''Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis'' is a book on matching markets in

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

and

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, particularly concentrating on the

stable marriage problem In mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from ...

. It was written by

Alvin E. Roth Alvin Eliot Roth (born December 18, 1951) is an American academic. He is the Craig and Susan McCaw professor of economics at Stanford University and the George Gund (philanthropist), Gund professor of economics and business administration emeri ...

and Marilda Sotomayor, with a preface by

Robert Aumann Robert John Aumann (Yisrael Aumann, ; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University ...

, and published in 1990 by the

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

as volume 18 in their series of

Econometric Society The Econometric Society is an international society of academic economists interested in applying statistical tools in the practice of econometrics. It is an independent organization with no connections to societies of professional mathematicians o ...

monographs. For this work, Roth and Sotomayor won the 1990

Frederick W. Lanchester Prize The Frederick W. Lanchester Prize is an Institute for Operations Research and the Management Sciences prize (U.S. $5,000 cash prize and medallion) given for the best contribution to operations research and the management sciences published in Engli ...

of the

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often s ...

Topics

The book's introduction discusses the

National Resident Matching Program The National Resident Matching Program (NRMP), also called The Match, is a United States–based private non-profit non-governmental organization created in 1952 to place U.S. Medical education in the United States, medical school students into res ...

and its use of stable marriage to assign medical students to hospital positions, and collects the problems in economics that the theory of matching markets is positioned to solve. Following this, it has three main sections. The first of these sections discusses the stable matching problem in its simplest form, in which two equal-sized groups of agents are to be matched one-to-one. It discusses the stability of solutions (the property that no pair of agents both prefer being matched to each other to their assigned matches), the lattice of stable matchings, the

Gale–Shapley algorithm In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm, propose-and-reject algorithm, or Boston Pool algorithm) is an algorithm for finding a solution to the stable matchi ...

for finding stable solutions, and two key properties of this algorithm: that among all stable solutions it chooses the one that gives one group of agents their most-preferred stable match, and that it is an honest mechanism that incentivizes this group of agents to report their preferences truthfully. The second part of the book, which reviewer Ulrich Kamecke describes as its most central, concerns extensions of these results to the many-one matching needed for the National Resident Matching Program, and to the specific economic factors that made that program successful compared to comparable programs elsewhere, and that have impeded its success. One example concerns the

two-body problem In classical mechanics, the two-body problem is to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two bodies are point particles that interact only with one another; th ...

of married couples who would both prefer to be assigned to the same place, a constraint that adds considerable complexity to the matching problem and may prevent a stable solution from existing. The third part of the book concerns a different direction in which these ideas have been extended, to matching markets such as those for real estate in which indivisible goods are traded, with money used to transfer utility. It includes results in

auction theory Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the design of real- ...

, linear and nonlinear utility functions, and the assignment game of

Lloyd Shapley Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally conside ...

and

Martin Shubik Martin Shubik (1926–2018) was an American mathematical economist who specialized in game theory, defense analysis, and the theory of money. The latter was his main research interest and he referred to it as his "white whale". He also coined th ...

Audience and reception

''Two-Sided Matching'' presents known material on its topics, rather than introducing new research, but it is not a textbook. Instead, its aim is to provide a survey of this area aimed at economic practitioners, with arguments for the importance of its material based on its pragmatic significance rather than its mathematical beauty. Nevertheless, it also has material of interest to researchers, including an extensive bibliography and a concluding list of open problems for future research. Compared to other books on stable matching, including ''Marriages Stables'' by

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of comp ...

and ''The Stable Marriage Problem: Structure and Algorithms'' by Dan Gusfield and Robert W. Irving, ''Two-Sided Matching'' focuses much more on the economic, application-specific, and strategic issues of stable matching, and much less on its algorithmic issues. Alan Kirman calls the book a "clear and elegant account" of its material, writing that its focus on practical applications makes it "of particular interest". Theodore Bergstrom writes that it will also "delight economists who want to think beautiful thoughts about important practical problems". Benny Moldovanu predicts that it "will become the standard source of reference" for its material. And

Uriel Rothblum Uriel George "Uri" Rothblum (; Tel Aviv, March 16, 1947 – Haifa, March 26, 2012) was an Israeli mathematician and operations researcher. From 1984 until 2012 he held the Alexander Goldberg Chair in Management Science at the Technion – Israel ...

calls it the kind of once-a-generation book that can "change the way in which an entire field of study is viewed."

References

{{reflist, refs= {{citation, last=Bergstrom, first=Theodore C., date=June 1992, issue=2, journal=

Journal of Economic Literature The ''Journal of Economic Literature'' is a peer-reviewed academic journal, published by the American Economic Association, that surveys the academic literature in economics. It was established by Arthur Smithies in 1963 as the ''Journal of Econo ...

, jstor=2727713, pages=896–898, title=Review of ''Two-Sided Matching'', volume=30 {{citation, last=Kamecke, first=Ulrich, date=November 1992, doi=10.2307/2554894, issue=236, journal=

Economica ''Economica'' is a peer-reviewed academic journal of generalist economics published on behalf of the London School of Economics by Wiley-Blackwell. Established in 1921, it is currently edited by Nava Ashraf, Oriana Bandiera, Tim Besley, Franc ...

, jstor=2554894, pages=487–489, series=New Series, title=Review of ''Two-Sided Matching'', volume=59 {{citation, last=Kirman, first=Alan P., date=July 1992, doi=10.2307/2234601, issue=413, journal=

The Economic Journal ''The Economic Journal'' is a peer-reviewed academic journal of economics published on behalf of the Royal Economic Society by Oxford University Press. The journal was established in 1891 and publishes papers from all areas of economics.The edito ...

, jstor=2234601, pages=975–976, title=Review of ''Two-Sided Matching'', volume=102 {{citation, last=Moldovanu, first=B., authorlink=Benny Moldovanu, date=January 1992, journal= Journal of Economics, pages=116–117, title=Review of ''Two-Sided Matching'', volume=55, id={{ProQuest, 1299512649 {{citation, last=Potters, first=Jos, journal=

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

, mr=1119308, title=Review of ''Two-Sided Matching'', year=1993 {{citation, last=Rothblum, first=Uriel G., authorlink=Uriel Rothblum, date=January 1992, doi=10.1016/0899-8256(92)90011-g, issue=1, journal=

Games and Economic Behavior ''Games and Economic Behavior'' (''GEB'') is a journal of game theory published by Elsevier. Founded in 1989, the journal's stated objective is to communicate game-theoretic ideas across theory and applications. It is considered to be the leadi ...

, pages=161–165, title=Review of ''Two-Sided Matching'', volume=4 {{citation, last=Wieczorek, first=A., journal=

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

, title=Review of ''Two-Sided Matching'', zbl=0726.90003 {{citation, last=Winters, first=Jan Kees, date=October 1992, doi=10.1016/0176-2680(92)90017-b, issue=3, journal=

European Journal of Political Economy The ''European Journal of Political Economy'' is a quarterly peer-reviewed academic journal covering research on economic phenomena, including collective decision making, political behavior, and the role of institutions. The editors-in-chief are To ...

, pages=510–514, title=Review of ''Two-Sided Matching'', volume=8 Economics books Mathematics books Stable matching 1990 non-fiction books