‘Game Theory and the Real World’ with IIM Calcutta’s Prof. Arijit Sen

picture-1770The External Relations Cell of IIM Calcutta brings forth the 7th Episode of Insight, a Faculty Interview/Talk series. For this episode we have Prof. Arijit Sen from the Economics group speaking on Game Theory and its applications in the Real World. Prof. Sen received his Ph.D. in Economics from Princeton University and has been teaching at IIM Calcutta from 2005. His research involves using tools from Decision Theory and Game Theory to study economic issues related to Industrial Organization, Social Interactions and Development. Please find below the detailed transcript of his talk.

Q1: What is Game Theory all about?

In a nutshell, game theory studies rational decision making in interactive environments. Now let me explain what I mean by rational decision making and what i mean by interactive environments. Suppose you are planning to climb Mount Everest. You have a bunch of very serious decisions to make: which route to take, what equipment to carry, so and so forth. Now you could make these decisions in one of many ways. You can either follow your gut instinct or you can mimic what the last climber did or you could sit down, enumerate your goals, your options, and your constraints and take a set of reasoned decisions on the basis of all that information. This last thought process which essentially involves solving a constrained optimization problem is what rational decision making is all about. In the terminology of Prof. Daniel Kahneman this is thinking slow, very slow. Now however complicated that decision making process is, it’s a decision that is being made against nature. It’s a decision that is being made against Mount Everest, and Mount Everest doesn’t play games with you which mean this decision is being made in a non-interactive environment. Mount Everest doesn’t cause an avalanche on your path of climb simply because you have chosen that particular path to climb the mountain. That’s the big difference between making decisions against nature versus making decisions against human beings. And when you are making decisions against human beings, you are making decisions in an interactive decision environment. Let’s say you are a new airline company who has come to India, Clearsky, and you have a small market share right now, and you are trying to increase your market share while maintaining a reasonable profit flow. Now that endeavour is no easier than climbing Mount Everest. And it also involves making a set of complex decisions regarding route selection, regarding pricing, marketing so on and so forth. But more importantly and in contrast to climbing Mount Everest your airline company decisions have to be made in an interactive environment where other incumbent airline companies will respond to your decision in a way so as to defeat your goals of increasing your market share. In that sense, you are involved in a strategic interaction with your competitors, and that’s precisely the decision scenario that game theory aims to study. Game theory aims to study an environment where the final outcome depends on the decisions of all players in the game and where every player is aware that other players will respond to her decision either after observing the decision or by anticipating it. And the outcome of this cross current of decision making is what game theory wants to study.

Insight Episode 7: Prof. Arijit Sen

Q 2: Is Game Theory just a “theory”, or can it be of some practical use to people?

It’s easy to give real world examples where the lessons of game theory are directly used. As we speak Mr. Vishwanathan Anand and Mr. Magnus Carlsen are involved in a high stake decision making in a very interactive environment, something we know as the game of Chess, and they are certainly using game theory logic either consciously or sub-consciously to determine their playing strategies. Alternatively, think of IPL auctions where franchise owners bid for cricketers in an IPL auction, their bidding strategies are, or at least should be, informed by game theory. On a completely different line of thought, think about very high stake diplomatic crisis, like the Cuban missile crisis. In international diplomacy of that kind, knowledge of game theory can help formulate appropriate strategies. Now these are very specific examples of explicit strategic interactions, and game theory certainly has a lot to say about these kinds of interactions. But I would like to emphasize that learning and understanding game theory has a deeper and a more lasting value to a decision maker. Knowledge of game theory enables a decision maker acquire a more intelligent way of thinking about how to make choices. Specifically in any interactive environment, game theory forces you to think about two very important points. One, when I make a particular decision I must ask myself how others will respond to my decision. And two, when making a particular decision I must put myself in other people’s shoes and try to understand how they value and view the problem and what kind of choices they might be contemplating. This second idea about putting myself in other people’s shoes in order to make a better decision for myself, is a very fundamental and very valuable game theoretic notion and let me try and clarify it a little bit more by rephrasing it in terms of Cricket. So your team is playing the opponents and you guys have done very well in the first innings, and you are in a position to impose follow-on on the other team. In such a scenario it’s not enough for you to ask what decision of mine will be good for my team. Are my bowlers tired? Do I want to bat in the last innings? So on and so forth. You must also ask what decision of mine will be bad for the opposition. If the answer of these two questions are the same, decision making is a piece of cake for you. But the answers are contradictory; you will have to think very hard about which one of these two issues is more critical in improving your chance of winning the match. And these are the kind of insights that decision theory and game theory brings forward.

Q 3: What about Behavioural Game Theory? Does that theory not reject the premise of “Rational decision making”?

Let me explain the subtle relationship between neo-classical game theory, the game theory that we have been talking about, and behavioural game theory. You see in a strategic game each player has to do two things. Predict how others will play, and given that prediction determine the best thing to do i.e. determine your best response. Now neo-classical game theory makes a consistent but optimistic assumption that every player makes a strategy choice in this way, and every player knows that every player makes a strategy choice in this way. In contrast, behavioural game theory takes a more ambiguous but often a more realistic position that most people do not make choices in such a rational manner. Rather they have specific behavioural biases and these biases influence their decision making. It could be status-quo bias, it could be endowment bias, it could be fending effects, so on and so forth. So behavioural game theory goes on to say when you are forming a prediction how others are going to play, please keep in mind that people are quite likely to be behavioural and not rational. So let’s say that you believe this theory, and you form your prediction by taking such behavioural biases of your rivals into account. But after that, what will you do? Will you best respond to your predictions or will you succumb to your own behavioural biases. If you were clever enough to form your prediction correctly, will you not possess the mental faculties to best respond, but if you do that you have engaged in rational decision making, and you’ve also behaved in a very schizophrenic manner by believing yourself to be the unique rational individual in a sea of behavioural people. This is the dichotomy between neo-classical game theory and behavioural game theory that is hard to reconcile. Now one way of achieving reconciliation, and it’s a not a very satisfactory way, but it’s one way is to say the following: As an outside observer trying to predict the outcome of a strategic interaction we should certainly make use of the teachings of behavioural game theory because we really do believe that many people in the world are behavioural. However, as a strategy consultant to a specific player in a specific game, we should give the following split advice, dichotomous advice. Assume that it is very likely that your rivals will be behavioural and use your information to form your predictions about rival play but having formed the prediction, be as rational as you can and play your best response against that. This is certainly dichotomous, but this most probably is the only way to reconcile neo-classical game theory with behavioural game theory.

Q 4: Can you give some real-world examples that you have heard or read about, and said to yourself: “Now that is great strategic thinking!”

Two examples come to mind. Nothing earth-shattering, but very good instances of clever strategic thinking. I will not reveal the identities of players, but I will simply describe what I have heard or read.

So story no. 1: Presidential elections were about to be held in a country, and there were two leading candidates X and Y vying for the job. While campaigning was going on, the country experienced a sudden financial crisis. Candidate X promptly announced that he would temporarily suspend his campaigning in order to help the government resolve the crisis. Candidate Y did not pre-emptively move, but in response to candidate X’s announcement, quietly announced that he would do two things. He would continue his campaign and he would help the government resolve the crisis. Candidate Y hinted that a serious contender for the presidency of the country should indeed be able to multitask and candidate Y eventually won the presidency. I do consider this to be a striking example of strategic thinking or lack thereof, where the inability of one player to deduce how his opponent would respond allowed the other player to secure a very important second mover advantage.

Story No. 2, in a very different context. In particular business school, it was tradition of job recruiters to make exploding job offers i.e. offers with very short time fuses, essentially to prevent students from shopping around while holding multiple job offers in their hands. But then the students shopped around after starting their first jobs and they remained in their first jobs for a very short time, on an average, less than a year. So one placement year, one particular recruiting company came in, selected the students and made the following offer to each of the recruited students. You have one year to make up your mind whether you want to work with us. Take your time, check out other jobs if you want to, and if you are convinced that we are worth it, come back and join us at the end of the year. In my view, this offer, what will I call it, an imploding offer as opposed to an exploding offer, was a very smart one, and it exhibited a much clearer understanding of the strategic constraints facing the students and tried to alleviate these constraints in a way that could indeed be beneficial for both parties. That’s certainly game theory at work.

Q 5: Is Game Theory only about being clever strategic thinkers who can out-smart their rivals, or can the theory also be used to generate “better social outcomes”?

The logical culmination of game theory is game design, or mechanism design as it is called. The basic idea is the following: If we indeed have a good understanding of how people play in different games, we can certainly get a bit more ambitious and start thinking about designing good games. Good games are those which have the following property: when players play in these games in order to achieve personal goals, good social outcomes emerge. Recall Adam Smith’s observation regarding the beneficial effects of the invisible hand of the market mechanism. So mechanism design in the business of designing nice invisible hands. Now game design, mechanism design, is a fascinating end point of game theory, and once the bug of game theory bites you, you start seeing its applicability all over the place. Let me briefly mention three instances of game design that can be relevant for people like you and me who are located in an academic institute.

One, schemes about students job placement, the issue being how to efficiently match graduating students with prospective employers by recognizing the students’ preferences over employers, and the employers’ preferences over students. Now there are many mechanisms out there. One of the most important ones are the national intern matching program in the US, that matches medical interns to hospitals. This is a specific mechanism for job placement, and we could think of related or even better mechanisms.

Two: faculty promotion schemes. The issue here is to identify and retain productive faculty. A very popular mechanism in the US, of course, is the academic tenure system, and this mechanism is now propagated through the rest of the world somewhat as well, and we can think of related mechanisms to ensure how to identify and retain productive faculties.

And three: alumni fund raising schemes. How to encourage affluent alumni to contribute towards improving your academic institution. Here a specific mechanism or a specific game could go as follows: The institute describes a particular a development process or a development project that it has in its mind and commit some seed-money to that project and having committed the seed money that it carries out in an alumni fund raising in multiple rounds, always keeping potential donors informed about how the gap between the financial needs and the committed pledge is narrowing overtime. That’s one mechanism, you can think of others but the fact remains there are many such mechanisms in various aspects of social life and economic life that we could be thinking about. Let me conclude by recognizing that it is precisely in this realm of game design that behavioural game theory can turn out to be very relevant. If many people in this world are indeed behavioural, it will be important for game designers to take the subjects’ behavioural biases into account while designing such games. And to the best of my knowledge this was precisely the idea behind the UK government setting up its behavioural insights team, better known as the Nudge Unit, for effective policy design.

IIM Calcutta

IIM Calcutta External Relations Cell