Testing Core Membership in Public Goods Economies

This paper develops a recent line of economic theory seeking to understand public goods economies using methods of topological analysis. Our first main result is a very clean characterization of the economy's core (the standard solution concept in public goods). Specifically, we prove that a point is in the core iff it is Pareto efficient, individually rational, and the set of points it dominates is path connected. While this structural theorem has a few interesting implications in economic theory, the main focus of the second part of this paper is on a particular algorithmic application that demonstrates its utility. Since the 1960s, economists have looked for an efficient computational process that decides whether or not a given point is in the core. All known algorithms so far run in exponential time (except in some artificially restricted settings). By heavily exploiting our new structure, we propose a new algorithm for testing core membership whose computational bottleneck is the solution of $O(n)$ convex optimization problems on the utility function governing the economy. It is fairly natural to assume that convex optimization should be feasible, as it is needed even for very basic economic computational tasks such as testing Pareto efficiency. Nevertheless, even without this assumption, our work implies for the first time that core membership can be efficiently tested on (e.g.) utility functions that admit "nice" analytic expressions, or that appropriately defined $\varepsilon$-approximate versions of the problem are tractable (by using modern black-box $\varepsilon$-approximate convex optimization algorithms).Comment: To appear in ICALP 201

Doryphoribius chetumalensis sp. nov. (Eutardigrada: Isohypsibiidae) a new tardigrade species discovered in an unusual habitat of urban areas of Mexico

A new species, Doryphoribius chetumalensis, is described from specimens collected in the city of Chetumal (Quintana Roo state, Mexico). The species was found in a new and unusual habitat for urban tardigrades, i.e. the soil sediment accumulated on the border of streets. This discovery shows that tardigrades can live in this habitat, demonstrating once again the wide capacity of this taxon to tolerate adverse habitats, and to survive in environments with high anthropogenic impact. Doryphoribius chetumalensis sp. nov. differs from all the other species of the genus in having enlarged and wide bulbous base of the claws. Within Doryphoribius, it belongs to the zappalai group, and differs from the species in this group, not only in the claw shape, but also by the orange body colour, the smooth cuticle, the absence of a tooth in the wall of the buccal ring, and the absence of lunules under the claws. This is the first record of tardigrades, identified to species level, in Quintana Roo state. A taxonomic key of the Doryphoribius genus is also presented