Hello and welcome to the world of game theory. Let's get started with a game, where we start with giving you $100 and a button. We can't do this for real, unfortunately, but please take the situation seriously. Imagine that 100 viewers in 100 rooms across the country are watching this video, and each has been given $100 and a button, just like us. In a moment we'll be asked to decide whether to push your button or not. That's the only decision we'll have to make, and in doing so, we'll be deciding upon a strategy. In every game, every player has a strategy. If you're a rational player, you're going to try to adopt a strategy that will maximize your expected payoff, given what you know or think you know about the other players in the game. Yet you don't know enough yet, to know whether to push it. What's it do?

Well, pushing this button has two affects, one that affects us, and one that affects everyone else. Actually, if one's actions affected no one else, it wouldn't be a game, since they are interactive by definition. So when you push your button, the first thing it does is to take $2 away from every other player. So if you push your button, then just like that, everyone else is down to $98. Yet you still have your $100. Sounds rather viscious on your part!

Yet other people may press their buttons too, you know. Everytime they do, you loose $2, along with everyone else. If 60 other people push their buttons, you're going to lose 2 time 60, or $120. Given that we only received $100 to start with, you're going to end up $20 in debt and will have to pay up.

Except that there's a way out of this for you. We said that pressing the button has two effects, and the second one targets you. If other people press their buttons and cause you damage, pusing your button will cut that damage in half. So when we said if 60 people push and you lose $120, but then you also push, then you only lose $60. So you're still $40 to the good. You've don $2 damage to everyone else, but you've saved yourself $60. So are you going to push?

You're probably made some assumptions about this game, reasonable ones as it turns out. You've assumed that everyone else's button works the same way that yours does. It does, because this game is symmetric and everyone's in the same boat. Also, since you're watching this on a DVD, you've probably assumed that everyone else has the same information that you do. That is, that the structure of the game is common knowledge to everyone. Yet actually, being common knowledge means quite a bit more than that. It's not just that everyone knows the rules of the game, but it's that everyone knows that everyone knows the rules of the game. Also it's that everyone knows that everyone knows that everyone knows the rules of the game, and you get the idea.

So you're right. Everyone knows the same information that you do. We need to think carefully now and decide what we're going to do, push or not push? We'll get about one more minute. You're probably entertaining several different lines of thought right about now. One line of reasoning is as follows. We all know how the game works, and it's obvious that if nobody pushes the button, everybody gets $100. I might not even be concerned about being a nice person, but I don't have to be. We can all get $100, so we'd be crazy to push. It's a good argument.

Yet a second line of argument, maybe even more compelling, is this. A group of 100 people we don't know. Some are going to push. No matter what the other people do, I'm at least as well off pushing as not pushing. If I don't push, I could end up $100 in debt. If I push, at least I end up breaking even. Heck, I'm a good person. If I'm thinking about pushing, I can imagine what the other people are thinking also. I have to push in self-defense.

Here's a third line. I'm not going to push. I'm not pushing because it's the right thing to do in a moral sense. I could lose up to $100, and could go $100 in debt. Yet it's worth it for the sake of my ethics.

Or you may have decided that $100 is not that much money. It would be too much fun to just stir things up and see what happens. So you Push the button.

Or you may have a competitive streak, and you know that if you don't push, everyone who does will end up ahead of you. Maybe you don't have much of a taste for being a chump.

Of these five lines of reasoning, It's interesting to know which if any actually are rational. That's a question that we'll revisit over and over as this course goes on.

OK, it's time to decide. Scott really wishes he could tally the votes coming in, in real time, but of course he can't. Yet what he can and will do, is tell us after we make the choice, the results of similar games played with other people. So make your choice, and please state it out loud! Keep yourself honest. Push or don't push, 3, 2, 1, done.

OK, with groups of strangers who had no training in game theory, generally between 30% and 70% push the button. That's a pretty wide range, but if you take the average you get 50%. So if you didn't push, that means that you're now broke. If you pushed, you still have $50.

This might not make that much of an impact on you, after all, this was just a game. No, that's the wrong way to say that. What we meant to say, of course, is that this is just pretend. Yet the game is real, not pretend. We're not talking about child's play here. We defined a set of possible moves by which players interacted with each other. They had common knowledge of the structure of the game and made rational decisions about strategies, which led to their best expected payoff.

These components of players, strategies, payoffs, and common knowledge, are what make a game, a game, in the game theoretic sense. If you change the context of the game by replacing the players with countries, and change pushing the button to being willing to engage in military conflict, then we have something which is much more than just a diversion.

Later in the course, we'll find out how game theory says this game should be played. Yet at the moment, what we know is how it is played. The variety of responses we've seen in this game, between 30-70% pushing, show that one of two things must be the case. Either the theory of game theory isn't sufficiently common knowledge that people are comfortable choosing rightly, or maybe this game is an inherently dangerous one. Maybe we need to find a way to keep pushing the button from being so tempting an option, because if 30-70% of the people in the nuclear version of this game, decide to press the button, we're all in for a very bad time.

In any case, the name game theory may be an unfortunate one. A more descriptive name would be strategic interactive decision making. Game theory sounds like child's play, and it's not. One of the landmark book in game theory was written in 1960 by Thomas Schelling, The Strategy of Conflict. He later won the Nobel Prize in Economics for his work in game theory. His book looked at issues such as nuclear disarmament and deterrence, resolution of international conflict, and a lot of issues as relevant today as they were in the 1960s during the Cold War. How do you make a threat, for example? If you do make one, how do you make it credible?

When most of us think of games, we think of hard games, board games, or sports. Game theory can be, and is, applied to such areas. In fact, it really got its start when John von Neumann 103-1957 started thinking about the optimal way to play poker. He was one of the most brilliant minds of the 20th century, and the father of modern game theory. Yet he wasn't actually that interested in poker per se. It was that poker contained, in a simplified and idealized way, a microcosm of human interaction. Groups of individuals, each with their own goals, power, information, beliefs, responding to the decisions of others.

John von Neumann wondered if it was possible to model something as quintessentially human as bluffing, in a mathematical way? By 1928, he published his first paper on game theory, the first important work in modern game theory. This included the minimax theorem that we'll discuss in a later lecture. Yet in the less than a century following this theory, game theory has made remarkable advances. In some ways, it has come full circle. A number of the winners in recent poker championships, have combined von Neumann's game theory with the number crunching power of modern computers to develop their winning strategies.

This is indeed impressive. yet board games, card games, and sports, aren't at the heart of game theory. Again, game theory is the study of strategic interaction among rational players. Anytime that people are interacting with one another, responding to the choices of others, or what they think those choices will be, they're playing a game. That's waht game theory is really all about.

What's the best way to play the game that we're in? How can we recognize a game that isn't so good for us? When that's the case, how can we change it so that perhaps we'll do better? Reinhard Selten b.1930, one of the winners of the 194 Nobel Prize in Economics for his work in game theory, says that most people don't ask these questions. Even when making professional decisions, they engage in what's called "ex post rationality." They are more likely to look backward to see how earlier situations could have been done better, than they are to look forward and examine the current situation in its own right.

Here's an example of failing to look ahead. Max Bazerman of the Harvard Business School, was speaking to a conference of about 75 Wall Street bigwigs. He auctioned off a $100 bill, with one odd twist. Whoever won it, paid their bid and got the $100. No surprises there. Yet the person who bid second highest, also had to pay their bid, yet got nothing.

So the auction was held, and the $100 bill went for $465, all for a $100 bill! How? Bidding got to $95, then $100. If it had stopped there, the $95 bidder would have been out $95 with nothing to show for it, in second place. Yet if they bid $105 and won, then they'd only be out $5, so they bid $105. Yet now the person who bid $100, was out $100, so they bid $110. This cycle repeated until someone finally got the message at $465.

Now the structure of this auction was unusual, yet again these bidders weren't yokels. They were titans of Wall Street, controllers of multi-million dollar portfolios. Bazerman says he's run this game at least 600 times and has never seen the bidding stop at less than $100. If you think the structure of this auction is just silly, Scott will point out that the war of attrition has just this structure. Costs keep on mounting up and up, until someone gives up. Everybody pays for the protracted war.

Later in the course, we'll look more closely at wars of attrition, and also look into auctions and see how the design can have a dramatic and sometimes surprising impact on the money raised. The $100 auction brings up a point we'll make at the start of this course. A lot of the games we'll study are pretty simple in structure, more than the things we face each day.

This simplicity of the examples is one of the common criticisms that are made of game theory Reinhard Selton addressed this point nicely, saying that our examples are indeed simple, which is precisely what makes them useful in developing an intution about how to solve real-world problems. Think for a minute about how effective decision-makers generate decisions. They blend previous real-world experience, with clear examples of general principles. Our games act as parables, in part because they are relatively simple. They're analogies for the more complicated games we face in normal life.

So we often choose our examples to be as clear as possible, like the $100 bill example, rather than trying to rip them from the headlines like a war of attrition. Game theory, properly applied, can be applied to eminently practical real-world problems. As an example, we'll be studying co-opetition, a game theoretic model of analyzing business interactions, developed by two business school faculty from Harvard and Yale. Co-opetition is thoroughly grounded in game theory and directly applicable to real-life decision making.

Yet game theory isn't a fantasia. There are places where the predictions of game theory and observed behavior, diverge dramatically. In this course, we'll be looking at the failures of game theory, as well as the successes. Even the failures can have practical value.

Ever travel to a foreign country? Then you know that one benefits of such travel is when you come home. You see your own society, its norms and values, in a new light. In the same way, when game theory predictions differ from the decisions we make in everyday life, it can lead us to looking more closely at the decisions we do make, and better-understand why we make them. Essentially, game theory provides a baseline for comparison.

People have ben trying to make strategic decisions for a long time, in war, politics, business, and love. So it's not surprising that game theory has been around for a long time. Even Greek mythology includes quite a few game theory stories, as we'll see later in the course. Yet modern game theory is less than a century old.

John von Neumann's mathematical work didn't catch the attention of the larger world until 1944. In that year, he teamed up with economist Oskar Morgenstern to write The Theory of Games and Economic Behavior, certainly the most famous game theory book of all time. They wanted to introduce people to this new field of study, and to show how it could be used in neoclassical economics. Well actually they were a lot more ambitious than that. What von Neumann wanted to do was to provide a foundation that would allow the study of economics to be conducted as a science, like physics. It was an ambitious goal, and the theory of games made a good start at it.

Earlier economic analysis, usually dealt with markets. These are essentially unaffected by the auctions of any one individual. You make your choices in response to the market, but your individual choice doesn't affect the market very much.

Yet with game theory, you can analyze which individual choices do do matter. The result has been a lot of good economics, and a long string of Nobel Prizes in Economics, for people who have done work in game theory. Like what, and what's it good for? Well a number of prizes have been rewarded for work involving auctions, so lets get another real-life example. One a little more complicated than the $100 game.

Federal governments generally regulate their radio spectrum. They sell the rights to various parts of that spectrum, to those interested in licensing them. This is generally done in one of four ways:

by an administrative process
by lottery
by first come first serve
by auction

Usually in most parts of the world, it has been done by an administrative process. That's how it was in the US, which meant long hearings with the FCC.

Yet them by the 1980s, the number of forms wanting licenses skyrockted. By 1982, the FCC adopted a lottery system. The licenses were given away to whoever won. It was thought that afterward, the telecom companies would sort it out amongst themselves by trading licenses back and forth.

It was not a great plan. Lotteries are inherently inefficient. Obviously those who win, are not necessarily those who will value the resource or be best able to use it. The reshuffling of licenses that came about, actually delayed the entry of the US in the wireless telecom market when compared to Europe.

Also, the FCC put no restrictions on who could enter the lottery. Sometimes this had embarrassing consequences. One year, the cellular license for Cape Cod went to a group of dentists, who were no fools and promptly sold it to Southwestern Bell for $41 million! By 1993, the lottery approach was deemed to be a failure by congress, and mandated that the FCC try some kind of auction. It was concerned about issues of inefficient of course, yet also wanted to get a slice of all that money being passed around by license exchanges.

Yet it turns out there are actually a lot of different ways to run an auction. We'll look at a number of them in a later lecture. So the government tried to address multiple objectives. Yes they wanted to raise money, but wanted to make sure that the spectrum was distributed efficiently. They wanted to channel business to minority owned businesses, avoid monopolies, and so on.

So the FCC hired a bunch of economic game theorists to design the auction. Their job was to analyze the problem and come up with the structure. The details don't matter here, but one aspect is important and we'll focus on it. They designed the auction so that all the frequencies would be auctioned off simultaneously in a number of rounds. Different markets were up for bid at the same time.

You see, bidding on frequencies one at a time, is kind of like bidding on shoes one at a time. If you're not sure you're going to get the left one, you're not going to pay as much for the right one. In the same way, a company might put a lot more value on the cellular licenses for, let's say, Washington, if they know that they can get the ones for Baltimore at the same time.

So with the help of game theory, the government created a game that was much better than the old one. Certainly it was much better for the government, who raised of $400 billion for the US Treasury in the first five years.

Yet it was demonstrably better for the other stakeholders as well. The structure of the auctions meant that the licenses went to those who valued them most, as opposed to say, dentists. That's game theory, strategic interactive decision making.

When Scott told his mother he was teaching this class, she thought it was going to be 24 lectures on Parker Brothers' Monopoly or Risk. The monopolies and risks we'll be talking about are of a much more serious nature. game theory sounds like fun, and it is fun to study, yet many of its applications are far from trivial. The Cuban Missle Crisis was a game. In fact, it was Thomas Schelling of the Straegy of Conflict fame we mentioned, who coined the term brinksmanship.

The leadup to the war in Iraq was full of games, a lot of them being games of incomplete information. Hans Blix was looking for weapons of mass destruction, and Sadam Hussein, if he had had them, would have been trying to hide them. This is a classic pursuit/evasion game, and in a later lecture we'll see how such games play out. As it was, Hussein didn't have WMDs and said as much. His problem was the one you often have when try to signal the truth of your claim. We'll see that signaling and signal jamming, it's opposite, are also important parts of game theory. The biggest problem Hussein faced was the one that people usually face, how do you make yourself believed?

Game theory applications don;t have to be geopolitical. Think of threats, promises, and commitments. Yes, they could be useful in brokering a treaty, but also in passing a piece of legislation or getting your supplier in coming down on a price for a supply, or getting your kid to do his homework. Threats, promises, and commitments, have their own lecture in this series, and can give you enormous leverage. Yet using them is a lot more subtle than many people think. Ever seen a mother in a grocery store yelling to a kid, "You come here right now, or I'm leaving without you." That's a very serious threat, yet also in general is completely and sensibly ignored by the kid. Schelling will teach us how to make threats, promises, and commitments, and how to make them credible to others.

As we go through the course, Scott will invite us to go beyond the typical example we're discussing. The power in science and mathematics is in generalizing, in seeing how apparently different problems, share a common, underlying structure. If you keep your eyes and minds open, you'll find a lot of other places to which our ideas apply.

For example, remember our button game? If you think about it for a bit, you can see it's a lot like the problem of global warming. So also the problem of overfishing of international waters, and traffic congestion. All of these fall under a game structure called the tragedy of the commons. We'll look at how all these things fit together in a later lecture. When we do analyze those things, we'll gain some other surprising insights, like why we use such an inefficient layout on our keyboards, or why we don't use the metric system, or why windows is the operating system for personal computers?

After we figure these things out, there will be a hundred other problems that yield the same kind of tools, like why taking illegal steroids is so common among professional athletes. We'll look at voting, and we all all know from recent history that deciding who wins isn't always simple. The popular vote versus the electoral vote, is only the tip of the iceberg though. The playwright Tom Stoppard said that it's not the voting that's democracy, it's the counting. We're going to see that it isn't even simply the counting.

There are a lot more ways to setting up a voting system than most people think. Each has its own strengths and weaknesses, and we'll see that the choice of which system we use, or even simply the order in which most votes are taken, can effectively decide the results of the election, before the ballots are even cast. Can we fix this? Well, we'll create a wish list of properties that an ideal voting system would have. Then we'll determine if such a system is even theoretically possible. Why do candidates who make it throught the primary process, often show so little difference in the general election? Well, we'll have an answer.

In the world of business, we'll look at pricing decisions game theoretic perspective that will allow you both to increase the size of the pie, as well as the fraction of it you get to keep.

We'll be crossing game theory with biology, and look at the recently developing theory of evolutionary game theory. It has applications in everything from bacterial drug resistance, to the evolution of cooperative behavior. We'll look at why the peacock has such a long tail, and why some gazelles jump straight up when being pursued by a cheetah. We'll see why an engagement ring makes sense, how world class soccer players and Nascar drives use game theory, whether they know it or not. We'll look at why you can never seem to buy a good used car, why pitches in the Nation League throw fewer bean balls than those on the American League, why car insurance costs more in Philadelphia than Pittsburgh, and why having more people witness a crime, can actually reduce the chance that anybody alerts the police.

We'll figure out why it often costs more to get your car repaired as a tourist, then when you're a local. We'll even look at terrorism and see what our game theory has to say about our approaches. Game theory has applications great and small. Someone even wrote a game theoretic analysis on whether to leave a toilet seat up or down in a married couples' home. We won't bother telling the results of that study, since we can all agree that it won't make a bit of difference.

So let's get started with game theory. We've defined it as the study of strategic interaction among rational decision makers. This phrase sounds more or less self-explanatory, yet there are some subtle issues to address here. There are three major components of any game, players, strategies, and payoffs. The players are just the people playing the game, easy enough.

Each player has available a possible set of strategies, what they'll do, how they'll respond. When those strategies interact, each player ends up with a payoff which specifies how much they like the result. If we told you we had a good strategy to follow, you'd probably assume we meant we had a good general plan. At most you might think we have a swt of rules we use, when making our decisions.

Yet what we mean by a strategy in game theory, is quite a bit more than this. In game theory, a strategy has to specify what decision you would make in every possible situation in which you could find yourself. Suppose we buy a vase full sale for $8, and we're deciding on whether to sell it for $10 or $20. You are a potential customer, and you're deciding whether to buy it.

Well our strategies are easy to describe. We only have two, either sell it for $10, or for $20. Your strategies as buyer, are actually more complicated, because you can find yourself in two different situations, depending on the price we set. One strategy for you, has to specify how you'll respond to either of those possibilities. For example, you might buy it for $10, but not for $20. You actually have four different strategies:

buy for $10, or for $20
buy for $10, but not for $20
buy for $20, but not for $10
don't buy for $10, or for $20

The idea of "buy for $20, but not for $10" might sound silly. Yet it might not be, since you're more likely to buy a reputed diamond for $200 then $20. We'll look at the idea of strategy in more detail next time, but today we're just sketching things in broad strokes.

With that in mind. let's take a minute to talk about the third component of our game, payoff. Each player has chosen a strategy. These strategies interact, and the game plays out to its conclusion. You might like the outcome of the game, or you might not. The degree to which a player is satisfied with the outcome, is reflected in their payoffs. These are numerical values, and we generally follow the convention that the more you like the outcome, the bigger the number.

In our retail game, we bought our vase for $8. If we sell it to you for $10, but you think it's worth $18, we've made $2 on the deal and you've made $8. Those would be our payoffs, if money is what we care about. Things aren't always that simple however. Next time, we'll take a more careful look at payoffs and strategies, also locking down two other key ideas about game theory, rationality and common knowledge.

As we'll see, rationality isn't what most people think it is. We'll also see a game where game theory does a horrible job of predicting human behavior. A careful look at this failure, will highlight an important point, that your payoff from a game, can e far different from the money that it pays you.

So come join us. Game theory isn't child's play,but it's going to be fun.