Mari Ida Sotomayor

Mari Ida Sotomayor

Past Awards

Frederick W. Lanchester Prize: Winner(s)

"When I received my PhD in Operations Research almost 20 years ago, game theory was as much at home in O.R. as in any other discipline. Today I sit in an economics department, and the situation is very different. Game theory has grown enormously and become the backbone of modern economic theory, but in operations research it seems to be studied and used relatively little. This is an enormous missed opportunity, and one of our hopes for the book is that it should help explain the nature of this opportunity. "

With those words, Alvin E. Roth summed up his reaction to winning the 1990 Lanchester Prize along with coauthor Mari Ida Sotomayor for their book, Two-Sided Matching: a Study in Game Theoretic Modeling and Analysis (Cambridge University Press, 1990).

The citation reads, in part:

  • "In their book, Alvin Roth and Mari lda Oliveira Sotomayor use policy evaluation and empirical observation as a guide to deep mathematical analysis. They demonstrate in precise, insightful detail how game theory in general, and matching markets in particular evolved into fields that are grounded in strong theory and, at the same time, are quite relevant to real issues of practice. The theory of matching markets, to which the authors have been major contributors, originated with the famous 1962 Gale-Shapley paper, 'College Admissions and the Stability of Marriage.'
  • "The practical importance of this theory is most dramatically demonstrated by the fact, discovered by Roth in 1984, that the Gale-Shapley algorithm has been in practical use since 1951 for the assignment of interns to hospitals in the United States.
  • "The book describes all the major developments in the field. However, it constitutes more than just a definitive description of modern game theoretic research on matching. The truly outstanding accomplishment of the authors is that their analysis bridges the gap between abstract concepts and practical knowledge. Because of this unique point of view, their book has the potential to change the way an entire field of study is viewed."
  • What makes the problems considered in the book different from the traditional assignment problem (e.g., in which jobs are assigned to machines) is that in these problems there are people on both sides of the assignment who care about the outcome (e.g., when workers are matched with supervisors). This matters for a variety of reasons, not least of which is that if a central planner makes an assignment not to the liking of the people involved, groups of them may be able to upset the assignment by making private arrangements among themselves. This imposes new constraints on what assignments can be achieved.
  • "For many classical problems in operations research it is reasonable to assume that a planner can gather the relevant information, so that an algorithm that uses this data to optimize some objective can be employed," adds Roth. "But in many modern applications, of which matching is just one, the relevant information has to be obtained from interested parties, who must then cooperate to some degree in the implementation of the plan.
  • "We study how this imposes new constraints on the problem both to take into account that the parties may be able to act independently of any plan if they see it as in their interests to do so, and, perhaps even more fundamentally, to take into account that the kind of information a planner collects will be influenced by the algorithm he chooses.
  • "That is, different algorithms give the parties who have the information different incentives about what to reveal...Game theoretic issues are therefore ubiquitous in the design and implementation of systems involving many decision makers, and particularly in those which depend on information gathered from interested parties."