Tuesday, January 17, 2017

Market Design and Operations Research: an interview by the journal Mathematics of Operations Research

The journal Mathematics of Operations Research, where the main paper from my dissertation was published in 1976, has published an interview with me in their Author Spotlight section: In Conversation with...ALVIN E. ROTH.

Here's the first question and answer:

INFORMS:  Your first published paper, “Subsolutions and the Supercore of Cooperative Games,” [2]based on your doctoral thesis, appeared in MOR in 1976. The paper was handled by Nobel winner and MOR Founding Area Editor Robert Aumann. Can you share with us how your first experience with the peer review process went?

ROTH:  I recall that experience vividly. Aumann, in his editor’s letter, told me to ignore the referees, but to revise the paper along the lines he would describe. One revision he wanted had to do with the proof of my main theorem, for which I had used Zorn’s Lemma. He advised me to try to construct a proof which instead used transfinite induction. I didn’t know what transfinite induction was, so I was very skeptical, but I grimly trudged to the math library and got a copy of Hausdorff’s book Set Theory [3] to repair this gap in my education. I still remember how my hopes lifted when I opened the book and saw that it had been translated from the German by…Aumann. It turned out that he knew what he was talking about, and the proof that appears in my published MOR paper uses transfinite induction.

At the Author Spotlight page they also link to the several papers I published in MOR:

  • Roth AE (1976) Subsolutions and the Supercore of Cooperative Games. Math. Oper. Res. 1(1):43–49.  
  • Roth AE (1977) Individual rationality and Nash’s solution to the bargaining problem. Math. Oper. Res. 2(1): 64–65. 
  • Roth AE (1982) The economics of matching: Stability and incentives. Math. Oper. Res. 7(4):617–628. 
  • Roth AE (1985) Conflict and coincidence of interest in job matching: Some new results and open questions. Math. Oper. Res. 10(3):379–389.*  
  • Roth AE, Rothblum UG, Vande Vate, JH (1993) Stable matchings, optimal assignments, and linear programming. Math. Oper. Res. 18(4): 803–828. 

  • Since becoming a notorious economist, I've had a number of conversations with operations researchers that begin with a question like "Why did you switch from OR to Economics?"

    My usual answer is that I got my Ph.D. in OR in 1974 with a dissertation in game theory, and it looked at that time as if OR would be a natural place for game theory to flourish, particularly since Bob Aumann was the founding game theory editor of MOR. But, as it turned out, game theory grew first and fastest in Economics. So I just stood my ground, while the disciplinary boundaries shifted around me. Today, market design has become the engineering part of game theory, and it's time for OR and Economics to reconnect around market design. And indeed at Stanford, many of the Ph.D. students in our market design classes in the econ department are OR students from our MS&E department or from our Business school, both of which in turn have market designers on their faculty.  So I'm optimistic that my dual identities as an economist and operations researcher may soon seem seamless.

    *Beware, my 1985 paper contains an error about the lattice structure of stable matchings, that was noted and corrected by
    Charles Blair (1988), "The Lattice Structure of the Set of Stable Matchings with Multiple Partners,"  Mathematics of Operations Research 13(4):619-628. http://dx.doi.org/10.1287/moor.13.4.619
    and also by
    Jianrong Li, (2013) A Note on Roth's Consensus Property of Many-to-One Matching. Mathematics of Operations Research 38(2):389-392. http://dx.doi.org/10.1287/moor.1120.0576 

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