profit. But if each uses an unpredictable or mixed strategy, together they might reduce the fierceness of the competition. The importance of randomized strategies was one of the early insights of game theory.

    The idea is simple and intuitive but needs refinement if it is to be useful in practice. He needs some idea of whether he should go to the forehand 30 percent or 64 percent of the time and how the answer depends on the relative strengths of the two sides. In Chapter 7 we develop methods to answer such questions. But son, do not bet this man, for as sure as you stand there you are going to wind up with cider in your ear. Nathan had just discovered the answer strudel and was willing to bet if Sky would bet on cheesecake.

    This example may sound somewhat extreme. Of course no one would take such a sucker bet. But look at the market for futures contracts on the Chicago Board of Exchange.

    Strategic thinking

    If another speculator offers to sell you a futures contract, he will make money only if you lose money. Hence if someone is willing to sell a futures contract, you should not be willing to download it. And vice versa. Of course, we should use this in conjunction with our own information concerning the matter and use all strategic devices to elicit more from others.

    In the Guys and Dolls example, there is a simple device of this kind. Sky should ask Nathan at what odds he would be willing to take the cheesecake side of the bet. If Nathan offers the same odds for both strudel and cheesecake, he is hiding his information at the cost of giving Sky the opportunity to take an advantageous gamble. In stock markets, foreign exchange markets, and other financial markets, people are free to take either side of the bet in just this way.

    Indeed, in some organized exchanges, including the London stock market, when you ask for a quote on a stock the market-maker is required to state both the downloading and selling prices before he knows which side of the transaction you want. The download and sell prices are not quite the same; the difference is called the bid-ask spread.

    In liquid markets the spread is quite small, indicating that little information is contained in any download or sell order. On the other hand, Nathan Detroit is willing to bet on strudel at any price and on cheesecake at no price; his bid-ask spread is infinity. Beware of such market-makers. A minute later he bet Nathan that Nathan did not know the color of his own bowtie. Sky cannot win: Game Theory Can Be Dangerous to Your Health Late one night, after a conference in Jerusalem, two American economists found a licensed taxicab and gave the driver directions to their hotel.

    Immediately recognizing them as American tourists, the driver refused to turn on his meter; instead, he proclaimed his love for Americans and promised them a lower fare than the meter. Naturally, they were somewhat skeptical of this promise. Why should this stranger offer to charge less than the meter when they were willing to pay the metered fare?

    How would they even know whether or not they were being overcharged? If they were to start bargaining and the negotiations broke down, they would have to find another taxi.

    Their theory was that once they arrived at the hotel, their bargaining position would be much stronger. And taxis were hard to find. They arrived. Who knew what fare was fair? Because people generally bargain in Israel, they protested and counter-offered 2, shekels.

    The driver was outraged. He claimed that it would be impossible to get from there to here for that amount. Before negotiations could continue, he locked all the doors automatically and retraced the route at breakneck speed, ignoring traffic lights and pedestrians.

    Were they being kidnapped to Beirut? This driver turned on his meter, and 2, shekels later they were home.

    Why Is Strategic Thinking Important to the Success of Business?

    Certainly the extra time was not worth the shekels to the economists. On the other hand, the story was well worth it. It illustrates the dangers of bargaining with those who have not yet read our book.

    More generally, pride and irrationality cannot be ignored. Sometimes, it may be better to be taken for a ride when it costs only two dimes.

    Think of how much stronger their bargaining position would have been if they had begun to discuss the price after getting out of the taxi.

    Of course, for hiring a taxi, this logic should be reversed. If you tell the driver where you want to go before getting in, you may find your taxi chasing after some other customer. Get in first, then say where you want to go.

    The Shape of Things to Come The examples have given us glimpses of principles that guide strategic decisions. Therefore, we cannot assume that when we change our behavior everything else will remain unchanged. The tale from the Gulag and the story of belling the cat demonstrate the difficulty of obtaining outcomes that require coordination and individual sacrifice. The example of trade policy highlights the danger of solving problems piece by piece. In technology races no less than in sailboat races, those who trail tend to employ more innovative strategies; the leaders tend to imitate the followers.

    Tennis and tax audits point out the strategic advantage of being unpredictable. Such behavior may also have the added advantage that it makes life just a little more interesting.

    We could go on offering more examples and drawing morals from them, but this is not the best way to think methodically about strategic games. That is better done by approaching the subject from a different angle.

    We pick up the principles—for example, commitment, cooperation, and mixing—one at a time. In each instance, we select examples that bear centrally on that issue, until the principle is clear. Then you will have a chance to apply the principle in the case studies that end each chapter. Case Study 1: Part of the festivities included a casino. The rest of the group had been effectively cleaned out.

    With his substantial lead, there was little reason to settle for half. To better understand the next strategic move, we take a brief detour to the rules of roulette. The betting in roulette is based on where a ball will land when the spinning wheel stops. There are typically numbers 0 through 36 on the wheel. When the ball lands on zero, the house wins. The safest bet in roulette is to bet on even or odd denoted by Black or Red. Even betting her entire stake would not lead to victory at these odds; therefore, the woman was forced to take one of the more risky gambles.

    She bet her entire stake on the chance that the ball would land on a multiple of three. She placed her bet on the table. At that point it could not be withdrawn. What should Barry have done? The woman had no other choice. If she did not bet, she would have lost anyway; whatever she bet on, Barry could follow her and stay ahead.

    Winning when Barry lost would be her only chance to take the lead, and that dictates a bet on Red. The strategic moral is the opposite from that of our tale of Martin Luther and Charles de Gaulle. In this tale of roulette, the person who moved first was at a disadvantage. The woman, by betting first, allowed Barry to choose a strategy that would guarantee victory. If Barry had bet first, the woman could have chosen a response that offered an even chance of winning.

    The general point is that in games it is not always an advantage to seize the initiative and move first.

    This reveals your hand, and the other players can use this to their advantage and your cost. Second movers may be in the stronger strategic position. At the last moment, Lucy pulls the ball away. Charlie Brown, kicking air, lands on his back, and this gives Lucy great perverse pleasure.

    Even if Lucy had not played this particular trick on him last year and the year before and the year before that , he knows her character from other contexts and should be able to predict her action. However, just because it lies in the future does not mean Charlie should regard it as uncertain. Therefore he should forecast that when the time comes, she is going to pull the ball away.

    The logical possibility that Lucy will let him kick the ball is realistically irrelevant. Reliance on it would be, to borrow Dr.

    Charlie should disregard it, and forecast that acceptance will inevitably land him on his back. These interactions arise in two ways. The first is sequential , as in the Charlie Brown story.

    The players make alternating moves. Each player, when it is his turn, must look ahead to how his current actions will affect the future actions of others, and his own future actions in turn. However, each must be aware that there are other active players, who in turn are similarly aware, and so on. Therefore each must figuratively put himself in the shoes of all, and try to calculate the outcome. His own best action is an integral part of this overall calculation. When you find yourself playing a strategic game, you must determine whether the interaction is simultaneous or sequential.

    Some games such as football have elements of both. Then you must fit your strategy to the context. In this chapter, we develop in a preliminary way ideas and rules that will help you play sequential games; simultaneous-move games are the subject of Chapter 3. We begin with really simple, sometimes contrived, examples, such as the Charlie Brown story. This is deliberate; the stories are not of great importance in themselves, and the right strategies are usually easy to see by simple intuition, so the underlying ideas stand out that much more clearly.

    The examples get increasingly realistic and more complex in the case studies and in the later chapters. So important is this idea that it is worth codifying into a basic rule of strategic behavior: Rule 1: Look ahead and reason back.

    Anticipate where your initial decisions will ultimately lead, and use this information to calculate your best choice. In the Charlie Brown story, this was easy to do for anyone except Charlie Brown. Most strategic situations involve a longer sequence of decisions with several alternatives at each, and mere verbal reasoning cannot keep track of them.

    Successful application of the rule of looking ahead and reasoning back needs a better visual aid. Let us show you how to use these trees.

    Decision Trees and Game Trees A sequence of decisions, with the need to look ahead and reason back, can arise even for a solitary decision-maker not involved in a game of strategy with others.

    For Robert Frost in the yellow wood: Two roads diverged in a wood, and I I took the road less travelled by, And that has made all the difference We can show this schematically. Each road might in turn have further branches. The road map becomes correspondingly complex. Here is an example from our own experience. Travelers from Princeton to New York have several choices. The first decision point involves selecting the mode of travel: Once in New York, rail and bus commuters must choose among going by foot, subway local or express , bus, or taxi to get to their final destination.

    For example, if you are commuting to the World Trade Center, the PATH train would be superior to driving because it offers a direct connection from Newark. We can use just such a tree to depict the choices in a game of strategy, but one new element enters the picture. A game has two or more players. At various branching points along the tree, it may be the turn of different players to make the decision. A person making a choice at an earlier point must look ahead, not just to his own future choices, but to those of others.

    He must forecast what the others will do, by putting himself figuratively in their shoes, and thinking as they would think. To remind you of the difference, we will call a tree showing the decision sequence in a game of strategy a game tree , reserving the term decision tree for situations in which just one person is involved. The story of Charlie Brown is absurdly simple, but you can become familiar with game trees by casting that story in such a picture.

    Start the game when Lucy has issued her invitation, and Charlie faces the decision of whether to accept. If Charlie refuses, that is the end of the game. If he accepts, Lucy has the choice between letting Charlie kick and pulling the ball away. We can show this by adding another fork along this road. Therefore he should figuratively prune the lower branch of her choice from the tree.

    Now if he chooses his own upper branch, it leads straight to a nasty fall. Therefore his better choice is to follow his own lower branch. To fix the idea, consider a business example that has the same game tree.

    To avoid impugning any actual firms, and with apologies to Graham Greene, suppose the market for vacuum cleaners in pre- Castro Cuba is dominated by a brand called Fastcleaners, and a new firm, Newcleaners, is deciding whether to enter this market.

    If Newcleaners enters, Fastcleaners has two choices: If Newcleaners stays away from this market, its profit is, of course, zero. We show the game tree and the profit amounts for each outcome: Newcleaners What should Newcleaners do? This is the kind of problem decision analysts solve, and business schools teach.

    They draw a very similar picture, but call it a decision tree. Therefore, they assign probabilities to the two. Then they can calculate the average profit that Newcleaners can expect from entry, multiplying each profit or loss figure by the corresponding probability and adding. Where do the probability estimates come from? Game theory provides the answer: Then the players can look forward and reason backward to predict what the other side will do. Then we can fill out the tree, adding in these payoffs.

    Since actions can be determined from the structure of the game, the tree is properly seen as a game tree, not a decision tree. Looking ahead in this way, and reasoning back, Newcleaners should mentally cut off the price-war branch. The decision might be different in other circumstances. For example, if there is a possibility that Newcleaners would go on to enter other islands where Fastcleaners has established markets, Fastcleaners may have an incentive to acquire a reputation for toughness, and may be willing to suffer losses in Cuba to this end.

    Newcleaners can see how any given payoffs translate into actions. It is the uncertainty about profits that translates into an uncertainty about actions. For example, Newcleaners might believe that there is a The chance of a price war is then The only way to find out what will actually happen is to enter. But one must be careful about where to place the uncertainty. The right place is at the end of the tree.

    Look at what goes wrong if we look if we try to jump ahead in our estimation. The probability is not percent. Nor does the presence of uncertainty mean that one should guess a probability of 50 percent. The correct way to analyze the problem is for Newcleaners to start at the end of the game and figure out what Fastcleaners should do in each case. More Complex Trees In reality, the games you play are more complex than the ones we used above for illustrative purposes.

    But the same principles apply as these saplings develop into trees. Perhaps the best example is chess. While the rules of chess are relatively simple, they produce a game that lends itself to strategic reasoning. White opens with a move, Black responds with one, and so on in turns. An example of such reasoning might be: I should protect the square to which the knight wants to move with my bishop, before I move the pawn.

    White can open with any one of 20 moves. The 20 moves he can make become 20 branches that emanate from this node. Each branch is labeled by the move it represents: We want only to convey the general idea, and so to avoid cluttering the picture, we have not shown or labeled all branches. Black can also make any of 20 moves, so there will be 20 branches emanating from each such B1 node.

    After one move from both sides, we are already looking at a total of possibilities. From here on, the number of branches will depend on the move previously made.

    You see how simply the tree is constructed in principle, and how complicated it quickly gets in practice. We can select a branch at each decision point node of the game tree, and follow a path down it. This will represent one particular way in which the game could evolve.

    Chess experts have examined many such paths in the early phases openings and speculated where they might lead. In a sport or a board game, this might be when one of the players wins or the game is a draw. More generally, the end result of the game can be in the form of monetary or nonmonetary rewards or penalties for the players. For example, a game of business rivalry might end with a sizable profit to one firm and bankruptcy of the other.

    If the game is going to end in a finite number of moves no matter which path is followed, then we can in principle solve the game completely. Solving the game means finding out who wins and how. This is done by reasoning backward along the tree. Once we have worked through the entire tree, we will discover whether or not we can win, and if so what strategy to use. For any game with a finite number of sequential moves there exists some best strategy. Chess is the prime example. Chess experts have been very successful at characterizing optimal strategies near the end of the game.

    Once the chessboard has been reduced to three or four pieces, expert players are able to see ahead to the end of the game and determine by working backward whether one side has a guaranteed winning strategy or whether the other side can force a draw. They can then use the desirability of different endgame positions to evaluate the strategies in the middle game. The problem is that nobody has ever been able to work through the tree all the way back to the opening move.

    Some simple games can be solved completely. For example, in three-by-three tic-tac-toe, a draw can always be obtained. Even the game of checkers is in danger. It is believed, although not yet confirmed, that the second player can always achieve a tie. In order to maintain interest, checkers tournaments start the players at an intermediate position, where a winning or tying strategy is not known. The day it becomes possible to solve chess completely in this way, the rules may have to be changed.

    In the meantime, what have chess players done? They do what we all should do when putting sequential strategies into practice: Then they look forward and reason backward toward a strategy that leads to the highest value five moves hence.

    Backward reasoning is the easy part. The hard problem is assigning a value to an intermediate position. The value of each piece must be quantified and trade-offs between material and positional advantage considered. A postal chess world champion, Berliner has built a computer dedicated to chess that can examine thirty million options in the three minutes allocated to each move and has a good rule for valuing intermediate positions.

    Fewer than three hundred human chess players can beat this computer program. In backgammon, Berliner has a program that has beaten the world champion. The combination of explicit logic from backward reasoning and rules of thumb for valuing intermediate positions based on experience is a useful way to tackle complicated games other than chess. Bargaining In business and in international politics, the parties often bargain or negotiate over the division of a total gain—the pie.

    We will examine this in more detail in Chapter Here we use it as an illustration of how backward reasoning enables us to predict the outcome of games with alternating moves.

    Most people follow social convention and predict that splitting the difference will be the outcome of a negotiation. There are two general features of bargaining that we must first take into account.

    We have to know who gets to make an offer to whom, i. And then we have to know what happens if the parties fail to reach an agreement. Different negotiations take place under differing rules.

    In the case of wage bargaining, a labor union makes a claim and then the company decides whether to accede.

    If it does not, it may make a counteroffer, or wait for the union to adjust its demand. In some cases the sequencing is imposed by law or custom; in others it may have a strategic role of its own. Below, we will examine a bargaining problem in which the two parties take turns making offers.

    An essential feature of negotiations is that time is money. When negotiations become protracted, the pie begins to shrink. Still, the parties may fail to agree, each hoping that the costs of negotiating will be outweighed by a more favorable settlement. In the same vein, if failure to reach a wage agreement leads to a labor strike, the firm loses profits and workers lose their wages. If nations enter into a prolonged round of negotiations to liberalize trade, they forgo the benefits of the enlarged trade while they are arguing about the division of the gains.

    The common thread is that all parties to the negotiations prefer to reach any given agreement sooner rather than later. In reality the shrinkage occurs in complex ways and at different rates in different situations. But we can adequately illustrate the idea in a very simple way: First suppose there is only one step involved. If Baba agrees, the division occurs as agreed; if not, the pie melts and neither gets anything.

    Now Ali is in a powerful position: Even if she proposes to keep percent of the pie for herself and just let Baba lick the knife at the end, the only thing Baba can do is to take that lick or get nothing.

    Of course Baba may turn down the offer from sheer anger at the unfairness of it. In practice Ali will have to think about such matters, and offer Baba just enough perhaps a small slice?

    To keep the exposition simple, we will leave these complications aside and suppose that Ali can get away with claiming percent. Again there is an ice-cream pie on the table but now it takes two rounds of bargaining before the entire pie melts. Now Ali must look ahead to the consequences of her initial offer.

    She knows that Baba can turn down her offer and come back in the powerful position of making a take-it-or-leave-it offer in splitting the remaining half of the pie. This will give Baba essentially all of that half. If Ali were to allow this second stage to come to pass, she would get nothing at all. Knowing this, she will open by offering Baba half, that is, just enough to induce acceptance while getting half for herself. They agree immediately to split the pie The principle is now clear, and we can easily add one more step.

    Again let the negotiations speed up or the pie melt more slowly. With each offer and counteroffer, the pie goes from whole to two-thirds to one-third to zero.

    If Ali makes the last offer, when the pie has shrunk to a third, she gets it all. Knowing this, Baba will offer her a third when it is his turn and two-thirds of the pie remains.

    Thus the best Baba can expect is one-third, i. Knowing this, Ali will open the bargaining by offering him the one- third just enough to induce acceptance and get two-thirds for herself.

    What happened to the It reappears every time the number of steps is even. More importantly, even when the number of steps is odd, the two sides get closer and closer to With four steps, Baba will make the last offer and get the quarter that is on the table at that point. Therefore Ali has to offer him a quarter at the last-but-one turn when there is half. Then at the turn before that, Baba can get Ali to accept only a quarter out of three- quarters.

    Therefore, looking ahead to all this, Ali opens the bargaining by offering Baba half and getting half herself. With five steps, Ali will open by offering Baba two-fifths of the pie and keeping three-fifths to herself. With six the division is once again More generally, when the number of steps is even each side gets half.

    In the typical negotiation process, the pie shrinks slowly so that there will be time for many offers and counteroffers before the pie disappears. The split- the-difference solution seems pretty hard to escape unless the negotiations have been deadlocked for a long time and there is hardly anything left to win. It is true that the person who goes last can get everything that remains. But by the end of the negotiations process there is hardly anything left to win. Getting all of nothing is winning the battle and losing the war.

    The later stages of the process are never called into play. This observation in turn suggests another dimension of strategy in bargaining.

    The principle of looking ahead and reasoning back may determine the outcome of the process even before it starts. The time for strategic maneuvering may be earlier, when the rules of negotiation are being decided.

    The same observation also leads to a puzzle. If the process of bargaining were exactly like that depicted here, there would be no labor strikes. Of course the prospect of a strike would affect the agreement reached, but the company—or the union, as the case may be—at its very first opportunity would make an offer that was minimally acceptable to the other party. The reality of strikes or, more generally, breakdowns of negotiations must arise from more subtle or complex features of reality that were excluded from the simple story above.

    We will touch upon some of these issues in Chapter War and Peace A second illustration of backward reasoning comes from considering how peace can be maintained through a series of bilateral antagonisms.

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