Marriage Matching with Correlated Preferences

Authors of experimental, empirical, theoretical and computational studies of two-sided matching markets have recognized the importance of correlated preferences. We develop a general method for the study of the effect of correlation of preferences on the outcomes generated by two-sided matching mechanisms. We then illustrate our method by using it to quantify the effect of correlation of preferences on satisfaction with the men-propose Gale-Shapley matching for a simple one-to-one matching problem.

Marriage Matching and Intercorrelation of Preferences

Men's and women's preferences are intercorrelated to the extent that men rank highly those women who rank them highly. Intercorrelation plays an important but overlooked role in determining outcomes of matching mechanisms. We study via simulation the effect of intercorrelated preferences on men's and women's aggregate satisfaction with the outcome of the Gale-Shapley matching mechanism. We conclude with an application of our results to the student admission matching problem.

Preference Structure and Random Paths to Stability in Matching Markets

This paper examines how preference correlation and intercorrelation combine to influence the length of a decentralized matching market's path to stability. In simulated experiments, marriage markets with various preference specifications begin at an arbitrary matching of couples and proceed toward stability via the random mechanism proposed by Roth and Vande Vate (1990). The results of these experiments reveal that fundamental preference characteristics are critical in predicting how long the market will take to reach a stable matching. In particular, intercorrelation and correlation are shown to have an exponential impact on the number of blocking pairs that must be randomly satisfied before stability is attained. The magnitude of the impact is dramatically different, however, depending on whether preferences are positively or negatively intercorrelated.

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.

A bidimensional model of matching in the marriage market with women labor decision

We construct a frictionless matching model of the marriage market where women have bidimensional attributes, one continuous (income) and the other dichotomous (home ability). Equilibrium in the marriage market determines intrahousehold allocation of resources and female labor participation. Our model is able to predict partial non-assortative matching, with rich men marrying women with low income but high home ability. We then perform numerical exercises to evaluate the impacts of income taxes in individual welfare and find that there is considerable divergence in the female labor participation response to taxes between the short run and the long run.

The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences

In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be considered when these blockings come from the grand coalition. This solution concept requires stability plus Pareto optimality. A characterization of the set of Pareto-stable matchings for the roommate and the marriage models is provided in terms of individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. These matchings always exist and give an economic intuition on how blocking can be done by non-trading agents, so that the transactions need not be undone as agents reach the set of stable matchings. Some properties of the Pareto-stable matchings shared by the Marriage and Roommate models are obtained.

The stability of the equilibrium outcomes in the admission games induced by stable matching rules

A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students` strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised.

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.''

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.

Consistency and population sensitivity properties in marriage and Rrommate markets

We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. Klaus (Games Econ Behav 72:172-186, 2011) introduced two new "population sensitivity" properties that capture the effect newcomers have on incumbent agents: competition sensitivity and resource sensitivity. On various roommate market domains (marriage markets, no-odd-rings roommate markets, solvable roommate markets),we characterize the core using either of the population sensitivity properties in addition to weak unanimity and consistency. On the domain of all roommate markets, we obtain two associated impossibility results.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Human Capital and Interethnic Marriage Decisions

Despite a longstanding belief that education importantly affects the process of immigrant assimilation, little is known about the relative importance of different mechanisms linking these two processes. This paper explores this issue through an examination of the effects of human capital on one dimension of assimilation, immigrant intermarriage. I argue that there are three primary mechanisms through which human capital affects the probability of intermarriage. First, human capital may make immigrants better able to adapt to the native culture thereby making it easier to share a household with a native. Second, it may raise the likelihood that immigrants leave ethnic enclaves, thereby decreasing the opportunity to meet potential spouses of the same ethnicity. Finally, assortative matching on education in the marriage market suggests that immigrants may be willing to trade similarities in ethnicity for similarities in education when evaluating potential spouses. Using a simple spouse-search model, I first derive an identification strategy for differentiating the cultural adaptability effect from the assortative matching effect, and then I obtain empirical estimates of their relative importance while controlling for the enclave effect. Using U.S. Census data, I find that assortative matching on education is the most important avenue through which human capital affects the probability of intermarriage. Further support for the model is provided by deriving and testing some of its additional implications.

Essays on economics of marriage

A sociedade mudou nas últimas décadas abrindo a possibilidade para cientistas sociais estudarem essas mudanças e analisar os seus impactos na unidade familiar. Nesta tese pretendemos analisar como as decisões dos agentes com relação a decisão de casar e estudar pode estar conectado considerando que homens e mulheres têm preferências pelo casamento intragrupo. No modelo estudado encontramos que as preferências para o casamento intragrupo podem aumentar a proporção de homens e mulheres que decidem se casar e estudar. Mostramos também que empiricamente há um positive assortative mating entre pessoas com as mesmas características, tais como, educação, religião ou raça. Além disso, a probabilidade de casais casados na mesma religião aumenta a probabilidade dos casais estarem casados dentro do mesmo nível de escolaridade. Considerando as mudanças em como os casais se formam, a composição educacional e os retornos da educação que aconteceram no Brasil nos últimos anos, investiga-se os impactos dessas mudanças na desigualdade de renda dos casais. Calculamos cenários contrafactuais para o Coeficiente de Gini mantendo uma dessas três variáveis fixas em um determinado ano, comparando o contrafactual estimado com o Gini real. Se o casamento for formado aleatoriamente com relação à educação, o Coeficiente de Gini seria menor do que o real. Mantendo os retornos da educação fixos no ano de 2014 encontramos um Gini contrafactual menor do que o real.

Análises do matching de identidade generalizado por contingências de três e quatro termos: implicações para equivalência de estímulos

A expansão da tríplice continência em unidades com quatro ou mais elementos abriu novas perspectivas para a compreensão de comportamentos complexos, como a emergência de respostas que derivam da formação de classes de estímulos equivalentes e que modelam comportamentos simbólicos e conceituais. Na investigação experimental, o procedimento de matching to sample tem sido frequentemente empregado para estabelecer discriminações condicionais. Em particular, a obtenção do matching de identidade generalizado é considerada demonstrativa da aquisição dos conceitos de igualdade e diferença. Segundo argumentamos, o fato de se buscar a compreensão desses conceitos a partir de processos discriminativos condicionais pode ter sido responsável pelos frequentes fracassos em demonstrá-los em sujeitos não humanos. A falta de correspondência entre os processos discriminativos responsáveis por estabelecer a relação de reflexividade entre estímulos que formam classes equivalentes e o matching de identidade generalizado, nesse sentido, é aqui revista ao longo de estudos empíricos e discutida com respeito às suas implicações.