Chen Yi-Chun joined the NUS Economics Department in 2009 and became a full professor in 2021. In addition to his responsibilities in the Department, he finds time (somehow!) to be Director of the NUS Risk Management Institute and a Vice-Dean at the Faculty of Arts and Social Sciences. In this article, Yi-Chun tells us of his research on game theory. More information on Yi-Chun’s research can be found on his personal website.

 

I studied accounting for my first degree, only to conclude that it was not for me. I switched to pursue a masters’ degree in economics and started my journey as a game theorist under the guidance of Professor Luo Xiao (now at NUS) who was then on the faculty at National Taiwan University. My early research was about epistemic game theory, which models what players believe and do when they play according to solution concepts such as Nash equilibrium. Ever since then, I have been intrigued by these foundational issues in game theory.

My deep interest in game theory led me to pursue a doctoral degree in economics at Northwestern University. During my studies, I was privileged to work with top-notch game theorists, among both faculty members and fellow students.  At that time, there was a lot of interest among economic theorists on the question of whether game predictions are robust to small changes in the information that players possess (about their own payoffs and about each other’s payoffs). Both my advisor Professor Eddie Dekel and my committee member Professor Jeff Ely were working on those topics. Conversations with them drew me into this topic and I began researching on it, with much of that carried out jointly with my classmate Xiong Siyang.

To motivate our questions, consider a model of an auction for a single object and assume that each bidder’s value is drawn from a uniform distribution whose realization is privately known to the bidder. Then we could solve for a Bayesian Nash equilibrium. For instance, in a first-price auction with n bidders there is a symmetric equilibrium where every bidder applies the same bidding rule (to be precise, bidding (n–1)/n of the bidder’s value), while in a second-price auction there is an equilibrium where every bidder adopts their dominant strategy (which is to bid their true value).

But what if the value distribution is in fact not uniform? How sensitive is the equilibrium bidding behaviour to such a misspecification?  Note that this misspecification changes not only the bidders’ beliefs (over other bidders’ values) but also their beliefs about other bidders’ beliefs and so on.  How will our prediction in this model differ from the predicted equilibrium in a “nearby” model?  How will the different equilibria affect the auctioneer’s revenue? These are important questions as long as a “perfect model” that precisely describes the bidders’ information structure remains unavailable.

My research goal has been to understand how model misspecification affects the set of equilibrium outcomes in games such as first-price and second-price auctions. In order to look at the set of possible equilibria across different models, it turns out that I need to analyse rationalizable --- as opposed to equilibrium strategies --- and to determine how they vary with the information structure.  (Rationalizable strategies are those that survive the iterated deletion of strictly dominated strategies and they form a larger class of strategies than the class of Nash equilibrium strategies.)

The bulk of my work shares an overarching theme that predictions of strategic behavior are in general sensitive to the tail properties of a player’s hierarchy of beliefs, i.e., a player’s belief about the payoff-relevant parameters (e.g., bidders’ values in an auction), his belief about the other players’ beliefs about the payoff-relevant parameters, and so on, ad infinitum. In particular, without precise knowledge of higher-order/tail beliefs, concepts (such as Nash equilibrium) which make sharper predictions than rationalizability are not likely to be robust.

With millions of flowers sold every day, the Aalsmeer Flower Auction, which takes place in Aalsmeer, Netherlands, is the largest flower auction in the world.  The auctions take the form of a Dutch auction in which the auctioneer begins with a high asking price and lowers it until some participant accepts the price, or it reaches a predetermined reserve price.  This distinguishes it from an English auction in which the auctioneer accepts increasingly higher bids from the participants, with the highest bidder paying his bid and winning the object.  The study of auctions is an important part of the study of mechanism design.  Under certain assumptions, it is known that Dutch auctions are strategically similar to first price sealed-bid auctions, while English auctions are similar to second price sealed-bid auctions.  (Photo by John-Mark Smith on Unsplash.)

After I joined NUS, I gradually developed an interest in another research topic, mechanism design. Mechanism design can be regarded as the reverse engineering of game theory. Examples include designing an auction, a voting rule, or a trading protocol, where the game is designed to achieve certain objectives, such as maximising revenue or efficiently allocating resources. I have focused my research on those mechanisms that achieve a desirable social outcome in every equilibrium. This is called full implementation, as opposed to partial implementation which is only concerned with the mechanism having one equilibrium that achieves the desirable outcome. For instance, while a second-price auction has an efficient equilibrium where everyone bids her/his true value, it also has an inefficient equilibrium where a low-value bidder bids more than the highest possible value of the other bidders and the other bidders all bid zero. As a result, a second-price auction partially, but not fully, implements efficient allocations.

I am interested in achieving full implementation using mechanisms that look ‘more similar’ to what we use for partial implementation. For instance, we only need to know the bidders’ true values in order to efficiently allocate the object in an auction.  This suggests that direct revelation mechanisms which only ask bidders to report their value would suffice, provided “truth-telling” can be made the unique equilibrium through a clever design of the direct revelation mechanism.   It turns out that full implementation using a direct revelation mechanism is generally impossible, but my research (mostly carried out jointly with Takashi Kunimoto and Sun Yifei) strives to achieve full implementation by augmenting a direct revelation mechanism with minimal additional input, such as asking for only one more value report from each bidder in the case of an auction. We have also carried out experiments to help verify that our mechanisms perform well in practice and not just in theory.

Unlike my first research topic, which fixes a game and studies how predictions vary with model misspecification, my second research topic fixes the information structure and studies which games work best in achieving a particular social goal.  Despite the differences, the two topics share numerous common insights, especially when the implementation of the mechanism is required to be robust to information perturbations.  I realized this only after going back and forth between the two research topics for quite some time. Sorting out this kind of unexpected connection has been the most rewarding part of my research career.

Chen Yi-Chun
September 2021

References

Robust Predictions in Games
Characterizing the Strategic Impact of Misspecified Beliefs, (with A. Di T.illio, E. Faingold, and S Xiong), Review of Economic Studies 84 (2017), 1424-1471.
A Structure Theorem for Rationalizability in the Normal Form of Dynamic Games, Games and Economic Behavior 75 (2012), 587-597.

Full Implementation
Maskin Meets Abreu and Matsushima, (with T. Kunimoto, Y. Sun, S. Xiong), working paper.
Getting Dynamic Implementation to Work, (with R. Holden, T. Kunimoto, Y. Sun, and T. Wilkening), working paper.