Evolutionary Dynamics of the Handicap Principle: An Example

International audienceFor a model developed in a companion paper, we investigate how adaptive dynamics might have led to the Bayesian equilibrium found. In an ap-pendix, we also explain from a dynamic viewpoint a lack of equilibrium in a closely related model also invesitgated in the companion paper

Modeling and control in physical, life, and social sciences: Some remarks

International audienceMathematical —or mathematico-numerical— models have pervaded all branches of knowledge, and once control theoreticians have become mainly model-builders. Their mathematical skills are called upon to analyze these models, much less to build them. This confers a renewed significance to an epistemological reflection upon what has become the heart of their occupation. We offer some general remarks, and then attempt to reflect on the different epistemological status of (mathematical) models in physics ("the unreasonable effectiveness of mathematics in the natural sciences") and engineering, life sciences, and social sciences, constrained by my limited experience of the second, and very limited experience of the third (except of mathematical finance, hardly a social science)

Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem

Simple signaling games of sexual selection (Grafen’s revisited)

International audienceWe investigate several versions of a simple game of sexual selection, to explore the role of secondary sexual characters (the "handicap paradox") with the tools of signaling theory. Our models admit closed form solutions. They are very much inspired by Grafen's (J Theor Biol 144:517-546, 1990a; J Theor Biol 144:473-516, 1990b) seminal companion papers. By merging and simplifying his two approaches, we identify a not so minor artifact in the seminal study. We propose an alternative model to start with Grafen's sexual selection theory, with several similarities with Getty (Anim Behav 56:127-130, 1998)

Dynamic equilibrium in games with randomly arriving players

This note follows our previous works on games with randomly arriving players [3] and [5]. Contrary to these two articles, here we seek a dynamic equilibrium, using the tools of piecewise deterministic control systems The resulting discrete Isaacs equation obtained is rather involved. As usual, it yields an explicit algorithm in the finite horizon, linear-quadratic case via a kind of discrete Riccati equation. The infinite horizon problem is briefly considered. It seems to be manageable only if one limits the number of players present in the game. In that case, the linear quadratic problem seems solvable via essentially the same algorithm, although we have no convergence proof, but only very convincing numerical evidence. We extend the solution to more general entry processes, and more importantly , to cases where the players may leave the game, investigating several stochastic exit mechanisms. We then consider the continuous time case, with a Poisson arrival process. While the general Isaacs equation is as involved as in the discrete time case, the linear quadratic case is simpler, and, provided again that we bound the maximum number of players allowed in the game, it yields an explicit algorithm with a convergence proof to the solution of the infinite horizon case, subject to a condition reminiscent of that found in [20]. As in the discrete time case, we examine the case where players may leave the game, investigating several possible stochastic exit mechanisms. MSC: 91A25, 91A06, 91A20, 91A23, 91A50, 91A60, 49N10, 93E03. Foreword This report is a version of the article [2] where players minimize instead of maximizing, and the linear-quadratic examples are somewhat different.On détermine les stratégies d'équilibre dans un jeu dynamique où des joueurs identiques arrivent de façon aléatoire, comme, par exemple, des congénères arrivant sur une même ressource. On considère aussi divers mécanismes de sortie aléatoire. On obtient des théorèmes d'existence et des algorithmes de calcul, plus explicites dans le cas particulier linéaire quadratique. Toute l'étude est conduite en horizon fini et en horizon infini, et en temps discret et en temps continu.Ce rapport est une version du working paper CRESE des mêmes auteurs (en économie mathématique), référence [2], mais où les joueurs minimisent au lieu de maximiser, et les exemples linéaires quadratiques sont un peu différents

Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem

International audienceWe prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete

Développer le concept de Smart Canton de Genève

Les villes sont aujourd’hui confrontées à de nombreux défis. En effet, elles doivent faire face aux problématiques liées aux changements climatiques, à l’augmentation de la population et à la préservation des ressources naturelles. Pour répondre à ces défis, il est nécessaire que les villes modifient leur fonctionnement, et c’est là que la technologie entre en jeu ! Les possibilités qu’offrent les nouvelles technologies en matière de gestion des données et de communication, permettent aux villes de devenir plus intelligentes et durables. C’est ce que l’on appelle des Smart Cities. Le concept de Smart City répond à ces enjeux en combinant plusieurs technologies dans le but d’utiliser et de créer les ressources de manière efficace, tout en réduisant l’impact environnemental, afin d’offrir une meilleure qualité de vie aux habitants. Ce concept n’est pas un nouveau phénomène et pourtant, il offre de grandes opportunités pour les collectivités. Dans le cadre de ma formation spécialisée en management durable, je suis consciente des challenges que rencontrent le canton de Genève pour favoriser la croissance économique et améliorer la qualité de vie de ses citoyens, tout en sauvegardant l’environnement. C’est pourquoi, la transition du canton de Genève, en Smart Canton pourrait être une réelle opportunité à saisir pour le futur. Ce travail a pour objectif de mettre en évidence comment développer le concept de Smart Canton de Genève. Pour ce faire, de nombreuses analyses ont été réalisées sur les différentes facettes des Smart Cities aux niveaux mondial et Suisse. Une analyse de terrain a également été effectuée afin d’identifier le contexte actuel dans lequel évolue le canton. Ensuite, des hypothèses d’applications de « smart » services à l’échelle du canton ont été réalisées, dans le but d’illustrer les réels avantages tant aux niveaux écologique, qu’économique, apportés par ces d’investissements. Ainsi, l’ensemble de ces analyses a permis d’élaborer des recommandations pour le développement du concept de Smart Canton de Genève qui nécessitent l’implication de nouveaux acteurs, grâce à une approche plus participative et transparente

Uncoupling Isaacs’equations in nonzero-sum two-player differential games : The example of conflict over parental care

International audienceWe use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore.On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux