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International audience; We consider a peer-to-peer electricity marketmodeled as a network game, where End Users (EUs) minimizetheir cost by computing their demand and generation whilesatisfying a set of local and coupling constraints. Their nominaldemand constitutes sensitive information, that they might wantto keep private. We prove that the network game admits aunique Variational Equilibrium, which depends on the privateinformation of all the EUs. A data aggregator is introduced,which aims to learn the EUs’ private information. The EUsmight have incentives to report biased and noisy readings topreserve their privacy, which creates shifts in their strategies.Relying on performative prediction, we define a decision-dependentgame G^stoch to couple the network game with adata market. Two variants of the Repeated Stochastic GradientMethod (RSGM) are proposed to compute the PerformativelyStable Equilibrium solution of G^stoch, that outperform RSGMwith respect to efficiency gap minimization, privacy preservation,and convergence rates in numerical simulations.

This thesis presents different novel resource allocation and pricing models for 5G network slicing. First, we devise a flexible sharing mechanism based on a bidding scheme which is provably overbooking-free even though the players’ bids are oblivious to infrastructure resources constraints. The proposed scheme can attain desirable fairness and efficiency figures to serve slice tenants and associated mobile users. This goal is attained by designing two coupled games entangled by the same Nash equilibrium. The first is a virtual game that generates the vector of prices of resources, and for which there exists a unique generalised Nash equilibrium. The Infrastructure Provider (InP) can use the price vector to drive the second game, a multidimensional Kelly mechanism based on the so-determined prices, where customers acquire a slice of resources at a price. We finally describe how to attain the Nash equilibrium of the game using an online procedure based on a primal-dual distributed algorithm. In the second work, we propose a flexible resource allocation and pricing scheme for slicing based on a combination of the Fisher market model and the Trading post mechanism. By properly pricing network resources, the desired allocation can be attained as a market equilibrium solution that not only maximizes network resource utilization but also assigns slice tenants with their favourite bundle. To make the scheme practically viable and enable tenants to reach market equilibrium in a decentralized manner, we devise budget distributing rules via trading post mechanisms that hand over tenants direct control to manage their preferences over resources under budget constraints. We theoretically evaluate the efficiency and fairness of the resulting allocations by comparing them with different baseline allocations.In our third endeavour, we study the business aspect of network slicing with a communication marketplace where slice tenants are in double-sided competition with each other. One competition is in terms of quality of service to attract the end-user to their services, and the second is to access the limited network resources for service provisioning. We model the competitive interaction between service providers (leaders) and end-users (followers) with the Stackelberg game, where end-users decide to choose their subscribers through an imitation process resulting in competition between the SPs as a multi-resource Tullock rent-seeking game. To determine resource pricing and allocation, we design two innovative market mechanisms. First, we assume that the Service providers (SPs) are pre-assigned with fixed infrastructure shares (budgets) and rely on a trading post mechanism to allocate the resource. Under this mechanism, the SPs can redistribute their budgets in bids and customise their allocations to maximise their profits. We investigate the strategic behaviour of SPs with a noncooperative game, which admits a unique Nash equilibrium when dealing with a single resource. Second, when SPs have no bound on their budget, we cast the problem as a coupled constraints game and show that the market prices can be obtained as the duals of the coupling constraints. Finally, we provide with different learning algorithms to compute solutions to the proposed market mechanisms., Cette thèse présente différents modèles novateurs d'allocation de ressources et de tarification pour le 5G network slicing. Dans un premier temps, nous élaborons un mécanisme de partage flexible basé sur un système d'enchères qui est démontré sans surréservation et ce même si les offres des joueurs ignorent les contraintes liées aux ressources. Le système proposé peut atteindre une équité et une efficacité adéquates permettant de répondre aux besoins des détenteurs de slices et des utilisateurs mobiles associés. Cet objectif est atteint par la création de deux jeux couplés qui sont liés par le même équilibre de Nash. Le premier est un jeu virtuel qui détermine le vecteur des prix des ressources, et pour lequel il existe un équilibre de Nash généralisé unique. Le fournisseur d'infrastructure peut ainsi utiliser le vecteur de prix pour piloter le deuxième jeu qui est un mécanisme de Kelly multidimensionnel basé sur les prix préalablement déterminés. Finalement, nous détaillons la méthode pour atteindre l'équilibre de Nash du jeu en utilisant un algorithme primal-dual distribué. Ensuite, nous proposons un schéma d'allocation des ressources et de tarification flexible pour le découpage en tranches reposant sur la combinaison du modèle de Fisher market et du mécanisme de trading post. En tarifant correctement les ressources du réseau, l'allocation recherchée peut être atteinte en tant que solution d'équilibre du marché qui non seulement maximise l'utilisation des ressources du réseau, mais aussi d'attribuer aux détenteurs de slices leur forfait (or paquet) de préférence. Afin de rendre le système pratique et de permettre aux détenteurs de slices d'atteindre l'équilibre du marché de façon décentralisée, nous concevons une règle de répartition des budgets via les mécanismes de trading post qui confèrent aux détenteurs de tranches un contrôle direct pour gérer leurs préférences sur les ressources sous contraintes budgétaires. Nous évaluons théoriquement l'efficacité et l'équité des allocations obtenues en les comparant à différentes allocations de référence .En dernier lieu, nous étudions l'aspect commercial du Network slicing dans le cadre d'un marché de la communication où les détenteurs de tranches, c'est-à-dire les fournisseurs de services, sont en double concurrence les uns avec les autres. Une concurrence se fait en termes de qualité de service pour inciter l'utilisateur final à utiliser leurs services, et la seconde est pour accéder aux ressources limitées du réseau pour la fourniture de services. Nous modélisons l'interaction concurrentielle entre les fournisseurs de services (leaders) et les utilisateurs finaux (suiveurs) par le jeu de Stackelberg où les utilisateurs finaux décident de choisir leurs abonnés par le biais d'un processus d'imitation, ce qui entraîne une concurrence entre les fournisseurs de services sous la forme d'un jeu Tullock rent-seeking multi-ressources. Pour déterminer la tarification et l'allocation des ressources, nous élaborons deux mécanismes de marché innovants. Premièrement, nous supposons que les fournisseurs de services se voient attribuer à l'avance des parts d'infrastructure fixes (budget) et utilisent un mécanisme de trading post pour allouer les ressources. Suivant ce mécanisme, les fournisseurs de services peuvent redistribuer leurs ressources dans les enchères et modifier leurs allocations pour maximiser leurs profits. Nous étudions le comportement stratégique des fournisseurs de services à l'aide d'un jeu non coopératif qui admet un équilibre de Nash unique lorsqu'il s'agit d'une seule ressource. Ensuite, lorsque les fournisseurs de services n'ont pas de limite budgétaire, nous considérons le problème comme un jeu à contraintes couplées et montrons ainsi que les prix du marché peuvent être obtenus en tant que duals des contraintes de couplage. Enfin, nous proposons trois algorithmes d'apprentissage différents destinés à déterminer les solutions aux mécanismes de marché proposés.

International audience; Network Slicing is one of the essential concepts that has been introduced in 5G networks design to support demand expressed by next generation services. Network slicing will also bring new business opportunities for service providers (SPs) and virtual network operators, allowing them to run their virtual, independent business operations on shared physical infrastructure. We consider a marketplace where service providers (SPs) i.e., slice tenants lease the resources from an infrastructure provider (InP) through a network slicing mechanism. They compete to offer a certain communication service to end-users. We show that the competition between SPs can be model using the multiresource Tullock contest (TC) framework, where SPs exert effort by expending costly resource to attract users. We study the competition between the SPs under a static and dynamic resource sharing scheme. In a dynamic resource sharing scheme, SPs are pre-assigned with fixed shares (budgets) of infrastructure, and they are allowed to redistribute their shares and customise their allocation to maximise their profit. The decision problem of SPs is analysed using non-cooperative game theory, and it is shown that the resultant game admits a unique Nash Equilibrium (NE). Furthermore, a distributed reinforcement algorithm is proposed that allows each SP to reach the game's unique Nash equilibrium. Finally, simulations results are conducted to analyse the interaction between market players and the economic efficacy of the network sharing mechanism.

In this paper, we present a resource allocation mechanism for network slices. We consider a dynamic resource allocation model with multiple independent resource providers. We call our allocation mechanism, the soft-max allocation mechanism, where the slices bid for resources and the resource providers allocate resources such that their revenue is close to the maximum revenue possible. We show that this mechanism translates into a game among the slices with a unique Nash equilibrium. We also show that the network utility obtained at this Nash equilibrium is close to the optimal social utility. We then present a stochastic dual sub-gradient algorithm that provably converges to the unique Nash equilibrium.

Ischaemum amboliense S.A.Bokil, Datar & R.K.Choudhary, sp. nov. (Fig. 2) Type: — INDIA. Maharashtra: Sindhudurg, Satuli, at the base of Amboli Ghat, 15.91719° N, 73.89581° E, 85 m. asl., 22 October 2019, M. N . Datar & S. A. Bokil 1605 (holotype: AHMA, isotypes: AHMA, BSI). Annuals. Culms tufted with stilt roots, erect, 150–180 cm tall, nodes hairy. Leaf-sheath laterally compressed, keeled on back, shorter than internodal region, 7–9 × ca. 0.6 cm; ligule sub-coriaceous, ovate, 0.4–0.5 cm long, hairy. Leaf blade lanceolate, 10–15 × 0.5–0.7 cm, rounded at the base without the petiole, apex acute, sparsely hairy on both sides. Racemes 2, paired, appressed, 7–9 cm long, well-exerted on long peduncle 7–8 cm from the leaf sheath, glabrous. Joints of rachis linear turbinate, 0.4–0.5 cm long, crustaceous, glabrous. Callus crustaceous, glabrous. Sessile spikelets: glabrous. Lower glume of sessile spikelets asymmetrically oblong 0.5–0.6 × ca. 0. 2 cm, with 3 – 4 distinct side nodules, margins entirely and evenly inflexed from base to apex with distinctly winged on one side and obscurely winged on another side, crustaceous in lower one-third region and herbaceous towards apical two-third regions. Upper glume of sessile spikelet boat-shaped, 0.4–0.5 × ca. 0.2 cm, apex bicuspidate, with a membranous wing on one side. Lower staminate florets: lower lemma lanceolate, 0.3–0.4 × ca. 0.1 cm, hyaline, distinctly winged on both sides towards apex, apex acute, hyaline; lower palea lanceolate, 0.3–0.4 × ca. 0.1 cm, hyaline, apex acute; stamens 3, ca. 0.2 cm long. Upper sterile florets: upper lemma oblong-lanceolate, 0.3–0.4 × ca. 0.1 cm, cleft at basal region, awned, hyaline, lobes acute at apex; awn geniculate, 1.5–2 cm long; upper palea oblong-lanceolate, 0.3–0.4 × ca. 0.1 cm, obtuse at apex, hyaline. Stamens and carpel absent. Pedicelled spikelets: asymmetrically oblong-lanceolate, 0.5–0.6 × ca. 0.1 cm, unawned, glabrous. Pedicel 0.1–0.2 cm long, crustaceous, glabrous, less than one third the length of sessile spikelet. Lower glume deltoid, asymmetrically oblong-lanceolate, 0.4–0.5 × 0.1–0.2 cm, coriaceous; margins narrowly and evenly inflexed from base to apex, broadly winged on one margin, lodicules 2, cuneate, 600–700 µm long. Upper glume boat-shaped, 0.4–0.5 × ca. 0.1 cm; apex acute. Lower staminate floret: lower lemma 0.4–0.5 × 0.1 cm, lanceolate, apex acute, hyaline; lower palea elliptic-lanceolate, 0.4–0.5 × 0.1 cm, apex sub-acute, sub-hyaline; stamens 3. Upper hermaphrodite florets: upper lemma ovate-oblong, 0.3–0.4 × ca. 0.1 cm; apex subacute, hyaline; upper palea ellipticlanceolate, 0.3–0.4 × ca. 0.1 cm, hyaline; stamens 3; ovary oblong-lanceolate; style, 0.1–0.2 cm long; stigma ca. 0.2 cm long, lodicules 2, 300–400 µm long. Caryopsis not seen. Phenology:— Ischaemum amboliense is a therophyte with stilt roots. Flowering is seen during October–December. Pollination occurs through anemophily. The plant starts drying in late December when the water surrounding it recedes. In the areas which retain water till the start of summer, flowering can be seen up to March. Though we have not observed caryopsis on the spikelet, the newly sprouted seedlings were observed in the surrounding region. In addition to its prominent vegetative reproduction by sprouting shoots on old tillers, the plant also seems to be propagated through caryopsis. Habitat:— Ischaemum amboliense grows in marshy places along the muddy banks of annual streams, where it grows in association with Isachne sp. and Cyperus sp. It is also found in the abandoned rice fields where monsoon water gets accumulated and stays till winter.