Hard and Soft Preparation Sets in Boolean Games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can set to true or false, and are primarily motivated to seek the satisfaction of some goal formula, while secondarily motivated to minimise the costs of their actions. We adopt (pure) preparation sets (prep sets) as our basic solution concept. A preparation set is a set of outcomes that contains for every player at least one best response to every outcome in the set. Prep sets are well-suited to the analysis of Boolean games, because we can naturally represent prep sets as propositional formulas, which in turn allows us to refer to prep formulas. The preference structure of Boolean games with costs makes it possible to distinguish between hard and soft prep sets. The hard prep sets of a game are sets of valuations that would be prep sets in that game no matter what the cost function of the game was. The properties defined by hard prep sets typically relate to goal-seeking behaviour, and as such these properties cannot be eliminated from games by, for example, taxation or subsidies. In contrast, soft prep sets can be eliminated by an appropriate system of incentives. Besides considering what can happen in a game by unrestricted manipulation of players’ cost function, we also investigate several mechanisms that allow groups of players to form coalitions and eliminate undesirable outcomes from the game, even when taxes or subsidies are not a possibility

A focus on focal surfaces

We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal surface (degree, class, class of its hyperplane section, sectional genus and degrees of the nodal and cuspidal curve). We study in particular the congruences of chords to a smooth curve and the congruences of bitangents or flexes to a smooth surface. We find that they possess unexpected components in their focal surface, and conjecture that they are the only ones with this property.Comment: Plain TeX, 33 pages with no figure

For Whom is MAI? A theoretical Perspective on Multilateral Agreements on Investments

Why do we observe some LDCs objecting the prospect of a Multilateral Agreement on Investment (MAI), although they have been keen to liberalize investment in preferential agreements in recent years? In this paper, we analyse the issue of MAI implementation and assess the welfare consequences of such kind of agreements. In our model, participation to MAI involves a trade-off between less rent extraction from multinational firms (MNEs) and more abundant FDI in‡ows. At equilibrium, either all countries enter MAI, or all countries stay out, or only some of them enter. Coordination problems may induce multiple equilibria: the three types of equilibria may coexist. So, the implementation of MAI may depend not only on structural factors but also on the general ”political climate”. When all countries join MAI, world welfare is maximized because this minimizes the hold-up problem faced by MNEs and stimulates investment. However, in an asymmetric world, welfare gains are not guaranteed for all countries.Foreign Direct Investment, International Agreements, Incomplete

The late accretion and erosion of Vesta's crust recorded by eucrites and diogenites as an astrochemical window into the formation of Jupiter and the early evolution of the Solar System

For decades the limited thickness of Vesta's basaltic crust, revealed by the link between the asteroid and the howardite-eucrite-diogenite family of meteorites, and its survival to collisional erosion offered an important constraint for the study of the early evolution of the Solar System. Some results of the Dawn mission, however, cast doubts on our understanding of Vesta's interior composition and of the characteristics of its basaltic crust, weakening this classical constraint. In this work we investigate the late accretion and erosion experienced by Vesta's crust after its differentiation and recorded in the composition of eucrites and diogenites and show that it offers an astrochemical window into the earliest evolution of the Solar System. In our proof-of-concept case study focusing on the late accretion and erosion of Vesta's crust during the growth and migration of Jupiter, the water enrichment of eucrites appears to be a sensitive function of Jupiter's migration while the enrichment in highly-siderophile elements of diogenites appears to be particularly sensitive to the size-frequency distribution of the planetesimals. The picture depicted by the enrichments created by late accretion in eucrites and diogenites is not qualitatively affected by the uncertainty on the primordial mass of Vesta. Crustal erosion, instead, is more significantly affected by said uncertainty and Vesta's crust survival appears to be mainly useful to study violent collisional scenarios where highly energetic impacts can strip significant amounts of vestan material while limitedly contributing to Vesta's late accretion. Our results suggest that the astrochemical record of the late accretion and erosion of Vesta's crust provided by eucrites and diogenites can be used as a tool to investigate any process or scenario associated to the evolution of primordial Vesta and of the early Solar System.Comment: 21 pages, 15 figures, accepted for publication on Icaru