Matchings with externalities and attitudes

Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real-life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas fully expressive representations of externalities in matchings require exponential space, in this paper we propose a compact model of externalities, in which the influence of a match on each agent is computed additively. Under this framework, we analyze many-to-many matchings and one-to-one matchings where agents take different attitudes when reasoning about the actions of others. In particular, we study optimistic, neutral and pessimistic attitudes and provide both computational hardness results and polynomial-time algorithms for computing stable outcomes

Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

Transfer Rate Rules and Core Selections in NTU Games.

Dans cette note, on propose quelques applications directes d’un résultat d’existence de Bonnisseau et Iehlé (2003). Ces auteurs ont montré l’existence d’allocations du cœur dans les jeux NTU qui satisfont un équilibre de taux de transfert sous une condition de balancement dépendant. Il s’avère que la notion de balancement dépendant procure en fait un outil manipulable pour sélectionner le cœur. Pour illustrer ce fait, nous montrons que cette notion permet d’obtenir des résultats d’existence dans des modèles de cœur avec partenariat, cœur socialement stable, prekernel moyen intersecté avec le cœur et de cœur interne faible.Different kinds of asymmetries between players can occur in core allocations, in that case the stability of the concept is questioned. One remedy consists in selecting robust core allocations. We review, in this note, results that all select core allocations in NTU games with different concepts of robustness. Within a unified approach, we deduce the existence of allocations in: the partnered core, the social stable core, the core intersected with average prekernel, the weak inner core. We use a recent contribution of Bonnisseau and Iehle (2003) that states the existence of core allocations with a transfer rate rule equilibrium under a dependent balancedness assumption. It shall turn out to be manipulable tools for selecting the core.Sélections du coeur dans les jeux NTU; Balancement dépendant; Jeux coopératifs; Core Selections in NTU Games; Dependent balancedness; Cooperative game;

Moduli spaces of coherent systems of small slope on algebraic curves

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction