Matching with Couples: a Multidisciplinary Survey

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists.matching; couples; stability; computational complexity; incentive compatibility; restricted domains; large markets

Stability, Specialization and Social Recognition

Yang s theory of economic specialization under increasing returns to scale (Yang 2001) is a formal development of the fundamental Smith-Young theorem on the extent of the market and the social division of labor.In this theory specialization and, thus, the social division of labor is firmly embedded within a system of perfectly competitive markets.This leaves unresolved whether and how such development processes are possible in economies based on more primitive, nonmarket organizations.In this paper we introduce a general relational model of economic interaction.Within this non-market environment we discuss the emergence of economic specialization and ultimately of economic trade and a social division of labor.We base our approach on three stages in organizational development: the presence of a stable relational structure; the presence of relational trust and subjective specialization; and, finally, the emergence of objective specialization through the social recognition of subjectively defined economic rolesnetworks;stability;social division of labor;specialization

Matching with couples: a Multidisciplinary Survey

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists. © 2013 World Scientific Publishing Company

Controlled Matching Game for Resource Allocation and User Association in WLANs

In multi-rate IEEE 802.11 WLANs, the traditional user association based on the strongest received signal and the well known anomaly of the MAC protocol can lead to overloaded Access Points (APs), and poor or heterogeneous performance. Our goal is to propose an alternative game-theoretic approach for association. We model the joint resource allocation and user association as a matching game with complementarities and peer effects consisting of selfish players solely interested in their individual throughputs. Using recent game-theoretic results we first show that various resource sharing protocols actually fall in the scope of the set of stability-inducing resource allocation schemes. The game makes an extensive use of the Nash bargaining and some of its related properties that allow to control the incentives of the players. We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as its MAC anomaly. The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer

Stable matching: An integer programming approach

This paper develops an integer programming approach on two-sided many-to-one matching by investigating stable integral matchings of a fictitious continuum market induced from the original matching market. Each stable integral matching of the continuum market corresponds to a stable matching of the original matching market. We show that a stable matching exists in the original matching market when firms' preference profile satisfies a unimodularity condition. Our result indicates that a stable matching is guaranteed to exist with various forms of complementary preferences

Matching with Externalities

We incorporate externalities into the stable matching theory of two-sided markets. Extending theclassical substitutes condition to markets with externalities, we establish that stable matchings exist whenagent choices satisfy substitutability. We show that substitutability is a necessary condition for the existenceof a stable matching in a maximal-domain sense and provide a characterization of substitutable choicefunctions. In addition, we extend the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, to settings with externalities even thoughthe standard fixed-point techniques do not appl

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion

How to Build an Institution

How should institutions be designed that “work” in bringing about desirable social outcomes? I study a case of successful institutional design—the redesign of the National Resident Matching Program—and argue that economists assume three roles when designing an institution, each of which complements the other two: first, the designer combines positive and normative modeling to formalize policy goals and to design possible mechanisms for bringing them about. Second, the engineer refines the design by conducting experiments and computational analyses. Third, the plumber implements the design in the real world and mends it as needed. © The Author(s) 2020

How to build an institution

How should institutions be designed that “work” in bringing about desirable social outcomes? I study a case of successful institutional design—the redesign of the National Resident Matching Program—and argue that economists assume three roles when designing an institution, each of which complements the other two: first, the designer combines positive and normative modeling to formalize policy goals and to design possible mechanisms for bringing them about. Second, the engineer refines the design by conducting experiments and computational analyses. Third, the plumber implements the design in the real world and mends it as needed