Abstract:
Without observational or theoretical modifications, Newtonian and general relativity seem to be unable to explain gravitational behavior of large structure of the universe. The assumption of dark matter solves this problem without modifying theories. But it implies that most of the matter in the universe must be unobserved matter. Another solution is to modify gravitation laws. In this article, we study a third way that doesn't modify gravitation neither matter's distribution, by using a new physical assumption on the clusters. Compare with Newtonian gravitation, general relativity (in its linearized approximation) leads to add a new component without changing the gravity field. As already known, this component for galaxies is too small to explain dark matter. But we will see that the galaxies' clusters can generate a significant component and embed large structure of universe. We show that the magnitude of this embedding component is small enough to be in agreement with current experimental results, undetectable at our scale, but detectable at the scale of the galaxies and explain dark matter, in particular the rotation speed of galaxies, the rotation speed of dwarf satellite galaxies, the expected quantity of dark matter inside galaxies and the expected experimental values of parameters $\Omega$\_dm of dark matter measured in CMB. This solution implies testable consequences that differentiate it from other theories: decreasing dark matter with the distance to the cluster's center, large quantity of dark matter for galaxies close to the cluster's center, isolation of galaxies without dark matter, movement of dwarf satellite galaxies in planes close to the supergalactic plane, close orientations of spin's vectors of two close clusters, orientation of nearly all the spin's vector of galaxies of a same cluster in a same half-space, existence of very rare galaxies with two portions of their disk that rotate in opposite directions...

A recent publication revealed unexpected
observations about dark matter. In particular, the observed baryonic mass should
probably be sufficient to explain the observed rotation curves (i.e. without dark matter) and their
observations gave an empirical relation for weak accelerations. This present
work demonstrated that the equations of general relativity allow explaining the
term of dark matter (without new matter) in agreement with the results of this
publication and allow retrieving this empirical relation (observed values and
characteristics of this correlation’s curve). These observations constrain
drastically the possible gravitational potential in the frame of general
relativity to explain the term of dark matter. This theoretical solution has
already been studied with several unexpected predictions that have recently
been observed. For example, an article revealed that early galaxies (ten
billion years ago) didn’t have dark matter and a more recent paper showed
unlikely alignments of galaxies. To finish the main prediction of this solution, it is recalled:
the term of dark matter should be a Lense-Thirring effect, around the earth, of
around 0.3 and 0.6 milliarcsecond/year.

Abstract:
Mai 1968 semble être sur toutes les lèvres et dans tous les esprits ces derniers jours. On ne compte plus les sorties d’ouvrages sur la question, plus ou moins opportunistes. La tonalité des débats oscille généralement entre deux extrêmes : d’un c té, la nostalgie d’une époque où l’espoir portait la puissance de devenirs meilleurs, car moins compassés et rigides ; de l’autre, la reconnaissance d’un ensemble de phénomènes à l’existence historique indéniable, mais désormais révolue voire à liqu...

Abstract:
Lors d’un colloque récent consacré aux métiers du nettoiement et à la gestion des déchets dans l’espace public, la majorité des intervenants, sinon tous, partageaient l’idée selon laquelle travailler sur de telles questions permettait d’étudier des problèmes fondamentaux et passionnants, au prix d’un certain risque de mise à l’écart académique. D’un point de vue symbolique (et spatial, si l’on considère les dynamiques du champ académique que cela implique), le chercheur paierait de fait son t...

Abstract:
De nombreux auteurs ont décrit et analysé le jeu sous l’angle des pratiques ouvrières résistancielles ou subversives renseignant sur l’autonomie du collectif face à l’organisation du travail. En partant de telles réflexions ancrées sur deux terrains empiriques contrastés (un atelier d’éboueurs, un centre d’appels téléphoniques), on s’interrogera sur les implications, au niveau des salarié·e·s, d’une utilisation, par les managers, de dispositifs ludiques visant à accentuer l’implication au travail. Many authors have described and analyzed games as resistant or subversive work practices providing information about the kind of autonomy that a group will manifest in its dealings with a work organisation. Starting with this kind of thinking – embedded in two contrasting empirical foundations (a streetsweeping depot, a call centre), the focus here is on the implications for employees – and on how managers use – “playful” mechanisms aimed at getting people more involved in their work. Muchos autores han descrito y analizado el juego desde la óptica de las prácticas obreras de resistencia o subversivas que arrojan información sobre la autonomía de lo colectivo frente a la organización del trabajo. Partiendo de esas reflexiones ancladas en dos terrenos empíricos contrastados (un taller de barrenderos, un centro de atención telefónica), nos interrogaremos sobre las implicaciones para los asalariados de una utilización por los directivos de dispositivos “lúdicos” que buscan acentuar la implicación en el trabajo.

Abstract:
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the existence of a winning strategy in games that involve two players and two outcomes saying who wins. In a multi-outcome setting, the notion of winning strategy is irrelevant yet usually replaced faithfully with the notion of (pure) Nash equilibrium. This article shows that every determinacy result over an arbitrary game structure, e.g. a tree, is transferable into existence of multi-outcome (pure) Nash equilibrium over the same game structure. The equilibrium-transfer theorem requires cardinal or order-theoretic conditions on the strategy sets and the preferences, respectively, whereas counter-examples show that every requirement is relevant, albeit possibly improvable. When the outcomes are finitely many, the proof provides an algorithm computing a Nash equilibrium without significant complexity loss compared to the two-outcome case. As examples of application, this article generalises Borel determinacy, positional determinacy of parity games, and finite-memory determinacy of Muller games.

Abstract:
The quest for optimal/stable paths in graphs has gained attention in a few practical or theoretical areas. To take part in this quest this chapter adopts an equilibrium-oriented approach that is abstract and general: it works with (quasi-arbitrary) arc-labelled digraphs, and it assumes very little about the structure of the sought paths and the definition of equilibrium, \textit{i.e.} optimality/stability. In this setting, this chapter presents a sufficient condition for equilibrium existence for every graph; it also presents a necessary condition for equilibrium existence for every graph. The necessary condition does not imply the sufficient condition a priori. However, the chapter pinpoints their logical difference and thus identifies what work remains to be done. Moreover, the necessary and the sufficient conditions coincide when the definition of optimality relates to a total order, which provides a full-equivalence property. These results are applied to network routing.

Abstract:
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium. Nash's approach to the problem for strategic games is probabilistic, \textit{i.e.} continuous, and static. CP and BR approaches for CP and BR games are discrete and dynamic. This paper proposes an approach that lies between those two different approaches: a discrete and static approach. multi strategic games are introduced as a formalism that is able to express both sequential and simultaneous decision-making, which promises a good modelling power. multi strategic games are a generalisation of strategic games and sequential graph games that still enjoys a Cartesian product structure, \textit{i.e.} where agent actually choose their strategies. A pre-fixed point result allows guaranteeing existence of discrete and non deterministic equilibria. On the one hand, these equilibria can be computed with polynomial (low) complexity. On the other hand, they are effective in terms of recommendation, as shown by a numerical example.

Abstract:
In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of Nash equilibria. In 1965, Selten named this proper subclass subgame perfect equilibria. In game theory, payoffs are rewards usually granted at the end of a game. Although traditional game theory mainly focuses on real-valued payoffs that are implicitly ordered by the usual total order over the reals, works of Simon or Blackwell already involved partially ordered payoffs. This paper generalises the notion of sequential game by replacing real-valued payoff functions with abstract atomic objects, called outcomes, and by replacing the usual total order over the reals with arbitrary binary relations over outcomes, called preferences. This introduces a general abstract formalism where Nash equilibrium, subgame perfect equilibrium, and ``backward induction'' can still be defined. This paper proves that the following three propositions are equivalent: 1) Preferences over the outcomes are acyclic. 2) Every sequential game has a Nash equilibrium. 3) Every sequential game has a subgame perfect equilibrium. The result is fully computer-certified using Coq. Beside the additional guarantee of correctness, the activity of formalisation using Coq also helps clearly identify the useful definitions and the main articulations of the proof.

Abstract:
In perfect-information games in extensive form, common knowledge of rationality triggers backward induction, which yields a Nash equilibrium. That result assumes much about the players' knowledge, while it holds only for a subclass of the games in extensive form. Alternatively, this article defines a non-deterministic evolutionary process, by myopic and lazy improvements, that settles exactly at Nash equilibrium (in extensive form). Importantly, the strategical changes that the process allows depend only on the structure of the game tree, they are independent from the actual preferences. Nonetheless, the process terminates if the players have acyclic preferences; and even if some preferences are cyclic, the players with acyclic preferences stop improving eventually. This result is then generalised in games played on DAGs or infinite trees, and it is also refined by assigning probabilities to the process and perturbing it.