Dynamic Matching Model Research Articles

Dynamic Stochastic Matching Under Limited Time

In centralized matching markets, such as kidney exchange schemes and car-pooling platforms, new participants constantly enter the market and remain available for potential matches during a limited period of time. To reach an efficient allocation, the timing'' of the matching decisions is a critical aspect of the platform's operations. There is a fundamental tradeoff between increasing market thickness and mitigating the risk that participants abandon the market. Nonetheless, the dynamic properties of matching markets have been mostly overlooked in the classic algorithmic literature. In this paper, we introduce a general dynamic matching model over edge-weighted graphs, where the agents' arrivals and abandonments are stochastic and heterogeneous. While the resulting Markov decision process is computationally intractable, we design new simple matching algorithms that admit strong worst-case performance guarantees. We devise a 3-approximation algorithm for the cost-minimization problem on graphs satisfying a metric-like property. In contrast, we show that the performance of widely used batching algorithms can be arbitrarily bad. We further devise a (e-1)/(2e)-approximation algorithm for the reward-maximization problem on arbitrary bipartite graphs. Our approach involves the development of a host of techniques, including linear programming benchmarks, value function approximations, and proxies for continuous-time Markov chains, that could be of broader interest. In extensive experiments, we simulate the matching operations of a car-pooling platform using real-world taxi demand data. The newly developed algorithms have the potential to significantly improve cost efficiency against widely used batching algorithms.

Price Discovery in a Matching and Bargaining Market with Aggregate Uncertainty

We introduce aggregate uncertainty into a Rubinstein and Wolinsky (1985)-type dynamic matching and bilateral bargaining model. The market can be either in a high state, where there are more buyers than sellers, or in a low state, where there are more sellers than buyers. Traders do not know the state. They randomly meet each other and bargain by making take-it-or-leave-it offers. The only information transmitted in a meeting is the time a trader spent on the market. There are two kinds of search frictions: time discounting and exogenous exit. We find that as the search frictions vanish, the market discovers the competitive price quickly: the prices offered in equilibrium converge in expectation to the true-state Walrasian price at the rate linear in the total search friction. This rate is the same as it would be if the state were commonly known.

Venture Capital Contracts

We estimate the impact of venture capital (VC) contract terms on startup outcomes and the split of value between the entrepreneur and investor, accounting for endogenous selection via a novel dynamic search and matching model. The estimation uses a new, large data set of first financing rounds of startup companies. Consistent with efficient contracting theories, there is an optimal equity split between agents, which maximizes the probability of success. However, VCs use their bargaining power to receive more investor-friendly terms compared to the contract that maximizes startup values. Better VCs still benefit the startup and the entrepreneur, due to their positive value creation. Counterfactuals show that reducing search frictions shifts the bargaining power to VCs and benefits them at the expense of entrepreneurs. The results show that selection of agents into deals is a first-order factor to take into account in studies of contracting. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

How Matching Creates Value: Cogs and Wheels for Human Capital Resources Research

Using selection- and adaptation-based logic, we develop a dynamic matching model to describe how employees are matched with positions to enhance human capital-based value creation. Matching, defined as the process by which individuals are dynamically aligned with organizations and the situations (roles, jobs, tasks, etc.) within them, has historically been examined in silos across a broad range of literatures. Consequently, we know little about how seemingly diverse HR activities, such as recruitment, job design, training, promotions, and terminations, might inform each other through the common lens of matching. Emanating from our review, we integrate relevant literatures to develop a comprehensive matching model (termed the “dynamic matching lifecycle model”). Our model extends prior, more static conceptualizations of matching (like attraction, selection, attrition, or ASA) to include four stages: creation, development, reconfiguration, and termination—based on two broad mechanisms—selection and adaptation. Furthermore, we describe how matching contributes to individual and organizational value creation. By evoking human capital theories, we explain how people and organizations engage in matching across the four stages of the model to create human capital-based value. Our model shows that information and information distribution, organization design, and complementarities play important roles in ensuring successful matching. Promising future research directions are discussed.

Dynamic Matching of Dual-mode Electro-mechanical Transmission (EMT) Based on the Optimal Motor Efficiency

Abstract Energy and environment has been the problem which is the most concerned by all over the world. Hybrid electric vehicle (HEV), which has the virtue of low exhaustion and low consumption, is the optimal choice to solve these problems at present. As an innovative power-split transmission (PST) technology, electro-mechanical transmission (EMT) is widely applied in military and civilian vehicles. In this paper, the dynamic matching problem of a dual-mode EMT is studied and a dynamic matching model is developed. A multi-objective optimization model is built to improve the motor energy utilization ratio through optimizing the design parameters. Sensitivity of the design parameters for dynamic matching performance are analyzed by design of experiments (DOE). Finally, the feasible region of the optimal parameters where the dynamic matching model get the optimal evaluation index is obtained.

House Prices and Vacancies after Hurricane Katrina: Empirical Analysis of the Search & Matching Model

I analyze Hurricane Katrina as a natural experiment that shocks housing demand by reducing the stock supply of housing and raising net migration. With empirical data from 57 metropolitan areas, I measure the impact of Katrina on housing price, new residential investment and net migration, and produce a difference-in-differences estimated elasticity of flow supply. I develop a structural dynamic search and matching model of the housing market that produces coincidental steady state equilibrium vacancies and prices. The structural model’s simulated response to Hurricane Katrina successfully predicts the empirical qualitative response of prices and the empirical quantitative response of new residential investment.

Identification and Estimation of Empirical Dynamic Matching Models

This paper first shows a monotone transformation of a new fixed point representation of the dynamic marriage matching model proposed by Choo (2015) is a contraction. The contraction implies the existence of a unique equilibrium of the model and allows to apply the Rust's Nested Fixed Point (NFXP) algorithm for parametrically estimating the model. Monte Carlo exercises show that the NFXP algorithm provides Maximum Likelihood (ML) estimators with smaller bias and standard deviations than those of Hotz-Miller's Conditional Choice Probability (CCP) estimators, but at higher computational costs.

How Do Regional Labor Markets Adjust to Immigration? A Dynamic Analysis for Post-War Germany

We draw on two decades of historical data to analyze how regional labor markets in West Germany adjusted to one of the largest forced population movements in history, the mass inflow of eight million German expellees after World War II. The expellee inflow was distributed very asymmetrically across two West German regions. A dynamic two-region search and matching model of unemployment, which is exposed to the asymmetric expellee inflow, closely fits historical data on the regional unemployment differential and the regional migration rate. Both variables increase dramatically after the inflow and decline only gradually over the next decade. We show that despite the large and long-lasting dynamics following the expellee inflow, native workers experience only a modest loss in expected discounted lifetime labor income of 1.38%. Per-period losses in native labor income, however, are up to four times as large. The magnitude of income losses also depends on the initial location and labor market status of native workers. In counterfactual analyses, we furthermore show that economic policy interventions that affect the nature of the immigration inflow can effectively reduce native income losses and dampen adjustment dynamics in regional labor markets. One such intervention is to distribute the inflow more evenly over time. Smaller immigration inflows, similar in magnitude to the refugee inflow that Germany is experiencing today, also reduce native income losses markedly but decrease the duration of labor market adjustment only modestly.

The Impact of Venture Capital on the Life Cycles of Startups

How do VCs select startups to fund over multiple rounds? To study this question, I develop a dynamic two-sided matching model of VC funding. Using a hand-collected database including both VC-funded and non-VC-funded startups, I estimate the joint determinants of investment selection and the effects of post- investment influence in a Bayesian framework. The results show that selection depends on startups’ quality and VCs’ influence – VCs may choose to invest in a startup with lower quality if their subsequent impact is large. Importantly, previously funded startups are of higher quality and thus are more likely to get additional funding. A simulation experiment shows that initial random differences in startups can magnify significantly under the joint effects of the selection and influence of VC funding.

Network Effects and the Black-White Wage Gap

We study the impact of segregation in social networks on the disparities in labor market outcomes between Black and White workers. We provide a dynamic search and matching model of the labor market where we incorporate two kinds of network effects: i) job finding through social contacts and ii) transmission of work norms by network neighbors. When considering the first type of network effect, an increase in the level of social segregation leads to higher unemployment rates and lower wages for both the Black and White worker groups. At the same time, inter-group disparities increase, however, social segregation can account for only a negligible share of the Black-White residual wage gap.When studying the norm transmission role of social networks, the model is able to explain the whole residual wage gap, however, predicts a negative relationship between the level of social segregation and the wage gap, which contradicts the empirical evidence. We show that combining the two kinds of network effects can account for both the empirically observed magnitude of the Black-White wage gap and it's increasing pattern in the level of social segregation. We use this latter model version to study the impact of policy changes on the inter-group inequality.

A dynamic generalization of Becker's assortative matching result

This paper considers a dynamic matching model in which each agent's future productivity depends in part on their current match, as in labor markets, schooling, intergenerational marriage markets, and other environments. The Planner's endogenous rankings of human distributions are characterized. These Planner rankings are then used to develop sufficient conditions for positive assortative matching to be dynamically efficient. One lesson that emerges is that complementarity assumptions alone are insufficient for a robust sorting theory — the curvature of the static production function is also critical to determine optimal sorting patterns. In addition, the Planner's ranking of distributions over human capital yield characterizations of individual attitudes toward human capital gambles in an associated market equilibrium. Finally, the implied dynamics for (1) individual wages and (2) wage distributions across age cohorts are characterized.

On Becoming an Experiential Educator

Background Becoming an experiential educator involves more than just being a facilitator or matching learning style with teaching style. Experiential education is a complex relational process that involves balancing attention to the learner and to the subject matter while also balancing reflection on the deep meaning of ideas with the skill of applying them. Aim To describe a dynamic matching model of education based on Experiential Learning Theory and to create a self-assessment instrument for helping educators understand their approach to education. Method A dynamic matching model for “teaching around the learning cycle” describes four roles that educators can adopt to do so—facilitator, subject expert, standard-setter/evaluator, and coach. A self-assessment instrument called the Educator Role Profile was created to help educators understand their use of these roles. Results Research using the Educator Role Profile indicates that to some extent educators do tend to teach the way they learn, finding that those with concrete learning styles are more learner-centered, preferring the facilitator role; while those with abstract learning styles are more subject-centered preferring the expert and evaluator roles. Conclusion A model for the practice of dynamic matching of educator roles, learner style, and subject matter can aid in the planning and implementation of educational experiences. With practice, both learners and educators can develop the flexibility to use all educator roles and learning styles to create a more powerful and effective process of teaching and learning—in Mary Parker Follett’s words to, “. . . free the energies of the human spirit . . . the highest potentiality of all human association.”

A decision support system for public logistics information service management and optimization

Transportation optimization usually aims at minimizing the empty load ratios (ELRs) of vehicles. Most Chinese vehicles for logistics are owned by individual entrepreneurs. Because China is very large, transport distances are typically long, and thus the ELR is very high. The ELR is the primary reason for high transport costs, considerable pollution, and high energy consumption. Many Chinese local governments try to build public transport information services that decrease the ELR. This work proposes a decision support system (DSS) for public logistics information service management and optimization (PLISMO) for vehicle drivers and owners, logistics customers and related logistics service providers and management institutes. The dynamic and real-time matching model between goods and vehicles, and the enabling technologies are important issues for the DSS for PLISMO. Therefore, intelligent positioning technologies are employed to acquire and manage the vehicle status. A model matching vehicles with goods is developed based on an assessment model of transport capability and service priority criteria. A multi-objective real-time scheduling model is devised to minimize the ELR. Based on the concepts and decision-making models for PLISMO, a DSS is created and the architecture of the system is investigated. The effectiveness of the DSS and decision-making models is demonstrated by a case of finished vehicle logistics (FVL). Analytical results show that the proposed DSS can reduce the ELR and logistics cost. This system helps governments construct DSSs for general PLISMO.

Analysis and Simulation on Recognition Algorithm for Dynamic Facial Images

In order to realize the recognition for dynamic facial images, the paper builds a dynamic matching model. First, this paper introduces a dynamic feature extraction algorithm of feature constraint optimization which can effectively extract the 2D dynamic facial features. Then, the paper analyzes the neurons mathematical model comprehensive expressing neurons operational mechanism and applies the model to dynamic facial feature expression. Finally, we study the learning rules how BP algorithm directs neural network, establish a corresponding mathematical model, and then use facial feature dynamic rules making dynamic features to be learned quickly and complete the recognition by the error compensation. The experiment results show that the model has a higher precision of geometric feature extraction for dynamic two-dimensional face images and better recognizes characteristic with error within 0.035mm which meets the requirements of stable, reliable, high precision and anti-interference ability etc.

Exclusive nightclubs and lonely hearts columns: Non-monotone participation in optional intermediation

In many decentralised markets, the traders who benefit most from an exchange do not employ intermediaries even though they could easily afford them. At the same time, employing intermediaries is not worthwhile for traders who benefit little from trade. Together, these decisions amount to non-monotone participation choices in intermediation: only traders of middle “type” employ intermediaries, while the rest, the high and the low types, prefer to search for a trading partner directly. We provide a theoretical foundation for this, hitherto unexplained, phenomenon. We build a dynamic matching model, where a trader's equilibrium bargaining share is a convex increasing function of her type. We also show that this is indeed a necessary condition for the existence of non-monotone equilibria.

Encouraging Participation in a Labor Market with Search and Matching Frictions

We analyze the transition of the labor market to a new steady state following a reduction of negative incentives for participation. Due to labor market search and matching frictions, the transition may temporarily increase unemployment while new participants search for jobs. The formal framework is a dynamic search and matching model with an endogenous participation decision and unemployment benefits that are not conditioned on search effort (in other words, non-participants are also entitled to unemployment benefits). We employ the model to explore the mechanisms at work, and their welfare implications, following a reduction of unemployment benefits. We show that, although social welfare may be higher in the new equilibrium, the transition period involves a temporary welfare loss. We consider two alternative policy approaches: a gradual reduction versus an immediate one. We conclude that the transition period associated with a gradual reduction involves a smaller welfare loss.

ADVERSE SELECTION IN DYNAMIC MATCHING MARKETS

We study the Akerlofian adverse selection problem in a dynamic matching model where the competitive situation varies across different meetings. The ‘lemons principle’ is shown to limit the high quality sales within a wider range of quality distributions than in the Walrasian benchmark. High quality goods can nevertheless be traded, albeit less frequently than the low quality goods. For certain quality distributions, there exists a ‘partially pooling’ steady state where high quality sellers are active whenever at least two buyers compete for the good. Otherwise, the model features cycles in a sense that high quality goods are traded only in non-consecutive periods.

The Relationship Between Identities and Segregation in Games and Networks

Modern societies face the challenge of diverse populations composed of groups of different origins with varying norms, beliefs, and backgrounds. In many countries this is approached passively with the expectation of integration or segregation by choice. Here integration is assumed to be desirable for reasons varying from ideological viewpoints to human capital traps. We assume groups of hosts and foreigners to be endowed with identities of their culture of origin, whereby identities can be adapted at a cost. These identities have effects on preferences, which we explore with two different utility functions. Using a dynamic matching model where agents update identities and play a coordination game in each period, we show that integration, possibly to a limited extent, can be achieved with a laissez-faire approach, but given circumstances, such as exogenous segregation or false beliefs, might not take place, despite being socially optimal. Analyzing fixed networks complemented with dynamic simulations we attempt to capture how identities evolve and propagate in society, finding that relative group sizes, network size and learning costs can make a difference, while initial network structures within groups seem insignificant.

Employment Fluctuations with Downward Wage Rigidity: The Role of Moral Hazard

This paper considers a dynamic matching model with imperfectly observable worker effort. In equilibrium, the wage distribution is truncated from below by a no-shirking condition. This downward wage rigidity induces the same type of inefficient churning and contractual fragility as in Ramey and Watson (1997). Nonetheless, the surprising lesson of our analysis is that workers' shirking motive reduces the cyclical fluctuations in job destruction, because firms are forced to terminate some marginal jobs in booms which they cannot commit to maintain in recessions. This time-inconsistency problem casts doubt upon the importance of inefficient churning as an explanation of observed employment fluctuations. On the other hand, the no-shirking condition implies that firms' share of surplus is procyclical, which can amplify fluctuations in job creation. Thus, our model is consistent with recent evidence that job creation is more important than job destruction in driving labor market fluctuations. Furthermore, unlike most models with endogenous job destruction, we obtain a robust Beveridge curve.

Employment Fluctuations with Downward Wage Rigidity: The Role of Moral Hazard

This paper considers a dynamic matching model with imperfectly observable worker effort. In equilibrium, the wage distribution is truncated from below by a no-shirking condition. This downward wage rigidity induces the same type of inefficient churning and contractual fragility as in Ramey and Watson (1997). Nonetheless, the surprising lesson of our analysis is that workers' shirking motive reduces the cyclical fluctuations in job destruction, because firms are forced to terminate some marginal jobs in booms which they cannot commit to maintain in recessions. This time-inconsistency problem casts doubt upon the importance of inefficient churning as an explanation of observed employment fluctuations. On the other hand, the no-shirking condition implies that firms' share of surplus is procyclical, which can amplify fluctuations in job creation. Thus, our model is consistent with recent evidence that job creation is more important than job destruction in driving labor market fluctuations. Furthermore, unlike most models with endogenous job destruction, we obtain a robust Beveridge curve.