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Market Design

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Encyclopedia of Complexity and Systems Science

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Introduction

Matching theory in economics began with the seminal contribution by Gale and Shapley (1962). Ever since, the theory has advanced considerably and has been applied to an increasing number of economic problems. Notably, it has proved useful in helping designs of mechanisms in a variety of markets. Examples include medical match (Roth 1984; Roth and Peranson 1999) and other entry-level labor markets (Roth 1991), school choice (Abdulkadiroğlu and Sönmez 2003), course allocation in education (Sönmez and Ünver 2010; Budish and Cantillon 2012), and organ donation (Roth et al. 2004, 2005, 2007). Application of matching theory to these and other practical problems is known as “market design.” Although market design is often used to refer to other types of research as well, in this article, we focus on market design as application of matching theory.

This paper describes matching theory and its applications. We begin by describing standard models in two-sided and one-sided (object...

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Notes

  1. 1.

    Note, however, terms may not vary substantially in some labor markets, especially in standardized entry-level markets. In such a case, the matching model in section “Basic Two-Sided Matching Model” may be appropriate.

  2. 2.

    Chen and Sonmez (2006) show evidence in lab experiments that strategy-proof school choice mechanisms indeed induce true preferences more often than those without truthful revelation. Nevertheless, there is some evidence in real-life matching markets that some agents still misreport even in strategy-proof mechanisms. See, for instance Rees-Jones (2017) and Hassidim et al. (2017).

  3. 3.

    Ex-ante Pareto efficiency implies ex-post Pareto efficiency because if any final allocation resulting from a lottery is not ex-post Pareto efficient, then the lottery can be improved by replacing the particular allocation with a more efficient one, implying that the lottery is not ex-ante Pareto efficient.

  4. 4.

    The main difference of this definition from the one in the basic model of section “Basic Two-Sided Matching Model” is that we consider a coalition composed of a couple of doctors and two hospitals each of which seeks to match with a member of the couple. See Roth (1984) for detail.

  5. 5.

    More precisely, this problem is in the class of “NP-hard” problems. NP-hardness is a notion in computational complexity theory describing the complexity of computation, which we will not describe in detail here.

  6. 6.

    How the authors proceed from the setup is notable as they approach the problem from a linear programming perspective. Formulating the matching problem as a linear program and applying the celebrated Scarf’s lemma, they find a random matching that satisfies a notion of stability. They then use an iterative rounding method to find an actual matching (corresponding to a 0–1 solution) such that the resulting matching satisfies stability. Such rounding corresponds to the perturbation of the capacities.

  7. 7.

    In Boston, first priority consisted of students who lived in a proximal neighborhood and had a sibling that attended the school. The second tier consisted of students with a sibling at the school. Third priority is of the students who live in the “relevant” area. Finally, the remaining students are grouped within the last priority block.

  8. 8.

    The study of employment discrimination began in the second half of the 20th century. The two main theories of discrimination are a theory based on tastes, pioneered by Becker (1957), and a statistical theory, pushed forth by Phelps (1972) and Arrow (1973). Economists such as Glenn Loury and Roland Fryer have further developed the literature around race-based affirmative action.

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Authors and Affiliations

  1. Department of Economics, Stanford University, Stanford, CA, USA

    Fuhito Kojima, Fanqi Shi & Akhil Vohra

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  1. Fuhito Kojima
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  2. Fanqi Shi
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Correspondence to Fanqi Shi .

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Kojima, F., Shi, F., Vohra, A. (2017). Market Design. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_655-1

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_655-1

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