Two-sided Matching Research Articles

A matching method for elderly care service personnel with multiple types of service expectations.

With the rapid growth of the global aging population, the problem of providing for the elderly has become increasingly prominent. As a new model of providing for the elderly in China, home-based care has attracted more and more attention from all walks of life. The research on how to realize reasonable and effective matching between elderly care service personnel and the elderly under the home care model deserves attention and has important practical significance. In this paper, a matching method for elderly care service personnel considering multi-type service expectations is proposed. This approach involves first obtaining the actual values of the expectation indexes for each other, as well as the expectation requirements of the elderly and the service personnel. Next, we compute the satisfaction of the elderly and the service personnel for each other based on the elastic service expectation type, and finally, we make a decision about whom to choose based on the inelastic service expectation indexes. On this basis, the situation is considered that there are sufficient and insufficient elderly care service personnel, the two-sided matching models are constructed, respectively, and the optimal matching results are obtained by solving the models. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method.

Respect for Improvements and Comparative Statics in Matching Markets

One of the oldest results in the theory of two-sided matching is the entry comparative static, which shows that under the Gale-Shapley deferred acceptance algorithm, adding a new agent to one side of the market makes all the agents on the other side weakly better off. Here, we give a new proof of the entry comparative static, by way of a well-known property of deferred acceptance called respect for improvements. Our argument extends to yield comparative static results in more general settings, such as matching with slot-specific preferences.

Exploring the evolution and collaboration in two-sided matching: a comprehensive bibliometric and topic modeling analysis

PurposeThis study aims to provide a comprehensive analysis of two-sided matching (TSM) research, an interdisciplinary field that integrates both theoretical and practical perspectives. By examining 756 research articles from the Web of Science database, this paper seeks to identify key trends, collaboration patterns and emerging research topics within the TSM domain.Design/methodology/approachThe research utilizes bibliometric analysis combined with a structural topic model to analyze TSM-related articles published between January 1, 2000, and September 30, 2022. The study identifies leading subfields, journals, countries/regions and institutions based on publication volume, total citations and average citations per article. Interaction and collaboration patterns among these entities are examined through co-occurrence and coupling networks. Additionally, five major research topics are identified and explored using topic modeling and co-word networks. This hybrid knowledge mining approach better reveals the inherent structural changes in topic clusters. Topic distribution and network analysis are beneficial in capturing the attention allocation of different entities to knowledge.FindingsThe analysis reveals five prominent research topics in TSM: communication resource allocation, stable matching research, computing task assignment, TSM decision-making and market matching mechanism design. These topics represent the main directions of TSM research. The study also uncovers a shift in research focus from theoretical aspects to practical applications. Furthermore, the distribution of knowledge and interaction patterns among key entities align with the identified research trends.Originality/valueThis study offers a novel and detailed overview of TSM research highlighting significant trends and collaboration patterns within the field. By integrating bibliometric methods with structural topic modeling the study provides unique insights into the evolution of TSM research making it a valuable resource for both academic and professional communities.

A perfectly robust approach to multiperiod matching problems

Many two-sided matching markets involve multiperiod interaction. Traditional cooperative solutions, such as pairwise stability or the core, often identify unintuitive outcomes (or are empty) when applied to such markets. As an alternative, this study proposes the criterion of perfect α-stability. An outcome is perfect α-stable if no coalition prefers an alternative assignment in any period that is superior for all plausible market continuations. The solution posits that agents have foresight, but cautiously evaluate possible future outcomes. A perfect α-stable matching exists, even when assignments are inter-temporal complements. The perfect α-core, a stronger solution, is nonempty under standard regularity conditions, such as history independence. Our analysis extends to markets with arrivals and departures, transfers, and many-to-one assignments.

Two-sided matching theory-based second-hand house transaction evaluation and recommendation by the modified PLC-DEMATEL method

To enhance the two-sided matching efficiency in a multi-source heterogeneous environment, this paper takes the randomness and unstructured features of the online comments into consideration, and proposes a new matching mechanism by introducing the complex information representation tool. Firstly, the concept of the probabilistic linguistic normal cloud (PLNC) model is introduced to preserve information cohesion and characteristic distribution. Next, the basic operation laws and corresponding operators are given. Then, an innovative maximum boundary concept skipping the indirect approach is presented to update the similarity degree and distance measures, also the correlation coefficient. Furthermore, for the multi-indicator systems with interactions, the peer experts are invited to evaluate the relationship between indicators, a modified algorithm based on the Decision-Making and Trial Evaluation Laboratory (DEMATEL) method is applied to obtain the subjective weights of indicators. After that, a whole matching process and a correlation coefficient cluster method-based recommendation algorithm are presented. A case study is provided to illustrate the method, wherein a new indicator system is constructed by analyzing the correlation of multiple indicators based on online linguistic evaluations. The random forest model is combined to obtain the objective weights and balance its reliability. Finally, sensitivity analysis and comparative analysis are employed to validate the effectiveness and applicability.

Multi-position two-phase person-position matching decision-making with intermediary participation

With the rapid development in society, intermediaries play an increasingly important role in person-position matching decision-making. To obtain reasonable enterprise-intermediary matching and enterprise-candidate matching schemes under multiple positions, preferences of enterprises, headhunting companies and candidates should be fully considered from a two-phase perspective. Thus, a two-sided matching decision-making method under the probabilistic linguistic environment is proposed to solve the multi-position two-phase person-position matching problem. First, related theories of probabilistic linguistic term sets and two-sided matching are given. On this basis, the problem of multi-position two-phase person-position matching under the probabilistic linguistic environment is described. The decision-making process is divided into the following two phases: In the first phase, satisfactions of enterprises and headhunting companies are calculated considering subject expectations based on prospect theory. Then, considering the maximization of satisfactions of two-sided subjects, the many-to-many two-sided matching model between enterprises and headhunting companies is established and solved to obtain the optimal many-to-many matching scheme. In the second phase, according to evaluation matrices and expectation matrices, satisfactions of enterprises and candidates under multiple positions are calculated considering intermediary evaluations. Then, considering the maximization of satisfactions of enterprises and candidates, one-to-many matching models and one-to-one stable matching models under multiple positions are developed and solved to obtain the optimal person-position matching schemes under multiple positions. Finally, an example of the person-position matching with intermediary participation is used to illustrate the feasibility and effectiveness of the proposed method.

A combined qualitative–quantitative method for adaptive configuration of urban flood mitigation measure

Inappropriately selecting flood mitigation measures can lead to ineffective governance and wastage of social resources. To address this issue, this research proposes a framework for adaptive configuration of urban flood mitigation measure. This framework aims to achieve a two-sided matching between the disaster reduction capacity of measures and the specific demands of the construction site. The framework was employed to the urban flood mitigation strategy in Longkungou drainage system, an optimal allocation scheme for addressing urban flood disasters under the design rainfall with 50-year return period was determined. The results revealed that green mitigation measures are primarily concentrated in the drainage system within the upstream catchment. Stormwater pumping stations are mainly situated at the drainage outlets and adjacent river channels in the study area. By reducing the water level in the river channel, these stations effectively prevent and manage flood volume resulting from river overflow. As a result of the flood mitigation strategy, the flood volume in the Longkungou drainage system was reduced by 591,186 m3, representing a peak total flood volume reduction rate of 42.44%. The severity of flood disasters in each sub-catchment has significantly diminished, indicating that the flood mitigation strategy has successfully achieved the desired improvement.

Traffic-Aware Energy-Efficient Resource Allocation for RSMA Based UAV Communications

Traffic measurement will play an essential role in future networks to reveal the traffic requirements of the users, which will support network operations like resource allocation. In this paper, we study the traffic-aware resource allocation problem for downlink rate-splitting multiple access (RSMA) based unmanned aerial vehicle (UAV) communications. Specifically, with the help of traffic measurement, user requirements on achievable rate are known as prior knowledge to the UAV. Considering user requirements, we maximize the energy efficiency of the UAV by jointly optimizing the UAV deployment, beamforming, rate allocation, and subcarrier allocation. To overcome the non-convexity of the above problem, a joint optimization is developed to solve it iteratively. First, a heuristic approach is proposed to find the three-dimensional location of the UAV. Then, successive convex approximation approach is utilized to optimize RSMA parameters. Moreover, we formulate the subcarrier allocation problem as a many-to-one two-sided matching game, which is tackled by the swap matching algorithm. Numerical results suggest that the proposed subcarrier allocation scheme outperforms benchmark schemes, and RSMA based schemes perform close to that based on non-orthogonal multiple access, which all outperform orthogonal frequency division multiple access based scheme.

The law of large numbers for large stable matchings

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges’ preferences while allowing students’ preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.

Matching with Nonexclusive Contracts

A variety of empirical papers document the coexistence of exclusive and nonexclusive contracts within a given market across a multitude of industries. However, the theoretical literature has not been able to generate a differentiable model with the coexistence of these contracts. I rectify the gap in the literature by developing a theoretical model of two-sided matching, in which principals and agents choose between exclusive and nonexclusive contracts with cost-of-effort inefficiencies. I find that the coexistence of contracts relies on cost-sharing between principals, relative bargaining power, and an endogenous outside option. I also find that the pattern of contracts is monotonic with respect to the type distributions of principals and agents.

Improved Bandits in Many-to-One Matching Markets with Incentive Compatibility

Two-sided matching markets have been widely studied in the literature due to their rich applications. Since participants are usually uncertain about their preferences, online algorithms have recently been adopted to learn them through iterative interactions. An existing work initiates the study of this problem in a many-to-one setting with responsiveness. However, their results are far from optimal and lack guarantees of incentive compatibility. We first extend an existing algorithm for the one-to-one setting to this more general setting and show it achieves a near-optimal bound for player-optimal regret. Nevertheless, due to the substantial requirement for collaboration, a single player's deviation could lead to a huge increase in its own cumulative rewards and a linear regret for others. In this paper, we aim to enhance the regret bound in many-to-one markets while ensuring incentive compatibility. We first propose the adaptively explore-then-deferred-acceptance (AETDA) algorithm for responsiveness setting and derive an upper bound for player-optimal stable regret while demonstrating its guarantee of incentive compatibility. This result is a significant improvement over existing works. And to the best of our knowledge, it constitutes the first player-optimal guarantee in matching markets that offers such robust assurances. We also consider broader substitutable preferences, one of the most general conditions to ensure the existence of a stable matching and cover responsiveness. We devise an online DA (ODA) algorithm and establish an upper bound for the player-pessimal stable regret for this setting.

Two-sided matching decision method and application based on subject differences in interval intuitionistic fuzzy environment

In this paper, a two-sided matching decision model based on interval-valued intuitionistic fuzzy environment is proposed to maximize the demand of individual differences. Firstly, the attribute feature table and weight matrix of both agents are constructed, and a formula for calculating the comprehensive advantage in the interval-valued intuitionistic fuzzy environment is given, namely the interval-valued intuitionistic fuzzy comprehensive advantage aggregation operator (IIFCAAO); Secondly, the interval-valued intuitionistic fuzzy decision matrix of both agents is calculated by using the comprehensive advantage aggregation operator, and the interval-valued intuitionistic fuzzy decision matrix is transformed into a score function matrix by using a score function formula; Thirdly, the two-sided matching model is established to maximize the score; Finally, the scientificity and practicability of the model are verified by an example of college students changing their majors.

Fair and stable matching decision-making with multiple hesitant fuzzy elements

The two-sided matching (TSM) decision-making is an interdisciplinary research field encompassing management science, behavioral science, and computer science, which are widely applied in various industries and everyday life, generating significant economic and social value. However, in the decision-making process of real-world TSM, the complexity of the decision-making problem and environment lead to the preference information provided by the two-sided agents being ambiguous and uncertain. The purpose of this study is to develop a new fair and stable matching methodology to resolve the TSM problem with multiple hesitant fuzzy element (HFE) information. The decision-making process is as follows. First, the TSM problem with four kinds of HFEs is described. To solve this problem, the HFE value of each index is normalized and then is transformed into the closeness degree by using the bidirectional projection technology. Second, based on the closeness degree, the weight of each index is calculated by using the Critic method. Then, the agent satisfaction is obtained by aggregating the closeness and the weights. Next, a fair and stable TSM model to maximizing agent satisfactions under the constraints of one-to-one stable matching is constructed. The best TSM scheme can be obtained by solving the TSM model. Finally, an example of logistics technology cooperation is provided to verify the effectiveness and feasibility of the presented model and methodology. The proposed methodology develops a novel fuzzy information presentation tool and constructs a TSM model considering the fairness and stability, which is of great significance to investigate the TSM decision-making and the resolution of real-life TSM problems under the uncertain and fuzzy environments. One future research direction is to consider multiple psychological and behavioral factors of two-sided agents in TSM problems.

Green technology investment selection with carbon price and competition: One-to-many matching structure

With the deterioration of natural resources and the aggravation of environmental pollution, there is a growing imperative to implement industrial green reform through green technology investment (GTI). This paper constructs a nonlinear dual-objective function by drawing on the theory of two-sided matching under the carbon trading regulation, aiming to examine GTI selection decisions made by two oligarchic manufacturers (i.e., oligarchs) and a monopoly supplier (i.e., supplier). The supplier offers multiple green technologies, while oligarchs rack their brains to buy green technologies in an attempt to exploit their social, economic and environmental potentials. Available technologies vary in terms of their environmental efficiency and cost. Then, a two-sided matching mechanism is constructed to explore the availability of stable matchings and examine the impacts of the carbon price and green improvement coefficient on GTI, product pricing decisions and profits within a competitive environment. Finally, a Monte-Carlo experiment is designed to analyze the impact of uncertain market risks on supplier's decisions. The results show that there is a two-sided matching mechanism that enables oligarchs and suppliers to obtain stable matching solution sets. Higher carbon prices lead to higher product prices, lower market demand, and improved environmental performance. Product price and market demand are positively correlated with investment volumes of oligarchs themselves and negatively correlated with those of their competitors. Investment risk has a certain negative impact on suppliers' profitability.

A Matching Model for Construction Subcontractor Selection in Engineering Bid Decisions Using Ordinal Priority Approach

ABSTRACT In recent years, the two-sided matching theory has been applied in various fields. Its influence in the engineering field is becoming more and more significant. In the construction engineering context, from the contractor’s perspective as the decision-maker, the mutual matching between project bidding and subcontractors is a complex and uncertain process. A suitable matching method needs to be selected according to the particular situation. Since this study requires considering both the highest satisfaction of parties and the weight of individual fulfillment, we use the two-sided matching theory to address the mutual matching between the engineering project bidding and subcontractor. At the same time, the Ordinal Priority Approach (OPA) is employed to determine the weights and evaluate the indicators of both parties and then determine the preference between the two parties, effectively avoiding the deviation caused by subjective influence in the process. As a result, a bilateral matching model is proposed with the highest satisfaction and considering individual satisfaction. Finally, an example is presented to verify the feasibility and effectiveness of the proposed model.

Shapley–Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. We show that, for strict preferences, the unique strong core allocation “respects improvement”—if an agent’s object becomes more desirable for some other agents, then the agent’s allotment in the unique strong core allocation weakly improves. We extend this result to weak preferences for both the strong core (conditional on nonemptiness) and the set of competitive allocations (using probabilistic allocations and stochastic dominance). There are no counterparts of the latter two results in the two-sided matching literature. We provide examples to show how our results break down when there is a bound on the length of exchange cycles. Respecting improvements is an important property for applications of the housing markets model, such as kidney exchange: it incentivizes each patient to bring the best possible set of donors to the market. We conduct computer simulations using markets that resemble the pools of kidney exchange programs. We compare the game-theoretical solutions with current techniques (maximum size and maximum weight allocations) in terms of violations of the respecting improvement property. We find that game-theoretical solutions fare much better at respecting improvements even when exchange cycles are bounded, and they do so at a low efficiency cost. As a stepping stone for our simulations, we provide novel integer programming formulations for computing core, competitive, and strong core allocations. Funding: P. Biró gratefully acknowledges financial support from the Hungarian Scientific Research Fund, OTKA [Grant K143858] and the Hungarian Academy of Sciences [Grant LP2021-2]. F. Klijn gratefully acknowledges financial support from AGAUR–Generalitat de Catalunya [Grants 2017-SGR-1359 and 2021-SGR-00416] and the Spanish Agencia Estatal de Investigación [Grants ECO2017-88130-P and PID2020-114251GB-I00] (funded by MCIN/AEI/10.13039/501100011033) and the Severo Ochoa Programme for Centres of Excellence in R&D (Barcelona School of Economics) [Grant CEX2019-000915-S]. Research visits related to this work were financed by COST Action [Grant CA15210 ENCKEP], supported by COST (European Cooperation in Science and Technology), http://www.cost.eu/ .

Fermatean fuzzy multi-attribute personnel-position matching group decision-making with unknown weight information

In view of the lack of research on two-sided matching group decision-making and the rare application of Fermatean fuzzy numbers in two-sided matching decision-making, a multi-attribute personnel-position matching group decision-making methodology is proposed. First, the group decision-making problem for multi-attribute personnel-position matching is described. To address this problem, a new algorithm is designed to determine the attribute weights. The group comprehensive Fermatean fuzzy evaluation matrix can be obtained by aggregating the attribute weights, the Fermatean fuzzy evaluation matrices given by the decision-makers and the weights of decision-makers. Moreover, another novel algorithm is designed to calculate the weight of the group consistency attribute. The synthetic Fermatean fuzzy evaluation matrix is obtained by aggregating the group consistency attribute weights and the Fermatean fuzzy evaluation matrices given by the candidates. Moreover, based on the group comprehensive Fermatean fuzzy evaluation matrix and the synthetic Fermatean fuzzy evaluation matrix, a multi-objective two-sided matching model is established to maximize the satisfaction of two-sided agents. The optimal two-sided matching scheme is obtained by the model solution. Finally, the feasibility, effectiveness and innovation of the proposed methodology are verified by an example analysis of personnel-position matching. The main contributions of this paper are listed as follows: (1) Group decision-making of two-sided matching based on Fermatean fuzzy information is explored. (2) A Fermatean fuzzy induced ordered weighted average (FFIOWA) operator that aggregates Fermatean fuzzy numbers is introduced. (3) Two new algorithms for calculating the unknown attribute weights are designed. (4) A satisfaction calculation method considering the accuracy coefficient is proposed. (5) The model for Fermatean fuzzy multi-attribute personnel-position matching group decision-making is developed.

Application of Two-sided Matching Theory in Financing of Small and Medium-sized Enterprises

The nation's small and medium-sized businesses (also known as SMEs) constitute an essential component of the economy as a whole; yet, many companies are right now struggling to obtain adequate funding. On the one hand, increasing the amount of capital invested in venture firms by venture capitalists can considerably promote the development of venture enterprises. On the other hand, venture capitalists look for businesses in which they may invest, with the goal of achieving high levels of success and gaining substantial profits. Therefore, in order to make a reasonable and stable match between venture capitalists and SMEs according to their respective preference lists, this paper makes use of the Gale-Shapley algorithm, which is part of the two-sided matching theory. This helps improve cooperation efficiency and maximizes the benefits for both parties. In addition to that, based on the algorithm, this article offers some policy recommendations for the venture capital market in China.

Research Process of Two-Sided Matching in Venture Capital

Venture capital supports not only to the continual increase of the size of start-up companies, but also to their research and innovation, thereby transforming scientific and technological advantages into competitive advantages. Venture capital would enhance the competitive advantage of businesses and assist them in reaping a double harvest of dollars and reputation. It is vital that venture capital institutions and startups are matched in a reasonable, steady, and effective manner. This study covers the evolution and research process of two-sided matching between venture capital institutions and start-up businesses through a literature review. With the ongoing evolution of society, matching decisions in venture capital are also evolving. The promotion of economic growth and technical innovation, as well as the improvement of international competitiveness, can be aided by the reasonable and efficient pairing of venture capitalists.

Stable and meta-stable contract networks

This paper studies a multilateral matching market in which each participant can sign contracts with any other agents. This market subsumes the two-sided matching and the roommate problem as special cases. We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices i∈I are interpreted as agents, and the edges c∈C as contracts that can be concluded between agents. The preferences of each agent i are given by a choice functionfi possessing the so-called path independent property. In this general setup we consider the notion of stable contract network.The paper contains two main results. The first one is that a general stable contract problem for (I,C,f) can be reduced to a special one in which preferences of the agents are given by weak orders, or, equivalently, by utility functions. However, stable contract systems may not exist. Trying to overcome this trouble, we introduce a weaker notion of meta-stability for contract systems. Our second result is that meta-stable systems always exist. A proof of this result relies on an appealing theorem on the existence of the so-called compromise function.