Introducing Hierarchy in Energy Games

In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energy-efficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energy-efficiency. Specifically, we introduce hierarchy in two different ways: 1. Assuming single-user decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader whereas the other users are assumed to be able to react to the leader's decisions; 2. Assuming neither leader nor followers among the users, we introduce hierarchy by assuming successive interference cancellation at the receiver. It is shown that introducing a certain degree of hierarchy in non-cooperative power control games not only improves the individual energy efficiency of all the users but can also be a way of insuring the existence of a non-saturated equilibrium and reaching a desired trade-off between the global network performance at the equilibrium and the requested amount of signaling. In this respect, the way of measuring the global performance of an energy-efficient network is shown to be a critical issue.Comment: Accepted for publication in IEEE Trans. on Wireless Communication

Constrained Cost-Coupled Stochastic Games with Independent State Processes

We consider a non-cooperative constrained stochastic games with N players with the following special structure. With each player there is an associated controlled Markov chain. The transition probabilities of the i-th Markov chain depend only on the state and actions of controller i. The information structure that we consider is such that each player knows the state of its own MDP and its own actions. It does not know the states of, and the actions taken by other players. Finally, each player wishes to minimize a time-average cost function, and has constraints over other time-avrage cost functions. Both the cost that is minimized as well as those defining the constraints depend on the state and actions of all players. We study in this paper the existence of a Nash equilirium. Examples in power control in wireless communications are given.Comment: 7 pages, submitted in september 2006 to Operations Research Letter

Situation du criquet marocain "Dociostaurus maroccanusThunb., 1815" par rapport aux différentes espèces acridiennes : morphométrie et capacités de déplacements

La faculté de déplacements par vol des criquets adultes permet aux populations acridiennes de se déplacer sur de grandes distances et de rechercher des habitats dont les caractéristiques répondent le mieux à leurs besoins. Dans le présent travail, nous étudions des traits morphologiques d’un certain nombre d’espèces migratrices et non migratrices de deux sous-familles d’Acrididae (Oedipodinae et Gomphocerinae). Par les mesures de différentes parties du corps des criquets adultes, nous avons pu situer le criquet marocain "Dociostaurus maroccanus Thunb., 1815" par rapport à l’ensemble des espèces étudiées. Cette étude morphométrique, souligne bien la liaison existante entre les capacités des déplacements des criquets et leurs traits morphologiques. Ainsi, on note bien une importante distinction morphologique entre l’espèce migratrice Locusta migratoria et les espèces non migratrices. Dociostaurus maroccanus se montre capable d’effectuer des déplacements importants, mais elle ne peut être migratrice comme Locusta migratoria.Mots-clés : Morphométrie, capacités de déplacements, traits morphologiques, Criquet marocain, espèces migratrices

Normalized equilibrium in Tullock rent seeking game

International audienceGames with Common Coupled Constraints represent manyreal life situations. In these games, if one player fails tosatisfy its constraints common to other players, then theother players are also penalised. Therefore these games canbe viewed as being cooperative in goals related to meetingthe common constraints, and non cooperative in terms ofthe utilities. We study in this paper the Tullock rent seekinggame with additional common coupled constraints. We havesucceded in showing that the utilities satisfy the property ofdiagonal strict concavity (DSC), which can be viewed asan extention of concavity to a game setting. It not onlyguarantees the uniqueness of the Nash equilibrium but also of the normalized equilibrium

A coherent picture of water at extreme negative pressure.

International audienceLiquid water at atmospheric pressure can be supercooled to 41 C (ref. 1) and superheated to C302 C (ref. 2). Experiments involving fluid inclusions of water in quartz suggest that water is capable of sustaining pressures as low as 140 MPa before it breaks by cavitation3. Other techniques, for which cavitation occurs consistently at around 30MPa (ref. 4), produce results that cast doubt on this claim. Here we reproduce the fluid-inclusion experiment, performing repeated measurements on a single sample--a method used in meteorology5, bioprotection6 and protein crystallization7, but not yet in liquid water under large mechanical tension. The resulting cavitation statistics are characteristic of a thermally activated process, and both the free energy and the volume of the critical bubble are well described by classical nucleation theory when the surface tension is reduced by less than 10%, consistent with homogeneous cavitation. The line of density maxima of water at negative pressure is found to reach 922:8 kgm3 at around 300 K, which further constrains its contested phase diagram