Dynamic Reserves in Matching Markets

We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM

Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2

Efficiency in Matching Markets with Regional Caps: The Case of the Japan Residency Matching Program

In an attempt to increase the placement of medical residents to rural hospitals, the Japanese government recently introduced "regional caps" which restrict the total number of residents matched within each region of the country. The government modified the deferred acceptance mechanism incorporating the regional caps. This paper shows that the current mechanism may result in avoidable ineffciency and instability and proposes a better mechanism that improves upon it in terms of effciency and stability while meeting the regional caps. More broadly, the paper contributes to the general research agenda of matching and market design to address practical problems.medical residency matching, regional caps, the rural hospital theorem, sta- bility, strategy-proofness, matching with contracts

Multi-Stage Generalized Deferred Acceptance Mechanism: Strategyproof Mechanism for Handling General Hereditary Constraints

The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered various forms of distributional constraints. Arguably, the most general class of distributional constraints would be hereditary constraints; if a matching is feasible, then any matching that assigns weakly fewer students at each college is also feasible. However, under general hereditary constraints, it is shown that no strategyproof mechanism exists that simultaneously satisfies fairness and weak nonwastefulness, which is an efficiency (students' welfare) requirement weaker than nonwastefulness. We propose a new strategyproof mechanism that works for hereditary constraints called the Multi-Stage Generalized Deferred Acceptance mechanism (MS-GDA). It uses the Generalized Deferred Acceptance mechanism (GDA) as a subroutine, which works when distributional constraints belong to a well-behaved class called hereditary M$^\natural$-convex set. We show that GDA satisfies several desirable properties, most of which are also preserved in MS-GDA. We experimentally show that MS-GDA strikes a good balance between fairness and efficiency (students' welfare) compared to existing strategyproof mechanisms when distributional constraints are close to an M$^\natural$-convex set.Comment: 23 page

Growth, Income Distribution, and Poverty: A Review

This paper reviews the recent literature dealing with the relationships between economic growth, income distribution, and poverty. This generally fails to find any systematic pattern of change in income distribution during recent decades. Neither does it find any systematic link from fast growth to increasing inequality. Some recent empirical evidence has tended to confirm the negative impact of inequality on growth, on the other hand. Others have found that the level of initial income inequality is not a robust explanatory factor of growth, though high inequality in the distribution of assets, such as land, has a significantly negative effect on growth. Possible channels are credit rationing, reduced possibilities for participation in the political process, and social conflicts. Among the strategic elements that contributed to reduced poverty are: an outward-oriented strategy of export-led growth, based on labour-intensive manufacturing; agricultural and rural development, with encouragement of new technologies; investment in physical infrastructure and human capital; efficient institutions that provide the right set of incentives to farmers and entrepreneurs; and social policies to promote health, education, and social capital, as well as safety nets to protect the poor. Countries that have been successful in terms of economic growth are also very likely to be successful in reducing poverty. Poverty can be reduced if there is sufficient economic growth. Growth can be substantial if the policy and institutional environment is right.Growth; income distribution; poverty; economic policy