Approximating the {Nash} Social Welfare with Budget-Additive Valuations

We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest

Approximating equilibrium under constrained piecewise linear concave utilities with applications to matching markets

We study the equilibrium computation problem in the Fisher market model with constrained piecewise linear concave (PLC) utilities. This general class captures many well-studied special cases, including markets with PLC utilities, markets with satiation, and matching markets. For the special case of PLC utilities, although the problem is PPAD-hard, Devanur and Kannan (FOCS 2008) gave a polynomial-time algorithm when the number of items is constant. Our main result is a fixed parameter approximation scheme for computing an approximate equilibrium, where the parameters are the number of agents and the approximation accuracy. This provides an answer to an open question by Devanur and Kannan for PLC utilities, and gives a simpler and faster algorithm for matching markets as the one by Alaei, Jalaly and Tardos (EC 2017). The main technical idea is to work with the stronger concept of thrifty equilibria, and approximating the input utility functions by ‘robust’ utilities that have favorable marginal properties. With some restrictions, the results also extend to the Arrow–Debreu exchange market model

Finding Fair and Efficient Allocations

We study the problem of allocating a set of indivisible goods among a set of agents in a fair and efficient manner. An allocation is said to be fair if it is envy-free up to one good (EF1), which means that each agent prefers its own bundle over the bundle of any other agent up to the removal of one good. In addition, an allocation is deemed efficient if it satisfies Pareto optimality (PO). While each of these well-studied properties is easy to achieve separately, achieving them together is far from obvious. Recently, Caragiannis et al. (2016) established the surprising result that when agents have additive valuations for the goods, there always exists an allocation that simultaneously satisfies these two seemingly incompatible properties. Specifically, they showed that an allocation that maximizes the Nash social welfare (NSW) objective is both EF1 and PO. However, the problem of maximizing NSW is NP-hard. As a result, this approach does not provide an efficient algorithm for finding a fair and efficient allocation. In this paper, we bypass this barrier, and develop a pseudopolynomial time algorithm for finding allocations that are EF1 and PO; in particular, when the valuations are bounded, our algorithm finds such an allocation in polynomial time. Furthermore, we establish a stronger existence result compared to Caragiannis et al. (2016): For additive valuations, there always exists an allocation that is EF1 and fractionally PO. Another contribution of our work is to show that our algorithm provides a polynomial-time 1.45-approximation to the NSW objective. This improves upon the best known approximation ratio for this problem (namely, the 2-approximation algorithm of Cole et al. (2017)). Unlike many of the existing approaches, our algorithm is completely combinatorial.Comment: 40 pages. Updated versio

Auction algorithms for market equilibrium with weak gross substitute demands and their applications

We consider the Arrow-Debreu exchange market model where agents' demands satisfy the weak gross substitutes (WGS) property. This is a well-studied property, in particular, it gives a sufficient condition for the convergence of the classical tâtonnement dynamics. In this paper, we present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands. Such auction algorithms have been previously known for restricted classes of WGS demands only. As an application of our technique, we obtain an efficient algorithm to find an approximate spendingrestricted market equilibrium for WGS demands, a model that has been recently introduced as a continuous relaxation of the Nash social welfare (NSW) problem. This leads to a polynomial-time constant factor approximation algorithm for NSW with budget separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known for this setting previously

Electricity Sector Reform in Developing Countries: A Survey of Empirical Evidence on Determinants and Performance

This paper reviews the empirical evidence on electricity reform in developing countries. We find that country institutions and sector governance play an important role in success and failure of reform; reforms appear to have increased operating efficiency and expanded access to urban customers; they have to a lesser degree passed on efficiency gains to customers, tackled distributional effects, or improved rural access. Moreover, some of the literature is not methodologically robust or on a par with general development economics literature and findings on some issues are limited and inconclusive while some important areas are yet to be addressed. Until we know more, implementation of reforms will be more based on ideology and economic theory rather than solid economic evidence.The World Bank Electricity Research Programme and the CMI Electricity Project (IR-45

Health Employment, Medical Spending, and Long Term Health Reform

This paper explores the relationships between the growth in the medical workforce in an aging society and employment in other sectors of the economy, based on data from the United States since 1985. Employment in medical services grew, but did not displace employment in other sectors uniformly. Instead, regression analysis shows that medical workforce growth produced contemporaneous reductions in relative employment in the manufacturing, construction, and information sectors, while being associated with growth in other services and public administration. Import penetration and productivity growth mattered, but much of the displacement remains even after controlling for these factors.

When the State Mirrors the Family: The Design of Pension Systems

This paper studies the transmission mechanism from family culture to economic institutions, by analyzing the impact of the within family organization on the original design of the public pension systems. We build a simple OLG model with families featuring either weak or strong internal ties. When pensions systems are initially introduced, in society with strong ties they replicate the tight link between generations by providing earnings related benefits; whereas in societies with weak family ties they only act as a safety net. To test this transition mechanism, we consider Todd (1982) historical classification of family types across countries. We find that in societies dominated by absolute nuclear families (i.e., weak family ties), pension systems act as a flat safety net entailing a large within-cohort redistribution, and viceversa in societies characterized by stronger family ties where pension systems are more generous. This link between the type of families and the design of pension systems is robust to testing for alternative explanations, such as legal origin, religion, urbanization and democratization of the country at the time of their introduction. Interestingly, historical family types matter for explaining the design of the pension systems, which represents a persistent feature, but not their size, which have largely changed over time.culture, institutions, historical evidence