You did your undergraduate degree in accounting at the National Taiwan University. Could you tell us about your undergraduate years?In Taiwan, the college entrance exam used to be a single exam, and the competition was so intense. The total score was 550, and I was just 0.5 point above the cut-off for accounting. I was extremely happy to be admitted into accounting because people were saying how accounting students will have a bright career and get multiple job offers upon graduation. Guess what was the course that’s one cut-off below? Economics. For an undergraduate studying accounting, the typical career path is to get a CPA. My peers were all talking about getting a CPA and working hard for 10 years or so. Once you become a partner at one of the top four accounting firms, you are basically set for life. You have to stay in good health because those 10 years of work will be super intense — physically and mentally. At that time, that’s what I was prepared to do. But one or two years into my accounting degree, I realised this was 100% not for me. It’s probably not the case anymore, but my under- graduate accounting training was much better suited for those who are willing to practise accounting. There was no flipped classroom or virtual exams then. Preparing for exams meant practising a lot of problems in the textbook (and yes, there was a solutions manual that every student would buy together with the textbook). Most professors would randomly select some questions and repeat them verbatim on the exams. You do well in those exams if and only if you put in enough time practising the textbook questions. There were more girls than guys back then and especially the girls had impeccable persistence in practising the questions. Some of them would practise every single problem in the textbook, check the solution, and then repeat that process three or four times on average. As for me, just before the exams, I would randomly select one or two problems from each chapter and then go straight to the solutions manual. I passed my exams but I didn’t exactly feel proud of my scores.

How did you go from a bachelor’s in accounting to a PhD in economics?Accounting students were required to take principles of economics, which was taught as an exposure module. I did my intermediate microeconomics with the Economics Department so it was more detailed and formal than the one the accounting students were doing. It’s similar to what’s taught in EC2101 and EC3101: forming the Lagrangian function, solving utility maximisation problems, equating the marginal rate of substitution to the price ratio, etc.I could manage those but I didn’t feel terribly inspired or interested in the subject. In the second half of my sophomore year, I came acrossa course called Game-Theoretic Marketing Models. It was jointly taught by two finance professors and a marketing professor. I was running out of elective modules to take, and I didn’t want to take accounting modules anymore. Alsomy understanding from my intermediate microeconomics module suggested that game theory was nothing buta bunch of two-by-two matrices. I expected to solve for the Nash equilibrium by underlining the choices with the better payoffs. It turned out that the module targeted advanced undergraduate and master’s students in marketing. The professors allowed me to take it only because they needed to enrol at least five students to offer the module, and I happened to be the fifth student. Some two-by-two matrices did appear but they were gone probably after the first 30 minutes of the course. It’s totally mathematical — probably like our 5000-level module on industrial organisation.

That sounds like a very difficult class!It was very tough. It was my first exposure to formal game theory, and I didn’t have any formal quantitative training as a sophomore accounting student. I knew the most basic calculus — probably the type of math taught in EC2104. To me, statistics was checking tables for the p-value. I had no idea what a distribution or a density function was. The module showed me the kind of math preparationI would need if I wanted to study economics at the graduate level. There is no better way to learn something than doing it. I basically self-studied the entire course because the professors answered my questions in a way that I could not really understand, e.g., they would tell me to go and check my textbook in probability theory. I realised that game theory can be applied to many interesting problems in different fields. I saw how researchers can formulate real-life situations such as firm competition in a game, how they analyse firm competition as a formal model, and how they express an equilibrium as a mathematical object. I started to pick up the required math in my third year of undergraduate studies after I saw how math was used in that module. I went to the math department to learn with the math students. If you want to do a graduate degree in economics, you will definitely need to know things like linear algebra, advanced calculus, real analysis, and mathematical statistics. I took these modules in the third and fourth years of my undergraduate studies. I had a lot of interest in learning these topics because I had seen how they are used in economics.

What have you noticed about students from your 12 years of teaching at NUS?I bet most professors can tell whether a student is askinga question to score points on the exam or to understand the material. Of course, the former is most often the case. Still, I feel I am getting fewer and fewer “challenging questions,” which come from students who truly want to understand at a deeper level. Economics takes nothing for granted. We learn that consumers have utility functions that represent their preferences and satisfy certain axioms. Why should we believe

ProfessorChen Yi-ChunStudent Interviewer: Huang Xiuqi

Accounting for Game Theory

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that? Students can challenge me and say that nobody at the supermarket uses their utility function and solves the Lagrangian to decide what to buy. So why do professors bother to teach utility maximisation? Students can argue that humans are never fully rational. We make mistakes, and sometimes our calculations are wrong, or we are logically inconsistent. So why am I teaching a theory that’s both logically consistent and calculation intensive? That’s what I mean by understanding. I feel that there are fewer and fewer questions of that sort. Maybe that’s because I have gradually learned what to avoid and what to say to pre-empt student’s questions. I have been teaching 4000-level modules and I enjoy interacting with students in my module. Still, I hope to get more questions of the “wanting to understand” kind because that’s the starting point of learning and research.

Do you think the different questions stem from students who want to do a PhD versus those who want to find a corporate job?I think many students tend to apply this sort of dichotomy and think that there are two separate career paths, especially in economics. My personal experience suggests that the dichotomy is not as clear as most people assume, at least at a higher level. When I was an assistant professor, teaching and research occupied all my time. But after I got tenure, I started to do more and more administrative duties. I was invited to serve in the Dean’s Office, starting as an Assistant Dean in the Undergraduate Studies Division. After my sabbatical, I was promoted to Vice Dean of International Relations and Special Duties where I am responsible for the Student Exchange Programme and the FASStrack summer school. I am now also the Director of the Risk Management Institute, which is a university-level research institute hosting the Master of Science in Financial Engineering programme. I have benefited a lot from keeping a researcher’s mind while carrying out my duties as an administrator.

Can you explain how research is connected to administration?Some of the things that students learn in university are directly related to their future work. For instance, if you become a civil servant doing policy planning, you will be writing policy reports, which will certainly require the knowledge gained in modules on econometrics, labour economics, or money and banking. This type of knowledge is directly related to your employability and has less to do with research because it’s mainly about applying the state-of-the-art economics knowledge. Research is about the creation and discovery of new knowledge. At some point, however, when you are promoted toa management role, you must start to think more about the organisation’s objectives and future plans. You will not have encountered every single problem before, nor can you just apply what your professors taught you or what your manager told you to do. Once you become a manager, you will encounter problems that you have to identify on your own, and you will have to come up with your own solutions. This component is very much like research in my experience. It’s also like what I’ve shared about learning the concepts in a new module without having the proper background. Research mirrors a lot of things you will encounter in your future job. You will get thrown new problems without having much background information because your boss will not care whether you have learned it before. They will not even help you frame the problem properly, let alone break it down into steps like your professors do on the midterm or final exam questions. They just want a solution, period. You discovering a solution for your organisation is similar to a researcher who is trying to contribute to the knowledge accumulation process.

Could you share more about your research in game theory?I have a few research agendas. My first research agenda involves studying the foundations and robustness of solution concepts in game theory. How do we know ifa particular solution — which is often some sort of equilibrium — is plausible? Why do we bother to solve a problem? Our typical justification is that the solution describes what rational people will do in various scenarios. Let’s use auctions as an example. In auctions, we analyse equilibria to understand participants’ bidding behaviour. Will they bid their true valuation of the good? Or will they bid half or a third of their true valuation? How will they try to outbid other bidders? These questions are highly relevant in practice. My goal is to understand how sensitive such an equilibrium-based prediction is to the misspecification ofa model. Let’s say we assume each bidder’s value is their own private information, which is unknown to other bidders or the auctioneer, and this is where the information asymmetry comes from. We may also assume that each bidder’s value is drawn from a uniform distribution, which is known to everyone including the auctioneer. We may also include additional assumptions such as the bidders are risk-neutral and have no liability constraint. Then we proceed to solve for some (Bayesian) Nash equilibrium. But what if a parameter of the model is misspecified? For example, suppose the value distribution is in fact not uniform. How wrong is your model? How sensitive willthe equilibrium prediction of the bidding behaviour be tosuch a misspecification? How will the change affect the auctioneer’s revenue? Will the auctioneer be better off if they reconfigure their auction design to “safeguard” their revenue against possible misspecification of the model? These are important questions as long as a “perfect model” that precisely describes any practical auction remains unavailable.

FASStrack Asia is the FASS summer school programme spearheaded by Professor Chen Yi-Chun and the International Relations and Special Duties Division at the Dean’s Office.

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Auctions go beyond Christie’s and Sotheby’s.

Setting aside the issue of model misspecification, we also tend to focus on one equilibrium or a few equilibria that admit tractable analytic solutions. However, the model may admit many other equilibria that entail very different bidding behaviours and revenue implications. For instance, it is well known that there are many different equilibria in a first-price or second-price auction. However, for tractability, we may focus on solving a symmetric equilibrium where every bidder applies the same bidding rule (which means to bid (n–1)/n of their value in a first-price auction with n bidders), or an equilibrium where every bidder adopts their dominant strategy (which means to bid their true value ina second-price auction). One of my goals is to understand how model mis- specification affects the set of equilibrium behaviours and predictions in a fixed game like a first-price or second-price auction. As I hinted above, I do not want to focus on just one particular equilibrium; instead, I want to look at the set of possible equilibria. To do so, I need to analysea different solution concept called rationalisability, and to determine how it varies with the information structure or model.

What about your second research agenda?My second research agenda concerns mechanism design. Mechanism design is typically regarded as the reverse engineering of game theory. Instead of taking the game as given, we try to come up with a game ourselves. Examples include designing an auction or a voting rule. The game will achieve certain objectives, such as maximising revenue or efficiently allocating resources. For instance, consider the Certificate of Entitlement (COE) allocation mechanism in Singapore. The objectiveis to efficiently allocate a quota. The COE auction isa uniform-price auction. All the winning bidders paya uniform price, which is the lowest winning bid. You may think of my first agenda as fixing a game and studying how predictions vary with model misspecification, and my second agenda as fixing the model or information

structure and studying which game works best in achieving a particular social goal. In both agendas, I encounter similar issues. Again, suppose we want to determine which type of auction we should hold. To determine which auction achieves the highest revenue or allocative efficiency, we need to know the equilibrium bidding behaviours in each type of auction. If participants bid their true valuation of the good, you can be sure that the auction results in an efficient allocation to the bidder with the highest valuation. But you don’t know whether participants are in fact bidding their true value. Even if they bid their true value in some equilibrium, maybe there is another way to shuffle their bids to form another equilibrium. For instance, some bidders bid half of their value and other bidders bid three times of their value; this might also be an equilibrium. Or maybe one bidder bids more than the highest possible value of the other bidders and the other bidders bid zero; this becomes a “non-truth-telling” equilibrium in a second- price auction. How “wild” the equilibrium can be now affects how well you are able to achieve your goal asa mechanism designer. My first agenda takes an agnostic view on equilibrium selection. Likewise, my second research agenda focuses on designing the “right game” in which a desirable social outcome is achieved not just in one equilibrium, but in every single equilibrium. This is called full implementation as opposed to partial implementation, which is only concerned with having one “good” equilibrium. The vast majority of theoretical developments in mechanism design is about partial implementation rather than full implementation. Here is where I sense a disconnect between theory and practice. People are interested in auctions because of its prevalence in practice. But in theory, we very often have to make a strong equilibrium selection assumption that people will somehow play certain equilibria, which we know how to solve. This is not to say that full implementation is necessarily more practical but I would say that it at least raises the right questions. We have not found the “right” answers because the mechanisms that are known to achieve full implementation mostly possess very limited practical appeal. Eric Maskin — who was awarded the Nobel Prize together with Leonid Hurwicz and Roger Myerson in 2007 — was one of the pioneers in the full implementation literature that started more than 40 years ago. There was very intensive research done back in the 1980s and 1990s, but it has since become a very specialised area in game theory. My main focus is to achieve full implementation using mechanisms that look more “natural”. For instance, if the social objective depends only on the preference profile of society, then we will naturally expect that the mechanism only asks agents to report their preferences. I was surprised that most papers in the literature do not offer suchmechanisms and instead require extraneous inputs suchas reporting an integer.

Besides auctions and mechanism design, are there any other research areas that you are beginning to explore?I’ve started working on matching. An example of this would be school choice, which my daughter just experienced after her Primary School Leaving Examination (PSLE). Each student ranks their top choices, and the system generates a match between a student and a school. Unlike auctions, there is no price involved. The system has to somehow match the “right people” to the “right schools”. Students want to enter the prestigious schools and schools want to admit the top students. Here we have a similar efficiency consideration just like in the auction problem. The system wants to match students

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The Southern Ridges encompasses 10 kilometres of green open spaces.

to the schools that they value most but it needs to account for the preference of schools as well. This process is much more complicated than auctions — especially when there’s incomplete information — because it involves the matching of multiple “objects” on each side. My research agenda is to formulate and analyse matching problems where the participants do not know one another’s preferences. In the school choice example, we may argue that there is little uncertainty about preferences since the schools’ cut-off points indicate how desirable they are to students, and the students’ PSLE results indicate how attractive they are to schools. However, this kind of approxi- mation by no means perfectly reflects the schools’ preferences or the students’ abilities. What about the labour market, which can also be recast as a matching problem? Job seekers have incomplete information about the firms they apply to, e.g., regarding wages, company benefits, promotion opportunities. If you think of the labour market as a “two-sided auction” where both workers and firms are auctioning themselves to the other party, it becomes a very difficult problem because there are multiple objects on either side, and there’s complementarity and substitutability among workers and among firms. I’m still at an early stage of thinking about theseproblems. They are very difficult to me but highly relevant in both theory and practice. Could you share with us your experience on collaboration in theoretical economics research?The labour division in collaboration on theoretical research is not very clear. We do not typically prove theorems separately. If someone knows how to prove a theorem, he is also likely to know how to prove other related results

and can just write the entire paper by himself. He does not need a collaborator. Theoretical research requires a lot of communication among co-authors. When we get stuck (whether in terms of finding a problem or a solution), we talk to our co-authors, who can suggest a different way of attacking an issue. We need passion in pursuing a common agenda as well as complementary skillsets and ways of thinking. We usually start by discussing open problems related to an agenda. Thereafter, we openly share further questions and answers with one another. In the process, we have to synchronise our thinking, value one another’s input, and also challenge one another. It is a stimulating process that we keep replaying until we settle on a problem and a solution. I have been privileged to work with a group of exceptionally capable co-authors and I learned a lot from each of them. I owe my deepest appreciation to Prof Luo Xiao who was my master’s thesis supervisor at the National Taiwan University. He was also my very first co-author and we have been working together since 2001. Prof Luo Xiao guided me into economics research and taught me how to write a research paper from scratch. He has fundamentally influenced my way of thinking and how I approacha research question.

You have been living in Singapore for over a decade. What are your favourite places in Singapore?I enjoy spending time with my family over the weekendsto try out different restaurants and navigate different shopping malls. We also enjoy hiking. There is a hiking trail — the Southern Ridges — from HortPark to HarbourFront that we frequently visit. But in all honesty, my favourite place is my office. I feel the most relaxed when I am working.

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