What makes people cooperate with others against their own immediate interests? Which institutions encourage cooperation or reinforce conflict? How do societies with diverse goals implement acceptable policies? Why does a financial bubble sustain even when everyone may know there is a bubble? These questions, their elegant answers, and more crown the Abreuvian legacy.
I first met Abreu in the pages of the Ratan Tata Library at the Delhi School of Economics. In an undergraduate text on game theory surfaced a remarkable theorem. It was marked “Abreu 1988". The references disclosed an Indian first name—Dilip, an oddity in the domain of Greek, Renaissance and American icons. Google revealed that he too had read through the pages of this library. Perhaps he too drank chai at that rustic café before class as we all did. V.S. Naipaul captures the emotion well: “After all, we make ourselves according to the ideas we have of our possibilities." It was the first tinge of academic ambition that many a 20-year-old may have felt on reading his work in that spot.
Princeton University witnessed a revolution in economic theory in the 1980s. Under the mentorship of the venerable Hugo Sonnenschein, a group of enthusiastic graduate students set out to shift the paradigm. In midst of this dazzle, Abreu wrote his PhD thesis on repeated games. “It changed everything," David Pearce, a luminous economist and an old friend, reminisces with excitement.
A theory is a lens that distils the key elements of a complicated reality into a simple mathematical framework. Game theory is the study of cooperation and conflict among “players" whose actions affect each other’s well-being. One of the central insights of the subject is that players settle on inferior outcomes because of strategic considerations. It is hard to get nations to emit less carbon in a global effort to temper climate change because it individually benefits them to do the opposite, especially if others commit to do their part. So in “equilibrium" everyone pollutes a lot.
Sometimes the threat of adverse outcomes can be used to discipline current behaviour. The theory of repeated games seeks to explain this, specifically the sustenance of cooperation or conflict when constitutional diktat is hard to enforce. It illustrates the constant give and take and gradual relationship building in long-term relationships. Marriage is an example, so is the evolution of social norms. It formalizes why certain communities, such as the 11th century Maghribi traders or modern Gujaratis, are able to run successful businesses across lands and oceans.
Think about collusion. How do airlines A and B collude to keep prices high when one of them could attract more fliers by reducing its price? If airline A deviates to a lower price, airline B can unleash lower prices, hurting both their profits. The key tenet of repeated games is that players can be induced to cooperate against their short-term interests. However, the threat of retaliation must be credible; it must be in the long-term interest of the retaliator to retaliate. All credible actions of form—if you do this, I’ll do this, but if you do that, then I’ll do something else and so on —need to be explored. How can we make sense of this complex space?
On a crisp 1980s afternoon, Abreu emerged with the answers. Pearce remembers it vividly: “Since he was doing the first two years of the PhD in one, Dilip was terribly late on the ‘second year paper’, typically a modest first pass at research that does not make it to the thesis. As I arrived at the department the morning after it had finally been submitted, I heard a commotion upstairs. The brilliant young professor who was assigned to read the manuscript was waving Dilip’s paper at the top of the stairs and calling out to passersby: ‘Have you seen? Have you heard? Everything has changed’."
By carefully designing regimes of rewards and punishments, Abreu had uncovered a simple way to identify the best and worst possible outcomes in any equilibrium and hence the space of all eventualities. “How much cooperation and conflict can credibly be sustained, and in what way," Sonnenschein announces animatedly. “Just a deep, a very deep understanding of a basic idea of how the world works."
Abreu’s PhD, finished in three years, earned him a postdoctoral fellowship at the University of Minnesota and an assistant professorship at Harvard. Over these years, he honed and further developed ideas from his thesis with his friends Pearce and Ennio Stacchetti. They provided a general methodology of finding all equilibria in repeated games. The trio came to be referred as APS, and their work would go on to have a profound impact on economics.
Soon Abreu heeded the azan of his alma mater, returning to Princeton—now as a professor. This followed an epoch of foundational explorations in the theory of implementation, bargaining, and financial bubbles.
As a child, my mother’s bargaining techniques in the bazaar amazed me. She would strategically signal that she is about to walk away to force the seller to reduce the price. And, she invariably succeeded, even when I knew she would have been willing to pay the higher price. Abreu and Faruk Gul formalized this intuitive way of thinking about bargaining. Both negotiators assume stubborn thresholds and try to build reputation until one of them eventually gives up. “The way to gain a good reputation," Socrates had said “is to endeavour to be what you desire to appear."
Before Abreu-Gul came along, bargaining was framed mainly in terms of waiting costs; if you can haggle longer, you win. Their paper crystallized the connection between reputation and bargaining. It is now standard in graduate syllabi.
In the late 1990s, as Abreu started to develop an interest in financial markets, a young Markus Brunnermeier, now a leading financial economist, joined Princeton. The duo teamed up to write a paper that explained why financial bubbles sustain. Investors are uncertain of when others will start trading against the bubble, making it worthwhile to continue riding it until its painful burst. For example, in the prelude to the 2008 financial crisis, banks kept issuing subprime mortgage backed securities, even as it was becoming clear that the mountain of debt was going to collapse. The then chief executive officer of Citigroup, Chuck Prince, uttered the now iconic words, “As long as the music is playing, you’ve got to get up and dance." Bubbles emerge and persist in many such situations, breaking the hypothesis that prices internalize all possible information. It was as if Prince had received the Abreu-Brunnermeier memo, but a tad late. Brunnermeier is effusive in his respect for Abreu: “He has been a mentor… He sets very high standards for himself. As we worked through many models of bubbles and I grew anxious as an assistant professor, he joked that bad papers take a lot of time too, so let us just write a good one." And boy they did.
Abreu’s research is often described by his peers as elegant and creative. When asked what elegance means, Abreu suggests “elegance is a deep conceptual understanding expressed through a minimal set of ideas." Elegance he exclaims “is visceral, is transparent, is self-evident". A creative theory lends relevance to elegance; it condenses a complex reality into a hitherto unexpected yet intuitive system of mathematical equations. “Dilip’s work is truly creative," Gul exclaims with pride. “It’s highbrow and widely applicable."
In the age of Big Data, the demand for theory is shrinking, be it economics, computer science or physics. While part of the reason is a current fad, another part, many argue, is theory’s own misguided obsession with elegance. “Elegance," Abreu observes, “can also be treacherous as it can become an end in itself...ultimately the theorist ought to offer tools and constructs that are useful to the wider (economics) community." Gul and Pearce point out that questions about collusion and anti-trust attracted Abreu to repeated games. Brunnermeier recollects that Abreu was open to all kinds of ideas in building a theory of bubbles. It is the pursuit of a good question, Abreu’s work teaches us, that creates a beautiful theory; one that tells a convincing story, or helps make sense of Big Data, or in Pearce’s words, provides a narrative that “makes us look at reality differently".
Abreu grew up in South Mumbai. He attended St Mary’s School, which counts music legends Freddie Mercury and Zubin Mehta, and technology giant Azim Premji as its alumni. He questioned everything, even going to church. “My instincts in terms of friends and world view were aggressively secular, growing up in a cosmopolitan Mumbai, a Mumbai recalled in (Salman) Rushdie’s writings." He would spend his summers in an ancestral abode in Goa, wherein reside many of his fondest childhood memories. It was somewhere in this harmony that Abreu imbibed a sufiana clarity, which Sonnenschein calls “a secure strength of character, and originality".
The brilliance though does come with its quirks. Abreu’s polite but notoriously high standards are a fabled fear among potential mentees. Perhaps he could attract a larger pool of good PhD students if he let their initially mediocre ideas meander for a bit. He also values infinite flexibility. “An iron law of Abreuvian dialectic", Gul remarks, “is that every plan with Dilip contains within it the seeds of its own cancellation".
On the day of his Nobel prize announcement, in an emotional address, Tom Sargent talked about a life of learning from people around him. I was fortunate to be there. “There were these three young boys at Minnesota," he said, “who were changing the way we thought about dynamic interactions." He was, of course, referring to the APS trinity. In that moment I was transported back to my first rendezvous with Abreu in the library and I thought how we learn not only from people we meet but also from those whose mere existence gives us the audacity to learn in the first place.
The Dilip Abreu Top 5:
1. On the theory of infinitely repeated games with discounting, Econometrica 1988. Based on his PhD thesis, which opened the floodgates to economic thinking on strategic long-term interactions such as between a government and its citizens, or two firms competing for the same product.
2. Towards a theory of discounted repeated games with imperfect monitoring (with David Pearce and Ennio Stacchetti), Econometrica 1990. Provided a very general methodology to find out the universe of predictions in repeated games. Its application now pervades economic modeling.
3. Virtual implementation in iteratively undominated strategies: incomplete information (with Hitoshi Matsushima), unpublished 1992. If society is willing to choose its desired objectives with some imperfections, it can do so in a strong way. Provided a creative new take on a widely discussed question.
4. Bargaining and reputation (with Faruk Gul), Econometrica 2000. While negotiating, both parties try to build a reputation of being tough, until one of them eventually finks. Presented a masterful perspective on the oldest economic reality- bargaining.
5. Bubbles and crashes (with Markus Brunnermeier), Econometrica 2003. Why does a financial bubble sustain even when the stakeholders know of its existence? They are unsure of when others will start trading against the bubble. So, everyone rides it until its painful burst. Elegantly explained an oft-observed inefficiency in financial markets.
Rohit Lamba is an assistant professor of economics at Pennsylvania State University. He did his PhD at Princeton University, where he learnt game theory from Dilip Abreu.
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