Corrigendum to "On randomized matching mechanisms" [Economic Theory 8(1996)377-381]

Ma (1996) studied the random order mechanism, a matching mechanism suggested by Roth and Vande Vate (1990) for marriage markets. By means of an example he showed that the random order mechanism does not always reach all stable matchings. Although Ma's (1996) result is true, we show that the probability distribution he presented - and therefore the proof of his Claim 2 - is not correct. The mistake in the calculations by Ma (1996) is due to the fact that even though the example looks very symmetric, some of the calculations are not as ''symmetric.''

Paths to stability for matching markets with couples

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from `satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from `satisfying' blocking coalitions that yields a stable matching.

Procedurally fair and stable matching

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al., 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and "endstate'' fairness. Aldershof et al. (1999) and Ma (1996) that exist on the probability distribution induced by both mechanisms. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

On bilateral agreements: just a matter of matching

This paper aims at assessing the importance of the initial technological endowments when firms decide to establish a technological agreement. We propose a Bertrand duopoly model where firms evaluate the advantages they can get from the agreement according to its length. Allowing them to exploit a learning process, we depict a strict connection between the starting point and the final result. Moreover, as far as learning is evaluated as an iterative process, the set of initial conditions that lead to successful ventures switches from a continuum of values to a Cantor set.

The principal-agent matching market

We propose a model based on competitive markets in order to analyze an economy with several principals and agents. We model the principal-agent economy as a two-sided matching game and characterize the set of stable outcomes of this principal-agent matching market. A simple mechanism to implement the set of stable outcomes is proposed. Finally, we put forward examples of principal-agent economies where the results fit into.

NAVA enhances tidal volume and diaphragmatic electro-myographic activity matching: a Range90 analysis of supply and demand.

Neurally adjusted ventilatory assist (NAVA) is a ventilation assist mode that delivers pressure in proportionality to electrical activity of the diaphragm (Eadi). Compared to pressure support ventilation (PS), it improves patient-ventilator synchrony and should allow a better expression of patient's intrinsic respiratory variability. We hypothesize that NAVA provides better matching in ventilator tidal volume (Vt) to patients inspiratory demand. 22 patients with acute respiratory failure, ventilated with PS were included in the study. A comparative study was carried out between PS and NAVA, with NAVA gain ensuring the same peak airway pressure as PS. Robust coefficients of variation (CVR) for Eadi and Vt were compared for each mode. The integral of Eadi (ʃEadi) was used to represent patient's inspiratory demand. To evaluate tidal volume and patient's demand matching, Range90 = 5-95 % range of the Vt/ʃEadi ratio was calculated, to normalize and compare differences in demand within and between patients and modes. In this study, peak Eadi and ʃEadi are correlated with median correlation of coefficients, R > 0.95. Median ʃEadi, Vt, neural inspiratory time (Ti_ ( Neural )), inspiratory time (Ti) and peak inspiratory pressure (PIP) were similar in PS and NAVA. However, it was found that individual patients have higher or smaller ʃEadi, Vt, Ti_ ( Neural ), Ti and PIP. CVR analysis showed greater Vt variability for NAVA (p < 0.005). Range90 was lower for NAVA than PS for 21 of 22 patients. NAVA provided better matching of Vt to ʃEadi for 21 of 22 patients, and provided greater variability Vt. These results were achieved regardless of differences in ventilatory demand (Eadi) between patients and modes.

Marriage as a Rat Race: Noisy Pre-Marital Investments with Assortative Matching

We study the incentive to invest to improve marriage prospects, in a frictionless marriage market with non-transferable utility. Stochastic returns to investment eliminate the multiplicity of equilibria in models with deterministic returns, and a unique equilibrium exists under reasonable conditions. Equilibrium investment is efficient when the sexes are symmetric. However, when there is any asymmetry, including an unbalanced sex ratio, investments are generically excessive. For example, if there is an excess of boys, then there is parental over-investment in boys and under-investment in girls, and total investment will be excessive.

Matching and Sorting in a Global Economy

We develop a neoclassical trade model with heterogeneous factors of production. We consider a world with two factors, labor and .managers., each with a distribution of ability levels. Production combines a manager of some type with a group of workers. The output of a unit depends on the types of the two factors, with complementarity between them, while exhibiting diminishing returns to the number of workers. We examine the sorting of factors to sectors and the matching of factors within sectors, and we use the model to study the determinants of the trade pattern and the effects of trade on the wage and salary distributions. Finally, we extend the model to include search frictions and consider the distribution of employment rates.

Local adaptation and matching habitat choice in female barn owls with respect to melanic coloration.

Local adaptation is a major mechanism underlying the maintenance of phenotypic variation in spatially heterogeneous environments. In the barn owl (Tyto alba), dark and pale reddish-pheomelanic individuals are adapted to conditions prevailing in northern and southern Europe, respectively. Using a long-term dataset from Central Europe, we report results consistent with the hypothesis that the different pheomelanic phenotypes are adapted to specific local conditions in females, but not in males. Compared to whitish females, reddish females bred in sites surrounded by more arable fields and less forests. Colour-dependent habitat choice was apparently beneficial. First, whitish females produced more fledglings when breeding in wooded areas, whereas reddish females when breeding in sites with more arable fields. Second, cross-fostering experiments showed that female nestlings grew wings more rapidly when both their foster and biological mothers were of similar colour. The latter result suggests that mothers should particularly produce daughters in environments that best match their own coloration. Accordingly, whiter females produced fewer daughters in territories with more arable fields. In conclusion, females displaying alternative melanic phenotypes bred in habitats providing them with the highest fitness benefits. Although small in magnitude, matching habitat selection and local adaptation may help maintain variation in pheomelanin coloration in the barn owl.

Fiscal multipliers in a two-sector search and matching model

This paper evaluates the effects of policy interventions on sectoral labour markets and the aggregate economy in a business cycle model with search and matching frictions. We extend the canonical model by including capital-skill complementarity in production, labour markets with skilled and unskilled workers and on-the-job-learning (OJL) within and across skill types. We first find that, the model does a good job at matching the cyclical properties of sectoral employment and the wage-skill premium. We next find that vacancy subsidies for skilled and unskilled jobs lead to output multipliers which are greater than unity with OJL and less than unity without OJL. In contrast, the positive output effects from cutting skilled and unskilled income taxes are close to zero. Finally, we find that the sectoral and aggregate effects of vacancy subsidies do not depend on whether they are financed via public debt or distorting taxes.

Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women employs truncation strategies or weakly successfully manipulates, then all other women weakly benefit and all men are weakly harmed. We show that our results do not appropriately generalize to the many-to-one college admissions model.

Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.