Partnership-enhancement and stability in matching problems

In two-sided matching problems, we consider “natural” changes in preferences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rank-enhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the “irrelevant” agents, whose preferences as well as whose original partners’ preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.     

Investments in education and welfare in a two-sector,random matching economy

We consider a random matching model where heterogeneous agents choose optimally to invest time and real resources in education. Generically, there is a steady state equilibrium where some agents, but not all of them, invest. Regular steady state equilibria are constrained inefficient in a strong sense. The Hosios (1990) condition is neither necessary nor sufficient for constrained efficiency. We also provide restrictions on the fundamentals sufficient to guarantee that equilibria are characterized by overeducation (or undereducation), present some results on their comparative statics properties, and discuss the nature of welfare improving policies.     

A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms

We consider a many-to-one matching market with externalities among firms where each firm’s preferences satisfy substitutability, increasing choice and no external effect by unchosen workers, which are defined by  Bando (2012). We first illustrate that a sequential version of the deferred acceptance (DA) algorithm with worker-proposing may not find a worker-optimal quasi stable matching. Then, we provide a modified DA algorithm in which (i) each worker simultaneously proposes to his most preferred firm that has not rejected him and (ii) each firm chooses its acceptable workers from the cumulative set of workers who have ever proposed to it, assuming that the other workers proposing to its rival firms are hired. We show that this algorithm finds a worker-optimal quasi stable matching. We also show that this algorithm can be generalized into a fixed point algorithm.     

Zero-intelligence agents looking for a job

We study a simple agent-based model of a decentralized matching market game in which agents (workers or job seekers) make proposals to other agents (firms) in order to be matched to a position within the firm. The aggregate result of agents interactions can be summarised in the form of a Beveridge curve, which determines the relationship between unmatched agents, unemployed job seekers and vacancies in firms. We open the black box of matching technology, by modelling how agents behave (make proposals) according to their information perception. We observe more efficient results—in the form of a downward shift of the Beverage curve in the case of simple zero-intelligent agents. Our comparative statics indicate that market conditions, such as the heterogeneity of agents’ preferences, will also shift the Beveridge curve downwards. Moreover, market thickness affects movement along the Beverage curve. Movement right-down along the curve if there is an increasing number of agents compared to positions within firms. Furthermore, we show that frictions in re-matching, such as commitment to a match, could be another factor shifting the Beveridge curve toward the origin.     

Constrained suboptimality when prices are non-competitive

The paper addresses the following question: how efficient is the market system in allocating resources if trade takes place at prices that are not competitive? Even though there are many partial answers to this question, an answer that stands comparison to the rigor by which the first and second welfare theorems are derived is lacking. We first prove a “Folk Theorem” on the generic suboptimality of equilibria at non-competitive prices. The more interesting problem is whether equilibria are constrained optimal, i.e. efficient relative to all allocations that are consistent with prices at which trade takes place. We discuss an optimality notion due to Bénassy, and argue that this notion admits no general conclusions. We then turn to the notion of p-optimality and give a necessary condition, called the separating property, for constrained optimality: each constrained household should be constrained in each constrained market. If the number of commodities is less than or equal to two, the case usually treated in the textbook, then this necessary condition is also sufficient. In that case equilibria are constrained optimal. When there are three or more commodities, two or more constrained households, and two or more constrained markets, this necessary condition is typically not sufficient and equilibria are generically constrained suboptimal.     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

Survival and the art of profit maximization

We study the relationship between rationality and economic survival in a simple dynamic model, where agents from different populations interact repeatedly through random matching. An explicit criterion (“bankruptcy”) determines whether agents survive each interaction; all agents are presumed to be aware of this criterion. Survival in each interaction depends on two factors: the strategies agents adopt when they interact, and the wealth levels they bring to the game. The model is completely symmetric with the only difference between the agents of different populations being their objectives. We consider the case where there are two populations of agents in which all agents from one group have as their objective, maximizing the expected profits from each interaction, while all agents from the other attempt simply to maximize the probability of surviving (i.e., not going bankrupt in) the interaction. We show that under the equilibrium dynamics, the proportions of each group in the total population must be bounded away from zero, but the balance is in favor of the survival-probability maximizers in that their numbers as a fraction of total population must always exceed 1/2, and can be arbitrarily close to unity. On the other hand, the fraction of total wealth controlled by the expected profit maximizers must also be at least 1/2, and can asymptotically tend to unity.     

Constrained mobility and the evolution of efficient outcomes

We study an evolutionary model akin to the one studied in Anwar (2002) where a set of agents use myopic best response learning to i) determine their action in a 2 × 2 coordination game and ii) to choose on which of multiple islands to interact. We focus on the case where the number of agents maximally allowed on each islands is constrained. We extend Anwar’s original analysis by considering the case when there may be more than two islands. We find that if the constraints are such that one island may be empty, universal coordination on the payoff dominant action is possible in the long run. If the constraints are such that all islands will be full, then for relatively mild constraints, and apart from special cases, the coexistence of conventions will occur, with one island coordinating on the risk dominant action and all remaining islands coordinating on the payoff dominant action. For relatively stringent constraints all agents will play the risk dominant action.     

Evolving Market Efficiency with an Application to Some Bulgarian Shares

With new technically advanced methods and computers at our disposal, the efficient market hypothesis is once again being debated. At the same time, we are witnessing an unprecedented growth in both existing and new financial markets. These new markets are often in economies which have just recently embraced free market economics; we term these stock markets infant markets. Such stock markets are obviously not efficient in allocating the supply of savings to productive capital. We do not test whether or not these infant markets are informationally efficient, but instead examine whether and how they are becoming more efficient. We propose modelling the excess returns of individual securities using a multi-factor model with time-varying coefficients and generalised auto-regressive conditional heteroskedastic (GARCH) errors. If the markets are becoming more informationally efficient or the agents are learning, we would expect this to manifest itself as the time-varying coefficients becoming more stable as time increases. We test our model using data on four Bulgarian shares. First, we estimate an AR(2) model and a GARCH-M(1,1) model for the shares. Then, we estimated our AR(2) model with time varying coefficients and GARCH type errors. We find varying levels of efficiency and varying speeds of movement towards efficiency within our sample of four shares. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strategy-proofness in many-to-one matching problems

We search forstrategy-proof solutions in the context of (many-to-one) matching problems (Gale and Shapley, 1962). In this model, whenever the firms can hire as many workers as they want (the capacities are unlimited) the stable set is a singleton. There exists aPareto efficient, individually rational, andstrategy-proof matching rule if and only if the capacities are unlimited. Furthermore, whenever the capacities unlimited, the matching rule which selects the unique stable matching is the only matching rule that isPareto efficient, individually rational, andstrategy-proof.     

Brokers’ contractual arrangements in the Manhattan residential rental market

We bring new evidence to bear on the role of intermediaries in frictional matching markets and on how parties design contracts with them. Specifically, we examine two features of contracts between landlords and agents in the Manhattan residential rental market. In our data, 72 percent of listings involve exclusive relationships between landlords and agents (the remaining 28 percent are non-exclusive); and in 21 percent of listings, the landlord commits to pay the agent’s fee (in the other 79 percent, the tenant pays the agent’s the fee). Our analysis highlights that these contractual features reflect landlords’ concerns about providing agents with incentives to exert effort specific to their rental units and to screen among heterogeneous tenants.     

Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men

Our paper estimates the effect of US internal migration on wage growth for young men between their first and second job. Our analysis of migration extends previous research by: (i) exploiting the distance-based measures of migration in the National Longitudinal Surveys of Youth 1979 (NLSY79); (ii) allowing the effect of migration to differ by schooling level and (iii) using propensity score matching to estimate the average treatment effect on the treated (ATET) for movers and (iv) using local average treatment effect (LATE) estimators with covariates to estimate the average treatment effect (ATE) and ATET for compliers.We believe the Conditional Independence Assumption (CIA) is reasonable for our matching estimators since the NLSY79 provides a relatively rich array of variables on which to match. Our matching methods are based on local linear, local cubic, and local linear ridge regressions. Local linear and local ridge regression matching produce relatively similar point estimates and standard errors, while local cubic regression matching badly over-fits the data and provides very noisy estimates.We use the bootstrap to calculate standard errors. Since the validity of the bootstrap has not been investigated for the matching estimators we use, and has been shown to be invalid for nearest neighbor matching estimators, we conduct a Monte Carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching. The data generating processes in our Monte Carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values. The estimated standard errors from the bootstrap are very close to those from the Monte Carlo experiments, which lends support to our using the bootstrap to calculate standard errors in our setting.From the matching estimators we find a significant positive effect of migration on the wage growth of college graduates, and a marginally significant negative effect for high school dropouts. We do not find any significant effects for other educational groups or for the overall sample. Our results are generally robust to changes in the model specification and changes in our distance-based measure of migration. We find that better data matters; if we use a measure of migration based on moving across county lines, we overstate the number of moves, while if we use a measure based on moving across state lines, we understate the number of moves. Further, using either the county or state measures leads to much less precise estimates.We also consider semi-parametric LATE estimators with covariates (Frölich 2007), using two sets of instrumental variables. We precisely estimate the proportion of compliers in our data, but because we have a small number of compliers, we cannot obtain precise LATE estimates.     

Dynamic coordination among heterogeneous agents

We study a dynamic model of coordination with timing frictions and payoff heterogeneity. There is a unique equilibrium, characterized by thresholds that determine the choices of each type of agent. We characterize equilibrium for the limiting cases of vanishing timing frictions and vanishing shocks to fundamentals. A lot of conformity emerges: despite payoff heterogeneity, agents’ equilibrium thresholds partially coincide as long as a set of beliefs that would make this coincidence possible exists. However, the equilibrium thresholds never fully coincide. In case of vanishing frictions, the economy behaves almost as if all agents were equal to an average type. Conformity is not inefficient. In the efficient solution, agents follow others even more often.     

A bargaining set for roommate problems

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.     

When do stable roommate matchings exist? A review

We compare different preference restrictions that ensure the existence of a stable roommate matching. Some of these restrictions are generalized to allow for indifferences as well as incomplete preference lists, in the sense that an agent may prefer remaining single to matching with some agents. We also introduce a new type of cycles and in greater detail investigate the domain of preferences that have no such cycles. In particular, we show how the absence of these cycles relates to the “symmetric utilities hypothesis” by Rodrigues-Neto (J Econ Theory 135:545–550, 2007) when applied to roommate problems with weak preferences.     

A decentralized and informationally efficient mechanism realizing fair outcomes in economies with public goods

We present a decentralized mechanism (called Lindahl Egalitarian), which yields Pareto efficient and envy free allocations (i.e. fair outcomes). We show that the mechanism is informationally efficient in general production economies with an arbitrary, but finite, number of private and public goods, and a finite number of agents. The mechanism reduces to the Walrasian mechanism starting from equal wealth when no agent cares about public goods. We also prove that the set of Public Competitive equilibrium allocations (from equal endowments and proportional taxation), and the set of the Lindahl Egalitarian equilibrium allocations are the same. We are grateful to Xavier Calsamiglia and Albert Marcet for helpful conversations, and to A. de la Fuente, I. Macho, and an anonimous referee for useful suggestions. A. Manresa’s research has been supported by the grant CICYT PB90-0172. J. Aizpurua acknowledges financial support from the Government of Navarra.     

Social networks,mass media and public opinions

Our opinions and ideas are shaped by what our friends said and what we read or watched on mass media. In this paper, we propose a concise and analyzable model to study the effects of mass media modeled as an applied external field, and social networks on public opinions based on the multi-state voter model, and a tuned parameter can control the relative intensity of the effects of mass media and social networks. We consider a generalized scenario where there exist committed or stubborn agents in the networks whose opinions are not affected by their friends or mass media. We find that the fraction of each opinion will converge to a value which only relates to the fractions and degrees of stubborn agents, and the relative intensity between media and network effects. The final agents with media opinion, except the stubborn agents, also include the increment produced by the internal impact of social networks and that caused by the external impact of media. Interestingly the second increment is composed of two parts, one is from the media effect when there are no interactions between agents and the other is from the influence of media on agent opinions caused by social network structure. That is the interactions among agents within social networks can amplify media influence. Finally we also discuss several extensions to the dynamics model which consider more realistic scenarios.     

Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.     

Firms’ linkages with public research organisations in Argentina: Drivers, perceptions and behaviours

This paper analyses firms’ drivers for linking to public research organisations (PRO) (first goal) and compares perceptions and behaviours of linked vs. unlinked firms (second goal). We used an original firm database constructed from a representative survey with information for linked and unlinked firms for year 2005 in Argentina. Drivers were estimated using a Probit model, while differences in perceptions and behaviours between linked and unlinked firms were assessed with propensity score matching techniques. For our first goal we found that (i) firms’ knowledge bases were not drivers for linking to PRO and (ii) networking capabilities matter but there is a substitution effect between interacting with PRO and interacting with other economic agents in the market when firms aim at exchanging information rather than doing joint research. These findings may imply that current linkages are not exploiting properly their knowledge potential; it may be worth designing a division of labour among PRO in their functions in PRO-industry interactions. For our second goal: we found that (i) linked firms invest more in innovative activities; (ii) they are more prone to patenting; (iii) both groups of firms value similarly PRO research outputs available at arm length (i.e. without direct linking). Given the asymmetric development on appropriability tools between PRO and firms and the fact that all firms benefit from PRO research outputs, the higher predisposition of linked firms towards patenting, suggests that special attention should be placed at analysing the risks of a private appropriation of publicly created knowledge.